This document provides an overview of concepts related to temperature, expansion, and the ideal gas law. It discusses:
- Brownian motion and how it helped establish that everything is made of atoms.
- Measurements of atomic size and mass.
- Early thermometers developed by Galileo using liquid expansion.
- Thermal expansion of solids and liquids, defined by coefficients of linear and volume expansion.
- Gas laws including Boyle's law relating pressure and volume at constant temperature, Charles's law relating volume and temperature at constant pressure, and the combined ideal gas law.
PHYS0412 Thermal Expansion and Gas Laws (1).pptxTJPlayz1
This document discusses heat and thermal expansion. It begins by defining key concepts in thermodynamics like temperature, thermal equilibrium, and the three laws of thermodynamics. It then covers topics related to thermal expansion, including linear expansion, volume expansion, and examples like the expansion of holes and bimetallic strips. The document also explains gas laws like Boyle's law, Charles' law, Gay-Lussac's law, and how these combine to form the ideal gas law. Examples are provided to demonstrate how to use these laws to calculate changes in pressure, volume, or temperature of an ideal gas.
The document discusses temperature and how it relates to the kinetic energy and motion of molecules. It defines temperature and explains that it is a measure of the average kinetic energy of molecules. It discusses different temperature scales including Celsius, Fahrenheit, and Kelvin and provides equations to convert between them. It also explains how temperature changes can cause materials to expand and contract as the molecules move faster or slower, taking up more or less space. Specific equations are provided to calculate the linear expansion and volume expansion of materials based on their coefficient of expansion, original length or volume, and temperature change. Examples are included to demonstrate using these equations.
This document discusses the kinetic molecular theory of gases and its development over 200 years. It provides background on key contributors like Van der Waals who published an equation of state in 1873 that accounted for interactions between gas molecules and volume, improving on the ideal gas law. It also discusses how the constant R was derived from experiments and used to relate the temperature and pressure of an ideal gas in the ideal gas law PV=nRT.
Thermodynamics is the study of heat and its relationship to other physical phenomena such as work, temperature and energy. It examines the macroscopic behavior of materials using variables like pressure, volume and temperature rather than their microscopic constitution. Thermodynamics establishes that heat is a form of energy transfer between systems due to a temperature difference, and explores the behavior of gases, liquids and solids through concepts like the ideal gas law, thermal expansion, and heat transfer via specific heat capacity.
The document describes the key properties and laws relating to gases. It discusses:
1) Kinetic molecular theory which describes how gas particles behave as having no volume, undergoing elastic collisions, and moving in random straight lines without attracting or repelling each other.
2) Real gases which differ in that particles have volume and can attract each other. Gases behave most ideally at low pressure, high temperature, and for nonpolar molecules.
3) Characteristics of gases such as expanding to fill their container due to random motion and low density. Gases can also be compressed, undergo diffusion and effusion.
4) Important gas laws including Boyle's law relating inverse relationship between pressure and volume at constant
1. The document discusses key concepts in heat and thermodynamics including temperature, heat transfer mechanisms, thermal expansion, and phase changes.
2. It provides examples of problems and their solutions involving concepts like specific heat, latent heat, temperature conversions, and heat transfer calculations.
3. The key heat transfer mechanisms of conduction, convection, and radiation are explained through examples of how they apply to insulating houses and minimizing energy costs.
Gas laws describe the behavior of gases and can be used to interconvert pressure, volume, temperature, and amount of gas. The three main gas laws are: [1] Boyle's law relates pressure and volume at constant temperature; [2] Charles' law relates volume and temperature at constant pressure; and [3] Gay-Lussac's law relates pressure and temperature at constant volume. Together these laws form the combined gas law. Standard temperature and pressure provide reference points for gas measurements and calculations.
Pressure is caused by gas particles striking the sides of their container. Standard atmospheric pressure is 101.3 kPa. Boyle's Law states that the pressure and volume of a gas are inversely proportional if temperature is kept constant. Charles' Law describes the direct proportional relationship between the volume and temperature of a gas when pressure is kept constant. Gay-Lussac's Law relates the direct proportionality of pressure and temperature for a gas at constant volume. Avogadro's Law shows that volume and pressure are directly proportional to the number of moles of gas present.
