This document outlines the program for a Physics 2 course covering fluid mechanics and thermal physics. It includes 5 chapters: fluid mechanics, heat and temperature, heat and the first law of thermodynamics, the kinetic theory of gases, and entropy and the second law of thermodynamics. References and websites for further information are also provided. The document then provides an in-depth overview of Chapter 4 on the kinetic theory of gases, covering topics like the molecular model of an ideal gas, the equipartition of energy, and the Boltzmann distribution law. It includes examples and problems related to these concepts.
Contents
The Atom
Materials Used in Electronics
Current in Semiconductors
N-Type and P-Type Semiconductors
The PN Junctions
Diode Operation, Voltage-Current (V-I) Characteristics
Bipolar Junction Transistor (BJT) Structure, Operation, and Characteristics and Parameters
Junction Field Effect Transistors (JFETs) Structure, Characteristics and Parameters and Biasing
Metal Oxide Semiconductor FET (MOSFET) Structure, Characteristics and Parameters and Biasing
The ATOM: Learning Objectives
Describe the structure of an atom
Discuss the Bohr model of an atom
Define electron, proton, neutron, and nucleus
Define atomic number
Discuss electron shells and orbits
Explain energy levels
Define valence electron
Discuss ionization
Define free electron and ion
Discuss the basic concept of the quantum model of the atom
Discuss insulators, conductors, and semiconductors and how they differ
Define the core of an atom
Describe the carbon atom
Name two types each of semiconductors, conductors, and insulators
Explain the band gap
Define valence band and conduction band
Compare a semiconductor atom to a conductor atom
Discuss silicon and germanium atoms
Explain covalent bonds
Define crystal
Describe how current is produced in a semiconductor
Discuss conduction electrons and holes
Explain an electron-hole pair
Discuss recombination
Explain electron and hole current
Describe the properties of n-type and p-type semiconductors
Define doping
Explain how n-type semiconductors are formed
Describe a majority carrier and minority carrier in n-type material
Explain how p-type semiconductors are formed
Describe a majority carrier and minority carrier in p-type material
Describe how a pn junction is formed
Discuss diffusion across a pn junction
Explain the formation of the depletion region
Define barrier potential and discuss its significance
State the values of barrier potential in silicon and germanium
Discuss energy diagrams
Define energy hill
An ideal gas is a theoretical gas that follows Boyle's, Charles's, and the ideal gas laws. It is made of particles with negligible volume that exhibit random motion and no intermolecular forces. Real gases deviate from ideal behavior at low temperatures or high pressures due to intermolecular forces or particle volume. The ideal gas law relates pressure, volume, amount of gas, and temperature as PV=nRT.
Ethan conducted a photoelectric effect experiment to calculate Planck's constant. The experiment involved measuring the stopping potential of electrons emitted from a metal surface under monochromatic light of varying wavelengths. Plotting average stopping potential versus the reciprocal of wavelength produced a straight line, from which Planck's constant could be calculated using the slope. Ethan's calculated value of Planck's constant had a 36% error compared to the accepted value, which was within an acceptable range for the experiment.
G-type antiferromagnetism results when the spins of electrons in a material are arranged in an antiferromagnetic pattern both within planes of atoms and between neighboring planes. An analysis of SrCr2As2 using neutron diffraction and magnetic susceptibility revealed it is a G-type antiferromagnet below 590K, with chromium magnetic moments aligned along the c axis. The ordered magnetic moment was found to be 1.9μB/Cr at 12K, reduced from the localized value due to itinerant electrons from Cr-As hybridization. Even with significant antisite disorder, G-type and other antiferromagnetic phases can still be detected through their characteristic peaks in the magnetic structure factor.
In this work, I am showing a faithful atomistic process of estimating the oxygen migration energetics within BSCF, oxygen migration energy exhibit a strong dependence on different local atomic structures of this doped perovskites. In addition, DFT calculations exhibit the reason of cubic phase stability of this doped perovskite in variable oxygen concentration.
This document provides solutions to problems about atomic structure and interatomic bonding. It defines the difference between atomic mass and atomic weight. It then calculates the average atomic weight of chromium based on the natural abundances of its four isotopes. Finally, it derives expressions for the force of attraction between ions and the bonding energy in terms of fundamental constants.
hey guyz this is the presentation iv made in my last year of engineering and got very nice feedbacks. my topic was oled(organic light emitting diodes).. iv given all its highlited informations with pictures
Surface coverage in atomic layer deposition - slides related to invited talk ...Riikka Puurunen
Invited talk given at the Workshop on Fundamentals of Atomic Layer Deposition (ALD): Modelling and ValidationTU Delft, The Netherlands, July 3, 2019. Talk was recorded by TU Delft staff and is to be shared later. Website: https://www.tudelft.nl/en/faculty-of-applied-sciences/about-faculty/departments/chemical-engineering/scientific-staff/van-ommen-group/workshop-fundamentals-of-ald/. Twitter hashtag: #ALDfun
Contents
The Atom
Materials Used in Electronics
Current in Semiconductors
N-Type and P-Type Semiconductors
The PN Junctions
Diode Operation, Voltage-Current (V-I) Characteristics
Bipolar Junction Transistor (BJT) Structure, Operation, and Characteristics and Parameters
Junction Field Effect Transistors (JFETs) Structure, Characteristics and Parameters and Biasing
Metal Oxide Semiconductor FET (MOSFET) Structure, Characteristics and Parameters and Biasing
The ATOM: Learning Objectives
Describe the structure of an atom
Discuss the Bohr model of an atom
Define electron, proton, neutron, and nucleus
Define atomic number
Discuss electron shells and orbits
Explain energy levels
Define valence electron
Discuss ionization
Define free electron and ion
Discuss the basic concept of the quantum model of the atom
Discuss insulators, conductors, and semiconductors and how they differ
Define the core of an atom
Describe the carbon atom
Name two types each of semiconductors, conductors, and insulators
Explain the band gap
Define valence band and conduction band
Compare a semiconductor atom to a conductor atom
Discuss silicon and germanium atoms
Explain covalent bonds
Define crystal
Describe how current is produced in a semiconductor
Discuss conduction electrons and holes
Explain an electron-hole pair
Discuss recombination
Explain electron and hole current
Describe the properties of n-type and p-type semiconductors
Define doping
Explain how n-type semiconductors are formed
Describe a majority carrier and minority carrier in n-type material
Explain how p-type semiconductors are formed
Describe a majority carrier and minority carrier in p-type material
Describe how a pn junction is formed
Discuss diffusion across a pn junction
Explain the formation of the depletion region
Define barrier potential and discuss its significance
State the values of barrier potential in silicon and germanium
Discuss energy diagrams
Define energy hill
An ideal gas is a theoretical gas that follows Boyle's, Charles's, and the ideal gas laws. It is made of particles with negligible volume that exhibit random motion and no intermolecular forces. Real gases deviate from ideal behavior at low temperatures or high pressures due to intermolecular forces or particle volume. The ideal gas law relates pressure, volume, amount of gas, and temperature as PV=nRT.
Ethan conducted a photoelectric effect experiment to calculate Planck's constant. The experiment involved measuring the stopping potential of electrons emitted from a metal surface under monochromatic light of varying wavelengths. Plotting average stopping potential versus the reciprocal of wavelength produced a straight line, from which Planck's constant could be calculated using the slope. Ethan's calculated value of Planck's constant had a 36% error compared to the accepted value, which was within an acceptable range for the experiment.
G-type antiferromagnetism results when the spins of electrons in a material are arranged in an antiferromagnetic pattern both within planes of atoms and between neighboring planes. An analysis of SrCr2As2 using neutron diffraction and magnetic susceptibility revealed it is a G-type antiferromagnet below 590K, with chromium magnetic moments aligned along the c axis. The ordered magnetic moment was found to be 1.9μB/Cr at 12K, reduced from the localized value due to itinerant electrons from Cr-As hybridization. Even with significant antisite disorder, G-type and other antiferromagnetic phases can still be detected through their characteristic peaks in the magnetic structure factor.
In this work, I am showing a faithful atomistic process of estimating the oxygen migration energetics within BSCF, oxygen migration energy exhibit a strong dependence on different local atomic structures of this doped perovskites. In addition, DFT calculations exhibit the reason of cubic phase stability of this doped perovskite in variable oxygen concentration.
This document provides solutions to problems about atomic structure and interatomic bonding. It defines the difference between atomic mass and atomic weight. It then calculates the average atomic weight of chromium based on the natural abundances of its four isotopes. Finally, it derives expressions for the force of attraction between ions and the bonding energy in terms of fundamental constants.
hey guyz this is the presentation iv made in my last year of engineering and got very nice feedbacks. my topic was oled(organic light emitting diodes).. iv given all its highlited informations with pictures
Surface coverage in atomic layer deposition - slides related to invited talk ...Riikka Puurunen
Invited talk given at the Workshop on Fundamentals of Atomic Layer Deposition (ALD): Modelling and ValidationTU Delft, The Netherlands, July 3, 2019. Talk was recorded by TU Delft staff and is to be shared later. Website: https://www.tudelft.nl/en/faculty-of-applied-sciences/about-faculty/departments/chemical-engineering/scientific-staff/van-ommen-group/workshop-fundamentals-of-ald/. Twitter hashtag: #ALDfun
Aadish Chopra will give a seminar on OLED technology and displays. The seminar will cover what OLEDs are, types of OLEDs including passive matrix OLEDs and active matrix OLEDs, the principle of OLED energy diagrams, differences between LCD, plasma and OLED displays, flexible displays using plastic substrates, and an electrical equivalent design and model for OLEDs. The document provides details on the development and characteristics of plastic substrate OLEDs, parameter identification and impedance analysis for the electrical equivalent model, and advantages and disadvantages of the model.