PHYS0412 Thermal Expansion and Gas Laws (1).pptxTJPlayz1
This document discusses heat and thermal expansion. It begins by defining key concepts in thermodynamics like temperature, thermal equilibrium, and the three laws of thermodynamics. It then covers topics related to thermal expansion, including linear expansion, volume expansion, and examples like the expansion of holes and bimetallic strips. The document also explains gas laws like Boyle's law, Charles' law, Gay-Lussac's law, and how these combine to form the ideal gas law. Examples are provided to demonstrate how to use these laws to calculate changes in pressure, volume, or temperature of an ideal gas.
The document discusses temperature and how it relates to the kinetic energy and motion of molecules. It defines temperature and explains that it is a measure of the average kinetic energy of molecules. It discusses different temperature scales including Celsius, Fahrenheit, and Kelvin and provides equations to convert between them. It also explains how temperature changes can cause materials to expand and contract as the molecules move faster or slower, taking up more or less space. Specific equations are provided to calculate the linear expansion and volume expansion of materials based on their coefficient of expansion, original length or volume, and temperature change. Examples are included to demonstrate using these equations.
This document discusses the kinetic molecular theory of gases and its development over 200 years. It provides background on key contributors like Van der Waals who published an equation of state in 1873 that accounted for interactions between gas molecules and volume, improving on the ideal gas law. It also discusses how the constant R was derived from experiments and used to relate the temperature and pressure of an ideal gas in the ideal gas law PV=nRT.
Thermodynamics is the study of heat and its relationship to other physical phenomena such as work, temperature and energy. It examines the macroscopic behavior of materials using variables like pressure, volume and temperature rather than their microscopic constitution. Thermodynamics establishes that heat is a form of energy transfer between systems due to a temperature difference, and explores the behavior of gases, liquids and solids through concepts like the ideal gas law, thermal expansion, and heat transfer via specific heat capacity.
The document describes the key properties and laws relating to gases. It discusses:
1) Kinetic molecular theory which describes how gas particles behave as having no volume, undergoing elastic collisions, and moving in random straight lines without attracting or repelling each other.
2) Real gases which differ in that particles have volume and can attract each other. Gases behave most ideally at low pressure, high temperature, and for nonpolar molecules.
3) Characteristics of gases such as expanding to fill their container due to random motion and low density. Gases can also be compressed, undergo diffusion and effusion.
4) Important gas laws including Boyle's law relating inverse relationship between pressure and volume at constant
1. The document discusses key concepts in heat and thermodynamics including temperature, heat transfer mechanisms, thermal expansion, and phase changes.
2. It provides examples of problems and their solutions involving concepts like specific heat, latent heat, temperature conversions, and heat transfer calculations.
3. The key heat transfer mechanisms of conduction, convection, and radiation are explained through examples of how they apply to insulating houses and minimizing energy costs.
Gas laws describe the behavior of gases and can be used to interconvert pressure, volume, temperature, and amount of gas. The three main gas laws are: [1] Boyle's law relates pressure and volume at constant temperature; [2] Charles' law relates volume and temperature at constant pressure; and [3] Gay-Lussac's law relates pressure and temperature at constant volume. Together these laws form the combined gas law. Standard temperature and pressure provide reference points for gas measurements and calculations.
Pressure is caused by gas particles striking the sides of their container. Standard atmospheric pressure is 101.3 kPa. Boyle's Law states that the pressure and volume of a gas are inversely proportional if temperature is kept constant. Charles' Law describes the direct proportional relationship between the volume and temperature of a gas when pressure is kept constant. Gay-Lussac's Law relates the direct proportionality of pressure and temperature for a gas at constant volume. Avogadro's Law shows that volume and pressure are directly proportional to the number of moles of gas present.
- Gases are composed of particles that move randomly in straight lines, colliding elastically with each other and the container walls. The average kinetic energy of gas particles depends on temperature.
- Boyle's law states that the pressure and volume of a gas are inversely related at constant temperature. Charles' law says volume and temperature are directly related at constant pressure.
- Students are reminded to bring materials for experiments on gas laws, including syringes, balloons, water, and thermometers. Problems involving Boyle's and Charles' laws are assigned.