The nature of particle waves or de Broglie waves. Long forgotten and misinterpreted. Now true nature found and mathematically verified. More details: new-physics.com
A DFT & TDDFT Study of Hybrid Halide Perovskite Quantum DotsAthanasiosKoliogiorg
Perovskite quantum dots (QDs) constitute a novel and rapidly developing field of nanotechnology with promising potential for optoelectronic applications. However, few perovskite materials for QDs and other nanostructures have been theoretically explored. In this study, we present a wide spectrum of different hybrid halide perovskite cuboid-like QDs with the general formula of FABX3 (A = (NH2)CH(NH2), B = Pb, Sn, Ge, and X = Cl, Br, I) with varying sizes below and near the Bohr exciton radius. Density functional theory (DFT) and time-dependent DFT calculations were employed to determine their structural, electronic, and optical properties. Our calculations include both stoichiometric model, proved to be close to experimental results where available, and our results reveal several materials with high optical absorption and application-suitable electronic and optical gaps. Our study highlights the potential as well as the challenges and issues regarding nanostructured halide perovskite materials, laying the background for future theoretical and experimental work.
The threat of global warming is high due to the extensive use of fossil fuels.Using non-renewable resources is a viable solution. Sunlight can be converted in two ways - into electrical energy and into chemical energy. Water splitting and CO2 are two important methods which can be used in solar cells.
This document discusses physics and physical measurements. It introduces physics as the study of natural phenomena and how it can be expressed through mathematical equations. It then discusses the International System of Units (SI) which provides standardized units for measurements like length, mass and time. Examples are given for typical distances, masses and times using SI units and order of magnitude estimates. The document also covers dimensional analysis, significant figures, unit conversions and expressing measurements with uncertainties.
Linear attenuation coefficient (휇) is a measure of the ability of a medium to diffuse and absorb radiation. In the interaction of radiation with matter, the linear absorption coefficient plays an important role because during the passage of radiation through a medium, its absorption depends on the wavelength of the radiation and the thickness and nature of the medium. Experiments to determine linear absorption coefficient for Lead, Copper and Aluminum were carried out in air. The result showed that linear absorption Coefficient for Lead is 0.545cm – 1, Copper is 0.139cm-1 and Aluminum is 0.271cm-1 using gamma-rays. The results agree with standard values.
This document provides an overview of nuclear reactions including:
- Four main types of nuclear reactions: radioactive decay, bombardment with energetic particles, fusion, and fission.
- Key principles of nuclear reactions such as conservation of charge and nucleon number.
- Calculation of the energy (Q) released in nuclear reactions from the mass defect.
- Examples of calculating energy and writing equations for various nuclear reactions including alpha decay, beta decay, and bombardment reactions.
The document describes an experiment to measure Planck's constant using three different methods with LEDs of varying wavelengths. The first method observes the voltage when light first becomes visible. The second measures voltage when current begins to flow. The third graphs voltage and extrapolates the threshold. The author hypothesizes the second method will be most accurate since it relies solely on multimeter readings. Results show the second method was closest to the accepted value of Planck's constant, with the first and third methods less accurate due to human judgment factors.
Photocatalysis uses light energy to facilitate chemical reactions. Photocatalysts generate holes and electrons when exposed to light that can oxidize or reduce organic matter, breaking it down into carbon dioxide and water. Photocatalysis has applications in renewable energy production like hydrogen fuel from water splitting and reducing carbon dioxide emissions. It can also degrade organic dyes and pollutants in wastewater via generation of radical species during photocatalyst excitation. In conclusion, photocatalysis shows promise as a green technology using sunlight for environmental and energy applications.
- An atom is made up of protons, neutrons, and electrons. The nucleus consists of protons and neutrons, and electrons orbit around the nucleus.
- Each element is defined by its atomic number, which is the number of protons. Isotopes are variants of an element that differ in the number of neutrons.
- Electrons can occupy different energy levels based on quantum numbers like the principal quantum number. Absorbing or releasing energy can cause electrons to change energy levels.
Traveling EM waves represent freely propagating energy. Standing waves represent stored energy. Light is a traveling wave disturbance in a polarizable vacuum. Matter consists of standing wave resonances. Matter in motion with respect to an inertial frame generates Lorentz contracted moving standing waves. Rest mass and inertia result from confinement of electromagnetic radiation.
The document summarizes research on modifying the bandgap of n-TiO2 through carbon doping to enable its use in photoelectrochemical water splitting using visible light. Carbon-modified n-TiO2 (CM-n-TiO2) films were synthesized using spray pyrolysis. Increased carbon doping was achieved by calcining in inert atmosphere. CM-n-TiO2 exhibited photoresponse in the visible spectrum due to carbon doping reducing the bandgap and introducing an intragap band. This modified the band structure of n-TiO2 to extend utilization of solar energy into the visible region.
Growth and Optimization of Aluminium-doped Zinc Oxide using Spray Pyrolysis T...Kevin V. Alex
This document is a project report submitted by Kevin V. Alex to the Department of Physics at Sacred Heart College in partial fulfillment of the requirements for a Master of Science degree in physics from Mahatma Gandhi University. The project involved growing and optimizing aluminum-doped zinc oxide thin films using the spray pyrolysis technique under the guidance of Dr. M.K. Jayaraj at the Centre for Advanced Materials, Department of Physics, Cochin University of Science and Technology. Characterization of the aluminum-doped ZnO films was carried out to study the effect of aluminum doping and deposition parameters like growth rate and temperature.
Pawan Homogeneous catalyst for CO2 reductionPawan Kumar
This document provides an overview of homogenous photocatalytic reduction of CO2. It discusses key topics such as what photocatalysis is, problems with CO2 reduction, classifications of photocatalysts including homogeneous and heterogeneous examples, and mechanisms of type I and type II catalysts. Molecular complexes like rhenium and ruthenium are described as promising homogeneous photocatalysts. The effects of catalyst structure, reaction conditions, and anchoring to surfaces are reviewed. Future areas of improvement include increasing turnover numbers and standardizing test conditions for fair catalyst comparisons.
solution for Materials Science and Engineering 7th edition by William D. Call...shayangreen
The document discusses several concepts relating to atomic structure and interatomic bonding:
1) It defines atomic mass and atomic weight, and provides an example calculation for the average atomic weight of silicon.
2) It discusses the relationship between atomic mass units (amu) and grams, and derives a conversion factor between the two units.
3) It describes two important concepts from the Bohr model of the atom and two refinements from the wave-mechanical model.
Synthesis of Cobalt ferrite by Solid Reaction Methodsank_sanjay
Cobalt ferrite nano-crystalline powder was synthesized from the powder mixture of cobalt carbonate and iron oxide by mixed oxide ceramic method. The effects of temperature of calcination as well as molar ratio of CoCO3/Fe2O3 on the phase structure, morphology and magnetic properties of the products were studied using X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM) and vibrating sample magnetometer (VSM) techniques, respectively. The samples calcined at 800 and 900˚C consisted of cobalt ferrite, iron oxide and cobalt oxide. In the sample calcined at 1000˚C, the reaction was completed and single phase CoFe2O4 with a mean crystallite and particle sizes of 49 and 300 nm, respectively was obtained.
Conducting polymers based nanocomposites for flexible supercapacitorsCharu Lakshmi
This document discusses conducting polymer-based nanocomposites for flexible supercapacitors. It begins by classifying supercapacitors and explaining why flexibility is needed. Nanocomposites contain at least one nano-dimensional component and can be made of polymers, ceramics, or metals. Specifically, the document explores carbon nanotube, graphene, and metal oxide reinforced polymer nanocomposites. It notes these materials increase conductivity, surface area, and flexibility while reducing weight and cost. The document concludes that incorporating carbon nanomaterials that form networks while retaining mesoporosity, along with two-dimensional materials and open structures, can further improve supercapacitor performance.
This document discusses the kinetic theory of gases and its assumptions. It introduces the concepts of pressure, temperature, volume, and kinetic energy at the microscopic and macroscopic levels. The relationships between these quantities are derived based on the assumptions of ideal gases. Specifically, the pressure of an ideal gas is shown to be proportional to the average kinetic energy of its molecules. The equipartition theorem is also discussed, relating the kinetic energy and degrees of freedom of gas molecules to temperature. Expressions are derived for specific heat capacity and the ideal gas law. The differences between real and ideal gases are explained using van der Waals equations.
- Thermodynamics describes the equilibrium states of systems and the spontaneous processes between those states.
- The first law of thermodynamics states that the total energy of an isolated system is conserved. It can be expressed as ΔU = Q + W, where ΔU is the change in internal energy, Q is heat, and W is work.
- For a closed system, the first law takes the form ΔU = Q - PΔV, where PΔV is the work done by expansion or compression. For a constant volume process where no work is done, ΔU = Q.
- The enthalpy H is a state function defined as H = U + PV. For a
- Thermal radiation is electromagnetic radiation emitted from objects due to their temperature. It includes infrared, visible light, and some ultraviolet wavelengths. A blackbody is a perfect emitter and absorber of radiation. According to Stefan-Boltzmann law, a blackbody's total emissive power is directly proportional to the fourth power of its absolute temperature. Planck's law describes the spectral distribution of a blackbody's radiative intensity as a function of wavelength and temperature. The emissivity of a surface is the ratio of radiation it emits compared to a blackbody. Kirchhoff's law states that emissivity of a surface is equal to its absorptivity at a given temperature and wavelength. The greenhouse effect
Aadish Chopra will give a seminar on OLED technology and displays. The seminar will cover what OLEDs are, types of OLEDs including passive matrix OLEDs and active matrix OLEDs, the principle of OLED energy diagrams, differences between LCD, plasma and OLED displays, flexible displays using plastic substrates, and an electrical equivalent design and model for OLEDs. The document provides details on the development and characteristics of plastic substrate OLEDs, parameter identification and impedance analysis for the electrical equivalent model, and advantages and disadvantages of the model.
The nature of particle waves or de Broglie waves. Long forgotten and misinterpreted. Now true nature found and mathematically verified. More details: new-physics.com
A DFT & TDDFT Study of Hybrid Halide Perovskite Quantum DotsAthanasiosKoliogiorg
Perovskite quantum dots (QDs) constitute a novel and rapidly developing field of nanotechnology with promising potential for optoelectronic applications. However, few perovskite materials for QDs and other nanostructures have been theoretically explored. In this study, we present a wide spectrum of different hybrid halide perovskite cuboid-like QDs with the general formula of FABX3 (A = (NH2)CH(NH2), B = Pb, Sn, Ge, and X = Cl, Br, I) with varying sizes below and near the Bohr exciton radius. Density functional theory (DFT) and time-dependent DFT calculations were employed to determine their structural, electronic, and optical properties. Our calculations include both stoichiometric model, proved to be close to experimental results where available, and our results reveal several materials with high optical absorption and application-suitable electronic and optical gaps. Our study highlights the potential as well as the challenges and issues regarding nanostructured halide perovskite materials, laying the background for future theoretical and experimental work.
The threat of global warming is high due to the extensive use of fossil fuels.Using non-renewable resources is a viable solution. Sunlight can be converted in two ways - into electrical energy and into chemical energy. Water splitting and CO2 are two important methods which can be used in solar cells.
This document discusses physics and physical measurements. It introduces physics as the study of natural phenomena and how it can be expressed through mathematical equations. It then discusses the International System of Units (SI) which provides standardized units for measurements like length, mass and time. Examples are given for typical distances, masses and times using SI units and order of magnitude estimates. The document also covers dimensional analysis, significant figures, unit conversions and expressing measurements with uncertainties.
Linear attenuation coefficient (휇) is a measure of the ability of a medium to diffuse and absorb radiation. In the interaction of radiation with matter, the linear absorption coefficient plays an important role because during the passage of radiation through a medium, its absorption depends on the wavelength of the radiation and the thickness and nature of the medium. Experiments to determine linear absorption coefficient for Lead, Copper and Aluminum were carried out in air. The result showed that linear absorption Coefficient for Lead is 0.545cm – 1, Copper is 0.139cm-1 and Aluminum is 0.271cm-1 using gamma-rays. The results agree with standard values.
This document provides an overview of nuclear reactions including:
- Four main types of nuclear reactions: radioactive decay, bombardment with energetic particles, fusion, and fission.
- Key principles of nuclear reactions such as conservation of charge and nucleon number.
- Calculation of the energy (Q) released in nuclear reactions from the mass defect.
- Examples of calculating energy and writing equations for various nuclear reactions including alpha decay, beta decay, and bombardment reactions.
The document describes an experiment to measure Planck's constant using three different methods with LEDs of varying wavelengths. The first method observes the voltage when light first becomes visible. The second measures voltage when current begins to flow. The third graphs voltage and extrapolates the threshold. The author hypothesizes the second method will be most accurate since it relies solely on multimeter readings. Results show the second method was closest to the accepted value of Planck's constant, with the first and third methods less accurate due to human judgment factors.
Photocatalysis uses light energy to facilitate chemical reactions. Photocatalysts generate holes and electrons when exposed to light that can oxidize or reduce organic matter, breaking it down into carbon dioxide and water. Photocatalysis has applications in renewable energy production like hydrogen fuel from water splitting and reducing carbon dioxide emissions. It can also degrade organic dyes and pollutants in wastewater via generation of radical species during photocatalyst excitation. In conclusion, photocatalysis shows promise as a green technology using sunlight for environmental and energy applications.
- An atom is made up of protons, neutrons, and electrons. The nucleus consists of protons and neutrons, and electrons orbit around the nucleus.
- Each element is defined by its atomic number, which is the number of protons. Isotopes are variants of an element that differ in the number of neutrons.
- Electrons can occupy different energy levels based on quantum numbers like the principal quantum number. Absorbing or releasing energy can cause electrons to change energy levels.
Traveling EM waves represent freely propagating energy. Standing waves represent stored energy. Light is a traveling wave disturbance in a polarizable vacuum. Matter consists of standing wave resonances. Matter in motion with respect to an inertial frame generates Lorentz contracted moving standing waves. Rest mass and inertia result from confinement of electromagnetic radiation.
The document summarizes research on modifying the bandgap of n-TiO2 through carbon doping to enable its use in photoelectrochemical water splitting using visible light. Carbon-modified n-TiO2 (CM-n-TiO2) films were synthesized using spray pyrolysis. Increased carbon doping was achieved by calcining in inert atmosphere. CM-n-TiO2 exhibited photoresponse in the visible spectrum due to carbon doping reducing the bandgap and introducing an intragap band. This modified the band structure of n-TiO2 to extend utilization of solar energy into the visible region.
Growth and Optimization of Aluminium-doped Zinc Oxide using Spray Pyrolysis T...Kevin V. Alex
This document is a project report submitted by Kevin V. Alex to the Department of Physics at Sacred Heart College in partial fulfillment of the requirements for a Master of Science degree in physics from Mahatma Gandhi University. The project involved growing and optimizing aluminum-doped zinc oxide thin films using the spray pyrolysis technique under the guidance of Dr. M.K. Jayaraj at the Centre for Advanced Materials, Department of Physics, Cochin University of Science and Technology. Characterization of the aluminum-doped ZnO films was carried out to study the effect of aluminum doping and deposition parameters like growth rate and temperature.
Pawan Homogeneous catalyst for CO2 reductionPawan Kumar
This document provides an overview of homogenous photocatalytic reduction of CO2. It discusses key topics such as what photocatalysis is, problems with CO2 reduction, classifications of photocatalysts including homogeneous and heterogeneous examples, and mechanisms of type I and type II catalysts. Molecular complexes like rhenium and ruthenium are described as promising homogeneous photocatalysts. The effects of catalyst structure, reaction conditions, and anchoring to surfaces are reviewed. Future areas of improvement include increasing turnover numbers and standardizing test conditions for fair catalyst comparisons.
solution for Materials Science and Engineering 7th edition by William D. Call...shayangreen
The document discusses several concepts relating to atomic structure and interatomic bonding:
1) It defines atomic mass and atomic weight, and provides an example calculation for the average atomic weight of silicon.
2) It discusses the relationship between atomic mass units (amu) and grams, and derives a conversion factor between the two units.
3) It describes two important concepts from the Bohr model of the atom and two refinements from the wave-mechanical model.
Synthesis of Cobalt ferrite by Solid Reaction Methodsank_sanjay
Cobalt ferrite nano-crystalline powder was synthesized from the powder mixture of cobalt carbonate and iron oxide by mixed oxide ceramic method. The effects of temperature of calcination as well as molar ratio of CoCO3/Fe2O3 on the phase structure, morphology and magnetic properties of the products were studied using X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM) and vibrating sample magnetometer (VSM) techniques, respectively. The samples calcined at 800 and 900˚C consisted of cobalt ferrite, iron oxide and cobalt oxide. In the sample calcined at 1000˚C, the reaction was completed and single phase CoFe2O4 with a mean crystallite and particle sizes of 49 and 300 nm, respectively was obtained.
Conducting polymers based nanocomposites for flexible supercapacitorsCharu Lakshmi
This document discusses conducting polymer-based nanocomposites for flexible supercapacitors. It begins by classifying supercapacitors and explaining why flexibility is needed. Nanocomposites contain at least one nano-dimensional component and can be made of polymers, ceramics, or metals. Specifically, the document explores carbon nanotube, graphene, and metal oxide reinforced polymer nanocomposites. It notes these materials increase conductivity, surface area, and flexibility while reducing weight and cost. The document concludes that incorporating carbon nanomaterials that form networks while retaining mesoporosity, along with two-dimensional materials and open structures, can further improve supercapacitor performance.
This document discusses the kinetic theory of gases and its assumptions. It introduces the concepts of pressure, temperature, volume, and kinetic energy at the microscopic and macroscopic levels. The relationships between these quantities are derived based on the assumptions of ideal gases. Specifically, the pressure of an ideal gas is shown to be proportional to the average kinetic energy of its molecules. The equipartition theorem is also discussed, relating the kinetic energy and degrees of freedom of gas molecules to temperature. Expressions are derived for specific heat capacity and the ideal gas law. The differences between real and ideal gases are explained using van der Waals equations.
- Thermodynamics describes the equilibrium states of systems and the spontaneous processes between those states.
- The first law of thermodynamics states that the total energy of an isolated system is conserved. It can be expressed as ΔU = Q + W, where ΔU is the change in internal energy, Q is heat, and W is work.
- For a closed system, the first law takes the form ΔU = Q - PΔV, where PΔV is the work done by expansion or compression. For a constant volume process where no work is done, ΔU = Q.
- The enthalpy H is a state function defined as H = U + PV. For a
- Thermal radiation is electromagnetic radiation emitted from objects due to their temperature. It includes infrared, visible light, and some ultraviolet wavelengths. A blackbody is a perfect emitter and absorber of radiation. According to Stefan-Boltzmann law, a blackbody's total emissive power is directly proportional to the fourth power of its absolute temperature. Planck's law describes the spectral distribution of a blackbody's radiative intensity as a function of wavelength and temperature. The emissivity of a surface is the ratio of radiation it emits compared to a blackbody. Kirchhoff's law states that emissivity of a surface is equal to its absorptivity at a given temperature and wavelength. The greenhouse effect
1. The first law of thermodynamics states that energy is conserved and can be changed from one form to another, but not created or destroyed. It describes the relationships between heat, work, and changes in internal energy of a system.
2. Enthalpy (H) is a state function that represents the total energy of a system at constant pressure. For a chemical reaction, the heat exchanged is equal to the change in enthalpy.