Kinetic Gas Theory including Ideal Gas Equation. Temperature, Volume, Applications
Boyle's Law, Charles' Law and Avogadro's Law. Ideal Gas Theory, Dalton's Partial Pressure
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.
Gases have no definite shape or volume, and their particles move in random motion with little attraction to one another. The behavior of gases is described by various gas laws relating the gas's pressure, volume, temperature, and amount. Specifically, Boyle's law states that pressure and volume are inversely proportional at constant temperature; Charles's law specifies that volume and temperature are directly proportional at constant pressure; and Avogadro's law establishes that volume and amount are directly proportional at constant temperature and pressure.
This document discusses thermal expansion, which is the change in dimensions of materials due to changes in temperature. It defines linear expansion as the expansion in length and volume expansion as expansion in overall volume. The key factors that affect thermal expansion are the temperature change, material type, and original dimensions. Common materials and their coefficients of thermal expansion are provided. Examples of applications like loosening tight jar lids are given. Finally, several problems involving calculating dimensional changes due to temperature changes are presented.
Thermodynamics part 1 discusses key concepts related to temperature, heat, and thermal equilibrium. It defines temperature as a measure of the average kinetic energy of particles in a sample and discusses how thermometers are used to measure hotness and coldness on different temperature scales. Thermal equilibrium occurs when two systems have the same temperature after interacting. Heat is the transfer of energy due solely to a temperature difference and can cause changes in temperature and phase changes with the absorption or release of latent heat. Specific heat is the amount of heat required to change an object's temperature by 1 degree.
New chm-151-unit-10-power-points-140227172226-phpapp02Cleophas Rwemera
This document provides an overview of gas laws and the kinetic molecular theory. It begins by distinguishing key properties of gases compared to liquids and solids, such as how gas volume is greatly affected by pressure and temperature. The document then covers gas pressure and its measurement using various units. The major gas laws - Boyle's law, Charles' law, and the combined gas law - are introduced and explained with molecular perspectives and example problems. Additional concepts covered include standard temperature and pressure, the ideal gas law, and determining molar mass from vapor density measurements.
This document provides an overview of gas laws and the behavior of gases. It begins by defining the three states of matter and distinguishing properties of gases. Gas pressure and its measurement are then discussed, including common pressure units. The document outlines the major gas laws - Boyle's Law relating pressure and volume at constant temperature, Charles' Law relating volume and temperature at constant pressure, and the Combined Gas Law combining these relationships. Examples are provided to demonstrate applications of the gas laws. The ideal gas law is defined as relating pressure, volume, temperature, and moles of gas. The behavior of gases at standard temperature and pressure is also covered.
The kinetic molecular theory of gases explains gas behavior using the idea that gases are made of molecules or atoms that are in constant, random motion and have space between them. It describes gases as having no intermolecular forces, occupying no volume, and undergoing elastic collisions. This theory allows for deriving gas laws such as Boyle's law (inverse relationship between pressure and volume at constant temperature), Charles's law (direct relationship between volume and temperature at constant pressure), and Gay-Lussac's law (direct relationship between pressure and temperature at constant volume). The combined gas law incorporates all three simpler gas laws. These gas laws allow for calculations involving pressure, volume, temperature, and amount of gas.
The document discusses the kinetic molecular theory and properties of gases. It explains that gas particles are in constant, random motion with no attraction between particles. It also describes gas pressure, temperature, volume, and the relationships between these properties as defined by Boyle's law, Charles' law, Gay-Lussac's law, and the combined gas law. Examples are provided for using these gas laws to calculate changes in gas properties like volume under different conditions.
The document discusses several gas laws including Boyle's law, Charles' law, Avogadro's law, and Gay-Lussac's law. It provides the formulas for each law and graphs demonstrating the relationships between pressure, volume, temperature, and number of moles for ideal gases. It also discusses how real gases deviate from ideal gas behavior and provides the combined gas law formula.
The document discusses the key gas laws and concepts:
1) Gases are highly compressible, occupy their container fully, exert uniform pressure, diffuse easily, and have low densities according to kinetic molecular theory.
2) The gas laws describe the relationships between pressure, volume, temperature, and moles of gas including Boyle's law, Charles' law, Gay-Lussac's law, Avogadro's principle, and the combined ideal gas law.