3. For an ideal gas undergoing an adiabatic (no heat exchange) process, the change in internal energy is equal to the pressure-volume work done, according to the first law of thermodynamics. The temperature of the gas decreases during expansion
The document provides information about the 4th International Conference on Medical Physics and Biophysics to be held July 27-28, 2017 in Rome, Italy. It invites attendees to the conference, discusses the scope and importance of medical physics, and provides market analysis on the medical physics field. Key details include over 200 participants anticipated, presentations and lectures on contemporary medical and biophysics approaches, and Rome chosen as the location due to its significance as an international city and center of business and culture.
The document discusses the Thevenin theorem which states that any active network with two terminals can be replaced by an equivalent circuit consisting of a voltage source in series with an internal resistance. The voltage source represents the open circuit voltage between the terminals and the internal resistance represents the equivalent resistance looking into the network with sources replaced by internal resistances. The document provides an example circuit and steps to derive the Thevenin equivalent circuit and determine the terminal voltage and current through a load resistance.
Teaching Medical Physics at Undergraduate levelAmmar Felemban
This document summarizes a presentation on teaching medical physics at the undergraduate level. It outlines the medical physics profession and qualifications, degrees offered in Saudi Arabia and other countries, and challenges with the current academic program, job market, and clinical training opportunities. The presentation recommends terminating all undergraduate medical physics programs, utilizing resources for master's programs instead, and developing a national residency program to properly qualify medical physicists according to international standards.
Pressure, temperature and ‘rms’ related to kinetic modelMichael Marty
The macroscopic properties of a gas, pressure and temperature, are explained in terms of molecule movement of the Kinetic Theory. The derivation of formulas are shown in logical steps for pressure, temperature and KE.
Medical Physics 102 - Clinical Leadership - PradoKarl Prado
This document provides an overview of effective clinical leadership for medical physicists. It discusses the motivation for medical physicists to develop leadership skills in addition to their technical physics expertise. The document outlines five principles of effective leadership: model the way, inspire a shared vision, challenge the process, enable others to act, and encourage the heart. It also discusses techniques for personal organization, project management, and balancing clinical responsibilities with leadership duties.
The document summarizes key concepts of kinetic theory of gases:
1) Ideal gases are made of molecules that move randomly and collide elastically, obeying Newton's laws and the ideal gas law.
2) Pressure results from molecular collisions with surfaces, and temperature is related to the average kinetic energy of molecular motion.
3) For monatomic gases, the internal energy depends only on translational motion, but for polyatomic gases it also includes rotational and vibrational energies according to the principle of equipartition of energy.
The superposition theorem allows the analysis of circuits with multiple sources by considering each source independently and adding their effects. It can be applied when circuit elements are linear and bilateral. To use it, all ideal voltage sources except one are short circuited and all ideal current sources except one are open circuited. Dependent sources are left intact. This allows the circuit to be solved for each source individually and the results combined through superposition. Examples demonstrate finding currents through specific elements in circuits with multiple independent and dependent sources. A limitation is that superposition cannot be used to determine total power due to power being related to current squared.
Kirchhoff's laws deal with the conservation of charge and energy in electrical circuits. There are two Kirchhoff's laws:
1. Kirchhoff's current law (KCL) states that the algebraic sum of currents in a network meeting at a point is zero.
2. Kirchhoff's voltage law (KVL) states that the directed sum of the potential differences around any closed network is zero.
Circuit analysis methods like mesh analysis, nodal analysis, and superposition theorem can be used to solve circuits using Kirchhoff's laws. Mesh analysis uses KVL to analyze loops in a planar circuit. Nodal analysis uses KCL to analyze connections (nodes) in a circuit. Superposition
The document discusses the kinetic model of an ideal gas from a microscopic perspective. It describes the assumptions of the model, which include molecules behaving as point particles that do not interact and obey Newton's laws. It then outlines the steps to relate the microscopic description to the macroscopic ideal gas law: (1) calculating molecule collisions with the wall, (2) resulting momentum change, (3) force exerted by the wall, (4) force exerted on the wall using Newton's 3rd law, (5) defining pressure, and (6) relating this to the ideal gas law. It further defines temperature microscopically in terms of molecular kinetic energy.
solution manual to basic and engineering thermodynamics by P K NAG 4th editionChandu Kolli
- There are three main temperature scales: Celsius (C), Fahrenheit (F), and Kelvin (K)
- Celsius and Kelvin have the same increments but different reference points, with 0°C being the freezing point of water and 100°C being the boiling point, while 0K is absolute zero
- Fahrenheit has a different increment than the other two scales, with 32°F being the freezing point of water and 212°F being the boiling point
- Conversions between the scales can be done using the following relationships:
(C − 0°C) = (F − 32°F) × 5/9 = (K − 273
The document summarizes key concepts from Chapter 14 on the ideal gas law and kinetic theory. Section 1 discusses molecular mass, the mole, and Avogadro's number. Section 2 covers the ideal gas law and how pressure, volume, temperature, and moles are related. Section 3 introduces the kinetic theory model, which describes gases as large numbers of constantly moving particles and explains gas properties and behaviors in terms of particle collisions and kinetic energy.
The document provides examples of solved problems involving ideal gas laws and gas stoichiometry calculations. The problems cover a range of concepts including determining gas pressures and volumes using the ideal gas equation under different temperature and pressure conditions, calculating mole fractions and partial pressures in gas mixtures, and stoichiometric calculations involving the production and reaction of different gases.
1. The document discusses the different states of matter and summarizes the key differences between gases, liquids, and solids.
2. It then covers various gas laws including Boyle's law, Charles' law, Avogadro's law, and the ideal gas equation.
3. The kinetic molecular theory is introduced to explain gas behavior at the molecular level in terms of molecule motion and interactions.
1) When a hot air balloon is heated, some of the air escapes from the top, lowering the density inside and making the balloon buoyant.
2) The atmosphere protects the planet and provides chemicals necessary for life, including oxygen for metabolism, nitrogen to dilute oxygen, and carbon dioxide and water vapor that trap heat.
3) Gases have indefinite volume and shape, low densities, and high kinetic energies according to their temperature as described by the kinetic molecular theory.
1. The kinetic theory of gases explains the macroscopic properties (pressure, volume, temperature) of gases using mechanical concepts of force and energy while considering the composition and motion of gas particles.
2. Boyle's law states that for a gas at constant temperature, the pressure and volume are inversely proportional. Charles' law states that for a gas at constant pressure, the volume is directly proportional to the absolute temperature.
3. The total kinetic energy of an ideal gas is proportional to the number of gas particles and the absolute temperature according to the formula: Ek = 3/2 nRT, where n is the number of moles, R is the gas constant, and T is the absolute temperature.
The document summarizes the kinetic molecular theory and gas laws relating pressure, temperature, volume and amount of gases. It defines key terms like ideal gas, diffusion and effusion. The kinetic molecular theory has 5 assumptions including gases being made of particles in random motion with no interparticle forces. Gas laws discussed include Boyle's law, Charles' law, Gay-Lussac's law and combined gas law. Dalton's law of partial pressures states the total pressure of a gas mixture equals the sum of partial pressures of individual gases.
G10 Science Q4- Week 1-2-Constant Temp of Gas.pptjinprix
The document discusses the relationship between volume, pressure, and temperature in gases based on kinetic molecular theory and gas laws. It explains that for an ideal gas, volume and pressure are inversely related at constant temperature according to Boyle's Law. Similarly, volume and temperature are directly related at constant pressure according to Charles' Law. The ideal gas law combines these relationships, stating that the product of pressure and volume is directly proportional to the number of moles of gas times the absolute temperature. Several examples demonstrate how to use the gas laws and ideal gas law to solve problems involving gases.
The document summarizes 12 gas laws including Boyle's law, Charles' law, Avogadro's law, and the ideal gas law. It provides examples of calculations using these laws to determine moles of gas, volumes at different temperatures and pressures, and identities of gases based on density. Key formulas covered are PV=nRT, relationships between volume, pressure and temperature, and stoichiometric calculations using gas volumes.
The document summarizes key gas laws including Boyle's law, Charles' law, Avogadro's law, Dalton's law of partial pressures, and the ideal gas law. It provides examples of using these laws to calculate volume, pressure, temperature, moles, and mass in gas reactions and mixtures. Key relationships covered are that pressure and volume are inversely related at constant temperature (Boyle's law), volume and temperature are directly related at constant pressure (Charles' law), and volume and moles are directly related at constant temperature and pressure (Avogadro's law).
This document discusses the kinetic molecular theory and gas laws. It explains that according to the kinetic molecular theory, gas particles are in constant, random straight-line motion and have kinetic energy directly related to temperature. The document then covers Boyle's law that pressure and volume are inversely related at constant temperature, Charles' law that volume and temperature are directly related at constant pressure, and the ideal gas law that combines these relationships. It provides examples of using the gas laws and kinetic molecular theory to solve problems involving gas pressure, volume, temperature, and amount.
Wk 6 p3 wk 7-p8_1.2-1.3 & 10.1-10.3_ideal gaseschris lembalemba
The document discusses Avogadro's constant and its relationship to moles. It defines a mole as the amount of a substance containing 6.02x1023 particles, which may be atoms, molecules, or ions. It then discusses how molar quantities allow expressing amounts of substances in moles rather than grams. For example, one can refer to the molar volume or molar mass of a gas. The document also discusses the kinetic theory of gases and how it relates the pressure and temperature of a gas to the motion of its molecules.
The document discusses key concepts from gas chemistry including the composition and properties of the atmosphere, gas laws such as Boyle's, Charles', and Avogadro's laws, kinetic molecular theory, and concepts such as molar volume, partial pressures, and gas stoichiometry. It provides examples of calculations using the ideal gas law to determine quantities such as moles of gas, volume, pressure, and temperature changes.
The document provides learning objectives and concepts for a chemistry chapter, including:
a) Proving the law of conservation of mass through experiments.
b) Using experimental data to prove laws such as Gay-Lussac's law and Proust's law of definite proportions.
c) Explaining concepts such as moles, molar mass, stoichiometry, and reaction stoichiometry.
It outlines key fundamental laws of chemistry and concepts students are expected to understand after completing the chapter.
The document discusses concepts related to gas pressure, gas laws, and gas properties. It defines pressure as force per unit area and provides the equation relating pressure, force, and area for gases. It then discusses atmospheric pressure, manometers for measuring gas pressure, and provides conversions between pressure units. The document also summarizes key gas laws including Boyle's law, Charles's law, the ideal gas law, molar mass calculations for gases, partial pressures in gas mixtures, kinetic molecular theory, and deviations from ideal gas behavior.
The document discusses key concepts about gases from the kinetic molecular theory and gas laws. It introduces gases in the atmosphere and how they were studied historically. It then covers gas pressure, units of pressure, Boyle's law, Charles' law, Avogadro's law, the ideal gas law, gas stoichiometry, Dalton's law of partial pressures, and the kinetic molecular theory of gases. Examples are provided to demonstrate calculations using these gas laws and concepts.
1) Gases expand to fill their containers, are highly compressible, and have low densities due to the large distances between molecules. Their physical properties are similar regardless of chemical properties.
2) Pressure is caused by molecular collisions with surfaces. It increases with more frequent or forceful collisions. Temperature increases collision frequency and force. Pressure also rises with increased amount or decreased volume of gas.
3) Kinetic molecular theory explains gas behavior by modeling gases as particles in random motion, where temperature corresponds to average kinetic energy. This enables understanding of gas laws and pressure in terms of molecular collisions.
1. Gases have no definite shape or volume but take the shape of their container. Gas particles are in constant random motion and collide with each other and the container walls.
2. The kinetic molecular theory provides an explanation for gas behavior at the molecular level. It states that gas particles are in constant random motion and exert pressure due to collisions with container walls.
3. The gas laws describe the macroscopic behavior of gases through relationships between pressure, volume, temperature, and amount of gas. The kinetic molecular theory qualitatively explains the gas laws based on gas particle motion and interactions.
UiPath Test Automation using UiPath Test Suite series, part 5DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 5. In this session, we will cover CI/CD with devops.
Topics covered:
CI/CD with in UiPath
End-to-end overview of CI/CD pipeline with Azure devops
Speaker:
Lyndsey Byblow, Test Suite Sales Engineer @ UiPath, Inc.
TrustArc Webinar - 2024 Global Privacy SurveyTrustArc
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See how organizational priorities and strategic approaches to data security and privacy are evolving around the globe.
This webinar will review:
- The top 10 privacy insights from the fifth annual Global Privacy Benchmarks Survey
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20 Comprehensive Checklist of Designing and Developing a WebsitePixlogix Infotech
Dive into the world of Website Designing and Developing with Pixlogix! Looking to create a stunning online presence? Look no further! Our comprehensive checklist covers everything you need to know to craft a website that stands out. From user-friendly design to seamless functionality, we've got you covered. Don't miss out on this invaluable resource! Check out our checklist now at Pixlogix and start your journey towards a captivating online presence today.
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Climate Impact of Software Testing at Nordic Testing DaysKari Kakkonen
My slides at Nordic Testing Days 6.6.2024
Climate impact / sustainability of software testing discussed on the talk. ICT and testing must carry their part of global responsibility to help with the climat warming. We can minimize the carbon footprint but we can also have a carbon handprint, a positive impact on the climate. Quality characteristics can be added with sustainability, and then measured continuously. Test environments can be used less, and in smaller scale and on demand. Test techniques can be used in optimizing or minimizing number of tests. Test automation can be used to speed up testing.
Dr. Sean Tan, Head of Data Science, Changi Airport Group
Discover how Changi Airport Group (CAG) leverages graph technologies and generative AI to revolutionize their search capabilities. This session delves into the unique search needs of CAG’s diverse passengers and customers, showcasing how graph data structures enhance the accuracy and relevance of AI-generated search results, mitigating the risk of “hallucinations” and improving the overall customer journey.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
Building RAG with self-deployed Milvus vector database and Snowpark Container...Zilliz
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In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
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One such alternative that has garnered significant attention and acclaim is Nitrux Linux 3.5.0, a sleek, powerful, and user-friendly Linux distribution that promises to redefine the way we interact with our devices. With its focus on performance, security, and customization, Nitrux Linux presents a compelling case for those seeking to break free from the constraints of proprietary software and embrace the freedom and flexibility of open-source computing.
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Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!
Phys2 ch4-kineticsgas
1. •• PROGRAM OFPROGRAM OF
“PHYSICS”“PHYSICS”Lecturer: Dr. DO Xuan Hoi
Room 413
E-mail : dxhoi@hcmiu.edu.vn
2. PHYSICS 2PHYSICS 2
(FLUID MECHANICS AND THERMAL(FLUID MECHANICS AND THERMAL
PHYSICS)PHYSICS)
02 credits (30 periods)
Chapter 1 Fluid Mechanics
Chapter 2 Heat, Temperature and the Zeroth
Law of Thermodynamics
Chapter 3 Heat, Work and the First Law of
Thermodynamics
Chapter 4 The Kinetic Theory of Gases
Chapter 5 Entropy and the Second Law of
Thermodynamics
3. References :References :
Halliday D., Resnick R. and Walker, J. (2005),Halliday D., Resnick R. and Walker, J. (2005),
Fundamentals of Physics, Extended seventh edition.Fundamentals of Physics, Extended seventh edition.
John Willey and Sons, Inc.John Willey and Sons, Inc.
Alonso M. and Finn E.J. (1992). Physics, Addison-WesleyAlonso M. and Finn E.J. (1992). Physics, Addison-Wesley
Publishing CompanyPublishing Company
Hecht, E. (2000). Physics. Calculus, Second Edition.Hecht, E. (2000). Physics. Calculus, Second Edition.
Brooks/Cole.Brooks/Cole.
Faughn/Serway (2006), Serway’s College Physics,Faughn/Serway (2006), Serway’s College Physics,
Brooks/Cole.Brooks/Cole.
Roger Muncaster (1994), A-Level Physics, StanleyRoger Muncaster (1994), A-Level Physics, Stanley
Thornes.Thornes.
5. CHAPTER 4
The Kinetic Theory of Gases
• Ideal Gases, Experimental Laws and the
Equation of State
• Molecular Model of an Ideal Gas The
Equipartition
of Energy
The Boltzmann Distribution Law
The Distribution of Molecular Speeds
Mean Free Path
• The Molar Specific Heats of an Ideal Gas
• Adiabatic Expansion of an Ideal Gas
6. 1. Ideal Gases, Experimental Laws and the
Equation of State
1.1 Notions
► Properties of gases
A gas does not have a fixed volume or pressure
In a container, the gas expands to fill the container
► Ideal gas
Collection of atoms or molecules that move randomly
Molecules exert no long-range force on one another
Molecules occupy a negligible fraction of the
volume of their container
► Most gases at room temperature
and pressure behave approximately
as an ideal gas
7. 1.2
Moles
► It’s convenient to express the amount of gas in
a given volume in terms of the number of
moles, n
mass
n
molar mass
=
► One mole is the amount of the substance that
contains as many particles as there are atoms
in 12 g of carbon-12
8. 1.3 Avogadro’s Hypothesis
“Equal volumes of gas at the same temperature and
pressure contain the same numbers of molecules”
Corollary: At standard temperature and pressure, one
mole quantities of all gases contain the same number of
molecules
This number is called NA
Can also look at the total number of particles: AN nN=
The number of particles in a mole is called
Avogadro’s Number
NA=6.02 x 1023
particles / mole
The mass of an individual atom :
atom
A
molar mass
m
N
=
9. The Hope diamond (44.5 carats) is almost pure
carbon and the Rosser Reeves (138 carats) is primarily
aluminum oxide (Al2O3). One carat is equivalent to a mass of
0.200 g. Determine (a) the number of carbon atoms in the
Hope diamond and (b) the number of Al2O3 molecules in the
ruby Rosser Reeves.
SOLUTION
(44.8 )(0.200 / ) 8.90Hopem carats g carat g= =
8.90
0.741
12.011 /
Hope
Hope
m g
n mol
mass per mole g mol
= = =
The mass of the Hope diamond :(a)
The number of moles in the Hope diamond :
(0.741 )H AN mol N=
The number of carbon atoms in the Hope diamond :
PROBLEM 1
23 23
(0.741 )(6.022 10 / ) 4.46 10mol atoms mol atoms= × = ×
10. The Hope diamond (44.5 carats) is almost pure
carbon and the Rosser Reeves (138 carats) is primarily
aluminum oxide (Al2O3). One carat is equivalent to a mass of
0.200 g. Determine (a) the number of carbon atoms in the
Hope diamond and (b) the number of Al2O3 molecules in the
ruby Rosser Reeves.
SOLUTION
(138 )(0.200 / ) 27.6Rm carats g carat g= =
27.6
0.271
101.9612 /
R
R
m g
n mol
mass per mole g mol
= = =
The mass of the Rosser Reeves :(b)
Molecular mass :
The number of moles in the Rosser Reeves :
PROBLEM 1
2(26.9815 ) 3(15.9994 ) 101.9612Rm u u u= + = 101.9612 /g mol=
11. (b)
The number of Al2O3 molecules in the Rosser Reeves :
(0.271 )R AN mol N=
23 23
(0.271 )(6.022 10 / ) 1.63 10mol atoms mol molecules= × = ×
The Hope diamond (44.5 carats) is almost pure
carbon and the Rosser Reeves (138 carats) is primarily
aluminum oxide (Al2O3). One carat is equivalent to a mass of
0.200 g. Determine (a) the number of carbon atoms in the
Hope diamond and (b) the number of Al2O3 molecules in the
ruby Rosser Reeves.