3) The ideal gas law combines all gas laws as PV=nRT, relating pressure, volume, moles of gas, temperature, and the universal gas constant R. It can be used to calculate gas properties.
- Gases are composed of particles that move randomly in straight lines, colliding elastically with each other and the container walls. The average kinetic energy of gas particles depends on temperature.
- Boyle's law states that the pressure and volume of a gas are inversely related at constant temperature. Charles' law says volume and temperature are directly related at constant pressure.
- Students are reminded to bring materials for experiments on gas laws, including syringes, balloons, water, and thermometers. Problems involving Boyle's and Charles' laws are assigned.
Kinetic Gas Theory including Ideal Gas Equation. Temperature, Volume, Applications
Boyle's Law, Charles' Law and Avogadro's Law. Ideal Gas Theory, Dalton's Partial Pressure
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.
Gases have no definite shape or volume, and their particles move in random motion with little attraction to one another. The behavior of gases is described by various gas laws relating the gas's pressure, volume, temperature, and amount. Specifically, Boyle's law states that pressure and volume are inversely proportional at constant temperature; Charles's law specifies that volume and temperature are directly proportional at constant pressure; and Avogadro's law establishes that volume and amount are directly proportional at constant temperature and pressure.
This document discusses thermal expansion, which is the change in dimensions of materials due to changes in temperature. It defines linear expansion as the expansion in length and volume expansion as expansion in overall volume. The key factors that affect thermal expansion are the temperature change, material type, and original dimensions. Common materials and their coefficients of thermal expansion are provided. Examples of applications like loosening tight jar lids are given. Finally, several problems involving calculating dimensional changes due to temperature changes are presented.
Thermodynamics part 1 discusses key concepts related to temperature, heat, and thermal equilibrium. It defines temperature as a measure of the average kinetic energy of particles in a sample and discusses how thermometers are used to measure hotness and coldness on different temperature scales. Thermal equilibrium occurs when two systems have the same temperature after interacting. Heat is the transfer of energy due solely to a temperature difference and can cause changes in temperature and phase changes with the absorption or release of latent heat. Specific heat is the amount of heat required to change an object's temperature by 1 degree.
New chm-151-unit-10-power-points-140227172226-phpapp02Cleophas Rwemera
This document provides an overview of gas laws and the kinetic molecular theory. It begins by distinguishing key properties of gases compared to liquids and solids, such as how gas volume is greatly affected by pressure and temperature. The document then covers gas pressure and its measurement using various units. The major gas laws - Boyle's law, Charles' law, and the combined gas law - are introduced and explained with molecular perspectives and example problems. Additional concepts covered include standard temperature and pressure, the ideal gas law, and determining molar mass from vapor density measurements.
This document provides an overview of gas laws and the behavior of gases. It begins by defining the three states of matter and distinguishing properties of gases. Gas pressure and its measurement are then discussed, including common pressure units. The document outlines the major gas laws - Boyle's Law relating pressure and volume at constant temperature, Charles' Law relating volume and temperature at constant pressure, and the Combined Gas Law combining these relationships. Examples are provided to demonstrate applications of the gas laws. The ideal gas law is defined as relating pressure, volume, temperature, and moles of gas. The behavior of gases at standard temperature and pressure is also covered.
The kinetic molecular theory of gases explains gas behavior using the idea that gases are made of molecules or atoms that are in constant, random motion and have space between them. It describes gases as having no intermolecular forces, occupying no volume, and undergoing elastic collisions. This theory allows for deriving gas laws such as Boyle's law (inverse relationship between pressure and volume at constant temperature), Charles's law (direct relationship between volume and temperature at constant pressure), and Gay-Lussac's law (direct relationship between pressure and temperature at constant volume). The combined gas law incorporates all three simpler gas laws. These gas laws allow for calculations involving pressure, volume, temperature, and amount of gas.
The document discusses the kinetic molecular theory and properties of gases. It explains that gas particles are in constant, random motion with no attraction between particles. It also describes gas pressure, temperature, volume, and the relationships between these properties as defined by Boyle's law, Charles' law, Gay-Lussac's law, and the combined gas law. Examples are provided for using these gas laws to calculate changes in gas properties like volume under different conditions.