SOLUTION
PROBLEM 1
12. 1.4 Experimental Laws
• Boyle’s Law
Experiment :
Conclusion :
When the gas is kept at a constant
temperature, its pressure is
inversely proportional to its volume
(Boyle’s law)
PV const=
13. • Charles’ Law
Experiment :
Conclusion :
At a constant pressure, the
temperature is directly proportional to
the volume
(Charles’ law)
V CT=
( C : constant )
14. • Gay-Lussac’s Law
Experiment :
Conclusion :
At a constant volume, the temperature
is directly proportional to the pressure
(Gay-Lussac’ law)
T CP=
( C : constant )
15. 1.5 Equation of State for an Ideal Gas
Gay-Lussac’ law : T CP=V = constant →
T = const →Boyle’s law : PV const=
Charles’ law : V CT=P = const →
• The number of moles n of a substance of mass m
(g) :
m
n
M
= (M : molar mass-g/mol)
→ Equation of state for an ideal
gas :
PV = nRT (Ideal gas law)
T : absolute temperature in kelvins
R : a universal constant that is the same for all
gases
R =8.315 J/mol.K
16. → Definition of an Ideal Gas :
“An ideal gas is one for which PV/nT is constant
at
all pressures”
AN nN=• Total number of molecules :
PV
R
nT
=
With Boltzmann’s constant :
A
N
PV = RT
N A
R
= nT
N
23
23 1
8.315 / .
1.38 10 /
6.22 10
J mol K
k J K
mol
−
−
= ×
×B
A
R
= =
N
BPV = Nk T→ Ideal gas law :
18. TestTest
An ideal gas is confined to a container with constant
volume. The number of moles is constant. By what
factor will the pressure change if the absolute
temperature triples?
a. 1/9
b. 1/3
c. 3.0
d. 9.0
19. An ideal gas occupies a volume of
100cm3
at 20°C and 100 Pa.
(a) Find the number of moles of gas in the container
SOLUTION
PV
n
RT
=
The number of moles of gas :(a)
PROBLEM 2
4 3
6(100 )(10 )
4.10 10
(8.315 / )(293 )
Pa m
mol
J mol K
−
−
= = ×
(b) How many molecules are in the container?
The number molecules in the
container : 6
(4.10 10 ) AN mol N−
= ×
6 23
18
(4.10 10 )(6.022 10 / )
2.47 10
mol atoms mol
molecules
−
= × ×
= ×
(b)
20. A certain scuba tank is designed to hold 66
ft3
of air when it is at atmospheric pressure at 22°C. When this
volume of air is compressed to an absolute pressure of
3 000 lb/in.2
and stored in a 10-L (0.35-ft3
) tank, the air
becomes so hot that the tank must be allowed to cool before it
can be used.
(a) If the air does not cool, what is its temperature? (Assume
that the air behaves like an ideal gas.)
PROBLEM 3
SCUBA (Self-Contained Underwater
Breathing Apparatus))
The number of moles n remains constant :
1 1 2 2
1 2
;
PV PV
n R
T T
= =
2 3
2 3
(3000 / . )(0.35 )
(295 ) 319
(14.7 / . )(66 )
lb in ft
K K
lb in ft
= =
2 2
2 1
1 1
=
PV
T T
PV
(a)
21. A certain scuba tank is designed to hold 66
ft3
of air when it is at atmospheric pressure at 22°C. When this
volume of air is compressed to an absolute pressure of
3 000 lb/in.2
and stored in a 10-L (0.35-ft3
) tank, the air
becomes so hot that the tank must be allowed to cool before it
can be used.
(b) What is the air temperature in degrees Celsius and in
degrees Fahrenheit?
PROBLEM 3
45.9°C;
115°F.
(b)
22. A sculpa consists of a 0.0150 m3
tank filled
with compressed air at a pressure of 2.02×107
Pa. Assume that
air is consumed at a rate of 0.0300 m3
per minute and that the
temperature is the same at all depths, determine how long the
diver can stay under seawater at a depth of
(a) 10.0 m and (b) 30.0 m
The density of seawater is ρ = 1025 kg/m3
.
PROBLEM 4
SOLUTION
2 1P P ghρ= +
5 3 2
1.01 10 (1025 / )(9.80 / )(10.0 )Pa kg m m s m= × +
1 1
2
2
PV
V
P
=
(a)
5
2.01 10 Pa= ×
3
1.51 m=
5 3
5
(2.02 10 )(0.0150 )
(1.01 10 )
Pa m
Pa
×
=
×
The volume available for breathing :
3 3 3
1.51 0.0150 1.50m m m− =
23. A sculpa consists of a 0.0150 m3
tank filled
with compressed air at a pressure of 2.02×107
Pa. Assume that
air is consumed at a rate of 0.0300 m3
per minute and that the
temperature is the same at all depths, determine how long the
diver can stay under seawater at a depth of
(a) 10.0 m and (b) 30.0 m
The density of seawater is ρ = 1025 kg/m3
.
PROBLEM 4
SOLUTION
(a)
3
3
1.50
50.0 min
0.0300 / min
m
t
m
= =
The compressed air will last for :
(b) 24.6 mint =
The deeper dive must have a shorter duration
24. A spray can containing a propellant gas at
twice atmospheric pressure (202 kPa) and having a volume of
125 cm3
is at 22°C. It is then tossed into an open fire. When
the temperature of the gas in the can reaches 195°C, what is
the pressure inside the can? Assume any change in the
volume of the can is negligible.
PROBLEM 5
The number of moles n remains constant :
1 1 2 2
1 2
PV PV
n R
T T
= =
(468 )
(202 ) 320
(295 )
K
kPa kPa
K
= =2
2 1
1
T
P P
T
=
SOLUTION
Because the initial and final volumes
of the gas are assumed to be equal :
1 2
1 2
;
P P
T T
=
25. An ideal gas at 20.0O
C at a pressure of 1.50
×105
Pa when has a number of moles of 6.16×10-2
mol.
SOLUTION
nRT
V
P
=
The volume :(a)
PROBLEM 6
2
5
(6.16 10 )(8.315 / )(293 )
(1.50 10 )
mol J mol K
Pa
−
×
=
×
(a) Find the volume of the gas.
2
5
(6.16 10 )(8.315 / )(293 )
(1.50 10 )
mol J mol K
Pa
−
×
=
×
3 3
1.00 10 1.00m L−
= × =
26. An ideal gas at 20.0O
C at a pressure of 1.50
×105
Pa when has a number of moles of 6.16×10-2
mol.
SOLUTION
nRT
V
P
=
The volume :(a)
PROBLEM 6
2
5
(6.16 10 )(8.315 / )(293 )
(1.50 10 )
mol J mol K
Pa
−
×
=
×
(b) The gas expands to twice its original volume, while the
pressure falls to atmospheric pressure. Find the final
temperature.
(b)
3 3
1.00 10 1.00m L−
= × =
1 1 2 2
1 2
;
PV PV
n R
T T
= =
5
5
(1.01 10 )(2.00 )
(293 )
(1.50 10 )(1.00 )
Pa L
K
Pa L
×
=
×
2 2
2 1
1 1
PV
T T
PV
= 395 K=
27. A beachcomber finds a corked bottle
containing a message. The air in the bottle is at the
atmospheric pressure and a temperature of 30.0O
C. The cork
has the cross-sectional area of 2.30 cm3
. The beachcomber
places the bottle over a fire, figuring the increased pressure
will pushout the cork. At a temperature of 99o
C the cork is
ejected from the bottle
PROBLEM
7
1 1 2 1
1 2
;
PV PV
n R
T T
= =
5 5(372 )
(1.01 10 ) 1.24 10
(303 )
K
Pa Pa
K
= × = ×2
2 1
1
T
P P
T
=
(a)
What was the the pressure in the bottle just before the
cork left it ?
(a)
SOLUTION
Message in a bottle found 24 years later - Yahoo!7
28. A beachcomber finds a corked bottle
containing a message. The air in the bottle is at the
atmospheric pressure and a temperature of 30.0O
C. The cork
has the cross-sectional area of 2.30 cm3
. The beachcomber
places the bottle over a fire, figuring the increased pressure
will pushout the cork. At a temperature of 99o
C the cork is
ejected from the bottle
PROBLEM
7
0 ;F =∑
5 5 4 2
(1.24 10 1.01 10 )(2.30 10 )Pa Pa m−
= × − × ×
1 0in out fricP A P A F− − =(b)
What force of friction held the cork in place?(b)
SOLUTION
5.29 N=
( )fric in outF P P A= −
29. A room of volume 60.0 m3
contains air
having an equivalent molar mass of 29.0 g/mol. If the
temperature of the room is raised from 17.0°C to 37.0°C, what
mass of air (in kilograms) will leave the room? Assume that the
air pressure in the room is maintained at 101 kPa.
PROBLEM
8
m
PV n RT RT
µ
= =
3 5 3
(29.0 10 / )(1.01 10 ) 60.0 1 1
(8.31 / . ) 290 310
kg mol Pa m
J mol K K K
−
× × ×
= − ÷
1 2
1 2
1 1PV
m m
R T T
µ
− = − ÷
SOLUTION
4.70 kg=
30. 2 Molecular Model of an Ideal Gas
2.1 Assumptions of the molecular model of an ideal
gas
• A container with volume V contains a very large number N of
identical molecules, each with mass m.
• The molecules behave as point particles; their size is small in
comparison to the average distance between particles and to the
dimensions of the container.
• The molecules are in constant
motion; they obey Newton's laws
of motion. Each molecule collides
occasionally with a wall of the
container. These collisions are
perfectly elastic.
• The container walls are perfectly
rigid and infinitely massive and do
not move.
A particle
having a
brownian
motion inside
a polymer like
network
Brownian
motion
31. 2.2 Collisions and Gas Pressure
• Consider a cubical box with sides of length
d containing an ideal gas. The molecule
shown moves with velocity v.
• Consider the collision of one molecule
moving with a velocity v toward the right-hand
face of the box
• Elastic collision with the wall → Its x component
of momentum is reversed, while its y component
remains unchanged :
• The average force exerted on the molecule :
• The average force exerted by the molecule on the wall :
∆ = − − = −( ) 2x x x xp mv mv mv
− − −
= = =
∆
2
1
2 2
2 /
x x x
x
mv mv mv
F
t d v d
−
− = − =
2 2
1
x xmv mv
F
d d
32. • The total force F exerted by all the
molecules on the wall :
• The average value of the square of the
velocity in the x direction for N molecules :
• The total pressure exerted on the wall:
( )= + +2 2
1 2 ...x x
m
F v v
d
+ + +
=
2 2 2
2 1 2 ...x x xN
x
v v v
v
N
= 2
x
Nm
F v
d
= + +2 2 2 2
;x y zv v v v = + +2 2 2 2
;x y zv v v v =2 2
3 ;xv v
= ÷
÷
2
3
N mv
F
d
= = = = ÷ ÷
2 2
2 3
1 1
;
3 3
F F N N
P mv mv
A Vd d
= ÷ ÷
22 1
3 2
N
P mv
V
33. • The equation of state for an ideal gas :
Temperature is a direct measure of average
molecular kinetic energy
The average translational kinetic energy per molecule is
Each degree of freedom contributes to the energy
of a system:
(the theorem of equipartition of energy)
= ÷
22 1
3 2
T mv
k
= ÷ ÷
22 1
3 2
N
P mv
V
=PV NkT
=21 3
2 2
mv kT
3
2
kT
=2 21
3xv v =21 1
;
2 2xmv kT =21 1
;
2 2ymv kT =21 1
2 2zmv kT
1
2
kT
34. • The total translational kinetic energy of N molecules of gas
: The number of moles of gas
: Boltzmann’s constant
=21 3
2 2
mv kT
= = = ÷
21 3 3
2 2 2transE N mv NkT nRT
=
A
N
n
N
=
A
R
k
N
• Assume: Ideal gas is a monatomic gas (which has
individual atoms rather than molecules: helium, neon, or
argon) and the internal energy Eint of ideal gas is simply the
sum of the translational kinetic energies of its atoms
= = =int
3 3
2 2transE E NkT nRT
35. • The root-mean-square (rms) speed of the molecules :
2 21 1 3
;
2 2 2rms Bmv mv k T= = = =
3 3
rms
kT RT
v
m M
M is the molar mass in kilograms per mole : M = mNA
= 2
rmsv v
36. Five gas molecules chosen at random are
found to have speeds of 500, 600,700, 800, and 900 m/s.
Find the rms speed. Is it the same as the average speed?
SOLUTION
PROBLEM 9
In general, vrms and vav are not the same.
37. A tank used for filling helium balloons has a
volume of 0.300 m3
and contains 2.00 mol of helium gas at
20.0°C. Assuming that the helium behaves like an ideal gas,
(a) what is the total translational kinetic energy of the
molecules of the gas?
SOLUTIO
N
PROBLEM 10
(a)
38. A tank used for filling helium balloons has a
volume of 0.300 m3
and contains 2.00 mol of helium gas at
20.0°C. Assuming that the helium behaves like an ideal gas,
(b) What is the average kinetic energy per molecule?
(c) Using the fact that the molar mass of helium is
4.00×103
kg/mol, determine the rms speed of the atoms
at 20.0°C.
SOLUTIO
N
PROBLEM
10
(b)
(c)
39. (a) What is the average translational kinetic
energy of a molecule of an ideal gas at a temperature of
27°C ?
(b) What is the total random translational kinetic energy of
the molecules in 1 mole of this gas?
(c) What is the root-mean-square speed of oxygen molecules
at this temperature ?
SOLUTIO
N
PROBLEM 11
(a)
(b)
40. (a) What is the average translational kinetic
energy of a molecule of an ideal gas at a temperature of
27°C ?
(b) What is the total random translational kinetic energy of
the molecules in 1 mole of this gas?
(c) What is the root-mean-square speed of oxygen molecules
at this temperature ?
SOLUTIO
N
PROBLEM 11
(c)
41. (a) A deuteron, 2
1H, is the nucleus of a
hydrogen isotope and consists of one proton and one
neutron. The plasma of deuterons in a nuclear fusion reactor
must be heated to about 300 million K. What is the rms
speed of the deuterons? Is this a significant fraction of the
speed of light (c = 3.0 x 108
m/s) ?
(b) What would the temperature of the plasma be if the
deuterons had an rms speed equal to 0.10c ?
SOLUTIO
N
PROBLEM 12
42. 2.3 The Boltzmann Distribution Law
The Maxwell–Boltzmann distribution
function
• Consider the distribution of molecules in our atmosphere :
Determine how the number of molecules per unit volume
varies with altitude
V Vmgn V mgn Ady= =
VdP mgn dy= −
Consider an atmospheric layer of
thickness dy and cross-sectional
area A, having N particles. The air is
in static equilibrium :
( )PA P dP A mgN− + =
where nV is the number density.
;BPV Nk T=
Law of Exponential Atmospheres
• From the equation of state : ;V BP n k T= B VdP k Tdn=
;V B Vmgn dy k Tdn− = ;V
V B
dn mg
dy
n k T
= −
0 0
;
Vn y
V
V Bn
dn mg
dy
n k T
= −∫ ∫
43. 0 0
;
Vn y
V
V Bn
dn mg
dy
n k T
= −∫ ∫ 0 0
ln Vn y
V n
B
mg
n y
k T
= −
0ln ln ;V
B
mg
n n y
k T
− = −
0
ln ;V
B
n mg
y
n k T
= −
0
expV
B
n mg
y
n k T
= − ÷
0
ln ;V
B
n mg
y
n k T
= −
0
expV
B
n mg
y
n k T
= − ÷
/
0
Bmgy k T
Vn n e−
=
/
0
BU k T
Vn n e−
=
The Boltzmann distribution law : the probability of
finding the molecules in a particular energy state varies
exponentially as the negative of the energy divided by kBT.
44. What is the number density of air at an
altitude of 11.0 km (the cruising altitude of a commercial
jetliner) compared with its number density at sea level?
Assume that the air temperature at this height is the same as
that at the ground, 20°C.
SOLUTIO
N
PROBLEM
13
/
0
Bmgy k T
Vn n e−
=The Boltzmann distribution law :
Assume an average molecular mass of :
−
= × 26
28.9 4.80 10u kg
45. Density of the number of molecules with speeds between v
and dv :
The Maxwell–Boltzmann distribution function
θ θ ϕ− −
µ =
2 2
/ 2 / 2 2
( ) sinmv kT mv kT
VN v dV e dV e v dv d d
r
π π
θ θ ϕ−
µ ∫ ∫
2
2
/ 2 2
0 0
( ) sinmv kT
VN v dv e v dv d d
π −
µ
2
/ 2 2
( ) 4 mv kT
VN v dv e v dv
π −
=
2
/ 2 2
( ) 4 mv kT
VN v dv A e v dv
With : =∫ ( )VN v dv N
π −
=∫
2
/ 2 2
4 mv kT
A e v dv N
47. Density of the number of molecules with speeds between v
and dv is
The rms speed :
The average speed:
The most probable speed:
π
π
−
= ÷
2
3 / 2
2 / 2
4
2
mv kT
V
m
N N v e
kT
= = =2
3 / 1.73 /rmsv v kT m kT m
π= =8 / 1.60 /v kT m kT m
= =2 / 1.41 /mpv kT m kT m
> >rms mpv v v
48. Definition: The average value of v n
:PROOF:
∞
= ∫
0
1n n
vv v N dv
N
π
π
∞
−
÷= ÷ ÷
∫
2
3/ 2
2 / 2
0
1
4
2
mv kTm
v v N v e dv
N kT
π
π
∞
−
÷= = ÷ ÷
∫
2
3/ 2
2 2 2 / 2
0
1
4 3 /
2
mv kTm
v v N v e dv kT m
N kT
The average speed:
π= =8 / 1.60 /v kT m kT m
The mean square speed:
→ = = =2
3 / 1.73 /rmsv v kT m kT m
The most probable speed:
π
π
−
= = ÷ ÷ ÷
2
3/2
2 /2
0 ; 4 0 ;
2
mv kTvdN d m
N v e
dv dv kT
= 2 /mpv kT m
49. For diatomic carbon dioxide gas ( CO2 , molar
mass 44.0 g/mol) at T = 300 K, calculate
(a) the most probable speed vmp;
(b) the average speed vav;
(c) the root-mean-square speed vrms.
SOLUTIO
N
PROBLEM 14
The rms speed :
The average speed:
The most probable speed:
= = =2
3 / 1.73 /rmsv v kT m kT m
π= =8 / 1.60 /v kT m kT m
= =2 / 1.41 /mpv kT m kT m
50. At what temperature is the root-mean-square
speed of nitrogen molecules equal to the root-mean-square
speed of hydrogen molecules at 20.00
C?
SOLUTIO
N
PROBLEM 15
The rms speed : = =2
3 /rmsv v kT m
A N2 molecule has more mass so N2 gas must be at a
higher temperature to have the same v rms .
51. 2.4 The mean free path
• A molecule moving through a gas
collides with other molecules in a random
fashion.
Notion of the mean free path
• Between collisions, the molecules move with constant
speed along straight lines. The average distance between
collisions is called the mean free path.
52. The mean free path for a gas molecule
• Consider N spherical molecules with radius r in a volume V.
Suppose only one molecule is moving.
• When it collides with another molecule,
the distance between centers is 2r.
• In a short time dt a molecule with speed v
travels a distance vdt ; during this time it
collides with any molecule that is in the
cylindrical volume of radius 2r and length vdt.