The document discusses several gas laws including Boyle's law, Charles' law, Avogadro's law, and Gay-Lussac's law. It provides the formulas for each law and graphs demonstrating the relationships between pressure, volume, temperature, and number of moles for ideal gases. It also discusses how real gases deviate from ideal gas behavior and provides the combined gas law formula.
The document discusses the key gas laws and concepts:
1) Gases are highly compressible, occupy their container fully, exert uniform pressure, diffuse easily, and have low densities according to kinetic molecular theory.
2) The gas laws describe the relationships between pressure, volume, temperature, and moles of gas including Boyle's law, Charles' law, Gay-Lussac's law, Avogadro's principle, and the combined ideal gas law.
3) The ideal gas law combines all gas laws as PV=nRT, relating pressure, volume, moles of gas, temperature, and the universal gas constant R. It can be used to calculate gas properties.
LinkedIn for Your Job Search June 17, 2024Bruce Bennett
This webinar helps you understand and navigate your way through LinkedIn. Topics covered include learning the many elements of your profile, populating your work experience history, and understanding why a profile is more than just a resume. You will be able to identify the different features available on LinkedIn and where to focus your attention. We will teach how to create a job search agent on LinkedIn and explore job applications on LinkedIn.
Khushi Saini, An Intern from The Sparks Foundationkhushisaini0924
This is my first task as an Talent Acquisition(Human resources) Intern in The Sparks Foundation on Recruitment, article and posts.
I invitr everyone to look into my work and provide me a quick feedback.
A Guide to a Winning Interview June 2024Bruce Bennett
This webinar is an in-depth review of the interview process. Preparation is a key element to acing an interview. Learn the best approaches from the initial phone screen to the face-to-face meeting with the hiring manager. You will hear great answers to several standard questions, including the dreaded “Tell Me About Yourself”.
Joyce M Sullivan, Founder & CEO of SocMediaFin, Inc. shares her "Five Questions - The Story of You", "Reflections - What Matters to You?" and "The Three Circle Exercise" to guide those evaluating what their next move may be in their careers.
In the intricate tapestry of life, connections serve as the vibrant threads that weave together opportunities, experiences, and growth. Whether in personal or professional spheres, the ability to forge meaningful connections opens doors to a multitude of possibilities, propelling individuals toward success and fulfillment.
Eirini is an HR professional with strong passion for technology and semiconductors industry in particular. She started her career as a software recruiter in 2012, and developed an interest for business development, talent enablement and innovation which later got her setting up the concept of Software Community Management in ASML, and to Developer Relations today. She holds a bachelor degree in Lifelong Learning and an MBA specialised in Strategic Human Resources Management. She is a world citizen, having grown up in Greece, she studied and kickstarted her career in The Netherlands and can currently be found in Santa Clara, CA.
2. Everything’s Made of Atoms
• This idea was only fully accepted about 100
years ago—in part because of Einstein’s
analysis of Brownian motion.
• Brown, who studied the sex life of plants,
noticed a lot of jiggling pollen grains under his
microscope in 1827. He assumed it was
because they were alive, but later found the
identical jiggling with definitely dead stone
powder.
• This was not understood for half a century….!
Applet Movie
3. Size and Mass of Atoms
• The hydrogen atom is about 10-10 m across,
others are a few times bigger.
• Avogadro’s Number: NA = 6.02 x 1023, the
number of atoms (or molecules) in one gram-
mole, 22.4 L volume at NTP.
• The atomic mass unit is 1.66 x 10-27 kg. The
mass of a molecule in amu = mass of NA atoms
in grams: one gram mole of H2O is 18 grams.
• NOTE: this is just a reminder—you should be
very familiar with all this from chemistry!
4. Clicker Question
• Assume the molecules Shakespeare breathed out in
his last breath (say, one liter) are now uniformly
distributed throughout the atmosphere. What is the
probability you breathed one in just now, in your
most recent breath?
A. 1 in 10,000
B. 1 in 1,000
C. 1 in 100
D. 1 in 10
E. More likely than not.
5. Clicker Answer
The answer is: more likely than not.