• The volume of the cylinder : π 2
4 r vdt
The number of the molecules with centers in this cylinder :
The number of collisions per unit time :
π= 2
(4 )
N
dN r vdt
V
π= 2
(4 )
dN N
r v
dt V
When all the molecules move at once : π= 2
2(4 )
dN N
r v
dt V
53. • The average time between collisions (the mean free time)
• The mean free path (the average distance
traveled between collisions) is
• For the ideal-gas :
→
=PV NkT
ππ
= = 2
2
1
2(4 )2(4 )
mean
V
t
N r v Nr v
V
λ
π
= = 2
4 2
mean
V
vt
r N
λ
π
= = 2
4 2
mean
kT
vt
r P
54. Approximate the air around you as a
collection of nitrogen molecules, each of which has a diameter
of 2.00 × 10-10
m.
How far does a typical molecule move before it collides with
another molecule?
SOLUTIO
N
PROBLEM 16
Assume that the gas is ideal:
The mean free path:
55. A cubical cage 1.25 m on each side contains
2500 angry bees, each flying randomly at 1.10 m/s. We
can model these insects as spheres 1.50 cm in diameter. On
the average, (a) how far does a typical bee travel between
collisions,
(b) what is the average time between collisions,
and (c) how many collisions per second does a bee make?
SOLUTIO
N
PROBLEM 17
56. 3. The Molar Specific Heats of an ldeal Gas
• Constant volume: = ∆VQ nC T
CV : the molar specific heat at constant volume
= ∆PQ nC T
• Constant pressure:
CP : the molar specific heat at constant pressure
First law of thermodynamics:
∆ = − = ∆ − = ∆int
3
0
2VE Q W nC T nR T
=
3
2VC R =int VE nC T→
57. C : molar specific heat of Various Gases
=
3
2VC R
Gas constant: R = 8.315 J/mol.K
=
5
2VC R
≈
7
2VC R
58. C : molar specific heat of Various
Gases
=
3
2VC R
=
5
2VC R
=
7
2VC R
• monatomic molecules:
• diatomic molecules:
(not vibration)
• polyatomic molecules:
f : degree of freedom (the number of independent
coordinates to specify the motion of a molecule)
=
2V
f
C R
59. V = const → dW = 0
PdQ nC dT=
VdQ nC dT=
• If the heat capacity is measured under constant- volume
conditions: the molar heat capacity CV at constant volume
First law → dU = dQ = nCVdT
• By definition :
dW PdV nRdT= =
(Ideal gas : PV = nRT)
First law : dQ = dU + dW PnC dT dU nRdT= +
VnC dT nRdT= +
P VC C R= +
Relating Cp and Cv for an Ideal Gas
60. The total work done by the gas as its volume changes from
V1 to Vf : f
i
V
V
W PdV= ∫
Ideal gas : PV nRT=
f
i
V
V
nRT
W dV
V
= ∫
Isothermal process: T const=
;
f
i
V
V
dV
W nRT
V
= ∫ ln f
i
V
W nRT
V
=
Work done by an ideal gas at constant temperature
61. Also : i i f fPV PV=
ln f
i
V
W nRT
V
=
ln i
f
P
W nRT
P
=
:f iV V> 0W >
When a system expands : work is positive.
When a system is compressed, its volume decreases and
it does negative work on its surroundings
62. • Work done by an ideal gas at constant
volume
= =∫ 0
f
i
V
V
W PdV
• Work done by an ideal gas at constant
pressure
= = = − = ∆∫ 0 ( )
f
i
V
f i
V
W PdV P V V P V
63. PROBLEM 18 A bubble of 5.00 mol of helium is submerged at
a certain depth in liquid water when the water (and thus the
helium) undergoes a temperature increase of 20.00
C at
constant pressure. As a result, the bubble expands. The helium
is monatomic and ideal.
a) How much energy is added to the helium as heat during the
increase and expansion?
SOLUTIO
N
64. PROBLEM 18 A bubble of 5.00 mol of helium is submerged at
a certain depth in liquid water when the water (and thus the
helium) undergoes a temperature increase of 20.00
C at
constant pressure. As a result, the bubble expands. The helium
is monatomic and ideal.
a) How much energy is added to the helium as heat during the
increase and expansion?
(b) What is the change in the internal energy of the helium
during the temperature increase?
SOLUTIO
N
65. PROBLEM 18 A bubble of 5.00 mol of helium is submerged at
a certain depth in liquid water when the water (and thus the
helium) undergoes a temperature increase of 20.00
C at
constant pressure. As a result, the bubble expands. The helium
is monatomic and ideal.
a) How much energy is added to the helium as heat during the
increase and expansion?
(b) What is the change in the internal energy of the helium
during the temperature increase?
(c) How much work is done by the helium as it expands
against the pressure of the surrounding water during the
temperature increase?
SOLUTIO
N
66. For adiabatic process : no energy is transferred by heat
between the gas and its surroundings: dQ = 0
dU = dQ – dW = -dW
= P
V
C
C
γ• Definition of the Ratio of Heat Capacities :
The Ratio of Heat Capacities
4 Adiabatic Expansion of an Ideal Gas
67. = − = − ;dU dQ dW dW
• For ideal gas : = + =;PV nRT PdV VdP nRdT
From : R = CP - CV :
=PV constγ
= −VnC dT PdV
+ = −
V
R
PdV VdP PdV
C
−
+ = − P V
V
C C
PdV VdP PdV
C
Divide by PV :
−
+ = − P V
V
C CdV dP dV
V P C V
= −(1 )
dV
V
γ
+ = 0 ;
dP dV
P V
γ + =ln lnP V constγ
=i i f fPV PVγ γ
68. • For ideal gas : =PV nRT
=PV constγ
=i i f fPV PVγ γ
−
= =1nRT
V nRTV const
V
γ γ
− −
=1 1
i i f fTV T Vγ γ−
=1
TV constγ
69. PROBLEM 19 One mole of oxygen (assume it to be an ideal
gas) expands at a constant temperature of 310 K from an initial
volume 12 L to a final volume of 19 L.
a/ How much work is done by the gas during the expansion?
SOLUTIO
N
70. PROBLEM 19 One mole of oxygen (assume it to be an ideal
gas) expands at a constant temperature of 310 K from an initial
volume 12 L to a final volume of 19 L.
a/ How much work is done by the gas during the expansion?
b/ What would be the final temperature if the gas had
expanded adiabatically to this same final volume? Oxygen
(O2 is diatomic and here has rotation but not oscillation.)
SOLUTIO
N
71. PROBLEM 19 One mole of oxygen (assume it to be an ideal
gas) expands at a constant temperature of 310 K from an initial
volume 12 L to a final volume of 19 L.
a/ How much work is done by the gas during the expansion?
b/ What would be the final temperature if the gas had
expanded adiabatically to this same final volume? Oxygen
(O2 is diatomic and here has rotation but not oscillation.)
c/ What would be the final temperature and pressure if,
instead, the gas had expanded freely to the new volume,
from an initial pressure of.2.0 Pa?
SOLUTIO
N
The temperature does not change in a free expansion:
72. PROBLEM 20 Air at 20.0°C in the cylinder of a diesel engine is
compressed from an initial pressure of 1.00 atm and volume
of 800.0 cm3
to a volume of 60.0 cm3
. Assume that air
behaves as an ideal gas with γ = 1.40 and that the compression
is adiabatic. Find the final pressure and temperature of the air.
SOLUTIO
N
73. PROBLEM 21 A typical dorm room or bedroom contains about
2500 moles of air. Find the change in the internal energy of this
much air when it is cooled from 23.9°C to 11.6°C at a constant
pressure of 1.00 atm.
Treat the air as an ideal gas with γ = 1.400.
SOLUTIO
N
74. PROBLEM 22 The compression ratio of a diesel engine is 15 to
1; this means that air in the cylinders is compressed to 1/15 of
its initial volume (Fig). If the initial pressure is 1.01 × 105
Pa and
the initial temperature is 27°C (300 K), (a) find the final
pressure and the temperature after compression. Air is mostly a
mixture of diatomic oxygen and nitrogen; treat it as an ideal gas
with γ= 1.40.
SOLUTIO
N(a)
75. The compression ratio of a diesel engine is 15 to
1; this means that air in the cylinders is compressed to 1/15 of
its initial volume (Fig). If the initial pressure is 1.01 × 105
Pa and
the initial temperature is 27°C (300 K),(b) how much work
does the gas do during the compression if the initial volume of
the cylinder is 1.00 L? Assume that CV for air is 20.8 J/mol.K
and γ = 1.40.
SOLUTIO
N(b)
PROBLEM 22
76. Two moles of carbon monoxide (CO) start at a
pressure of 1.2 atm and a volume of 30 liters. The gas is then
compressed adiabatically to 1/3 this volume. Assume that the
gas may be treated as ideal. What is the change in the internal
energy of the gas? Does the internal energy increase or
decrease? Does the temperature of the gas increase or
decrease during this process? Explain.
SOLUTIO
N
PROBLEM 23
77. Two moles of carbon monoxide (CO) start at a
pressure of 1.2 atm and a volume of 30 liters. The gas is then
compressed adiabatically to 1/3 this volume. Assume that the
gas may be treated as ideal. What is the change in the internal
energy of the gas? Does the internal energy increase or
decrease? Does the temperature of the gas increase or
decrease during this process? Explain.
SOLUTIO
N
The internal energy increases because work is done on the gas
(ΔU > 0) and Q = 0.
The temperature increases because the internal energy has
increased.
PROBLEM 23
78. On a warm summer day, a large mass of air
(atmospheric pressure 1.01 × 105
Pa) is heated by the ground
to a temperature of 26.0°C and then begins to rise through the
cooler surrounding air. (This can be treated as an adiabatic
process). Calculate the temperature of the air mass when it has
risen to a level at which atmospheric pressure is only 0.850 ×
105
Pa. Assume that air is an ideal gas, with γ = 1.40.
SOLUTIO
N
PROBLEM 24