There are 6 X 1023 molecules in 22.4 L, so about
3 X 1022 in one liter.
The Earth’s atmosphere has volume 4πR2d, take
R = 6 x 106 m, d = 2 x 104 m. This gives a
volume about 1015 m3, or 1021 L.
6. Measuring Temperature
• We can tell by touch if something
is hot or cold, but this is
unreliable. The first serious
attempt to measure temperature
was by Galileo in 1597.
• A glass bulb has a long thin neck,
the end of which is immersed in
liquid.
• As the temperature varies, the gas
in the bulb changes volume,
sucking up liquid or pushing it
down.
7. Clicker Question
• Why was Galileo’s thermometer no good for
comparing temperatures from day to day?
A. The fluid would evaporate.
B. The gas expansion was too small to see
clearly.
C. This instrument is also a barometer.
8. Thermometers
• Many thermometers use the
expansion of a liquid as a
measure of temperature.
• You should be familiar with the
two standard temperature scales
and how to convert between
them.
• Bimetallic strips, two metals with
differing expansion rates welded
together, bend when heated, and
make very robust thermometers.
9. Zeroth Law of Thermodynamics
• If two things at different temperatures are in
thermal contact, so heat can flow, and no heat is
being supplied from or being drained to the
environment, they will reach the same
temperature. They are then said to be in “thermal
equilibrium”.
• The Zeroth Law states that if A is in thermal
equilibrium with B, and B is with C, then A will be
with C.
• If this wasn’t true, thermometers would be
meaningless—but thermodynamics guys like to
see it written down…
10. Thermal Expansion
• A solid rod will increase in length when
heated, typically by of order 10-5 of its original
length for each degree celsius (centigrade). (It
will expand by the same proportion in the
other directions too.)
• This means there will only be a change of one
part in 1,000 over a 100°C temperature range,
so these changes are not visible to the naked
eye, some device is needed to detect them.
11. Thermal Expansion Notation
• The coefficient of linear expansion, denoted
by α, is defined by Δℓ/ℓ0 = αΔT.
• α = 1.2 x 10-5 for iron, 0.9 x 10-5 for glass.
• The coefficient of volume expansion β
is defined by ΔV/V0 = βΔT.
12. Relating Linear and Volume Expansion
• Imagine a cube of solid of side L, volume V = L3.
• On increasing the temperature by ΔT, the
length of each side goes from L to L(1 + αΔT), so
the volume increases from L3 to L3(1 + αΔT)3.
• Now αΔT is a very small number, so
L3(1 + αΔT)3 = L3(1 + 3αΔT + 3(αΔT)2 + (αΔT)3)
= L3(1 + 3αΔT) – those other terms are
really tiny! (for solids, α ~10-5)
• Recall the volume goes to V(1 + βΔT): so β = 3α
13. Clicker Question
• I have a square brass plate with a
hole in it. I put it in the oven until it
reaches a high uniform
temperature, then immediately
measure the hole very accurately.
• What do I find?
A. The hole is bigger than it was
before heating.
B. The hole is smaller.
C. It’s the same size.
• z
14. Clicker Question
• Coefficient of linear expansion of aluminum: 2.5 x 10-5.
• An aluminum plate 2cm x 3cm is heated through 10°C.
By how much does its area increase?
A. 1.5 x 10-3 cm2.
B. 3.0 x 10-3 cm2.
C. 4.5 x 10-3 cm2.
D. 6.0 x 10-3 cm2.
15. Clicker Question
• Coefficient of linear expansion of aluminum: 2.5 x 10-5.
• A solid aluminum sphere is heated through 1°C.
What is its fractional change in density?
A. 2.5 x 10-5 cm2.
B. 5.0 x 10-5 cm2.
C. 7.5 x 10-5 cm2.
D. -7.5 x 10-5 cm2.
E. -2.5 x 10-5 cm2.
16. Volume Expansion Coefficients for Liquids
• Most common organic
liquids have coefficients
around 10-3: much
greater than solids, and
a good reason for not
filling a gas tank to the
very top!
• But mercury has a low
expansion coefficient for
a liquid: 1.8 x 10-4. (Still
20 times that for glass—
mercury thermometers
work fine.)
°C range β (units
10-3) H2O
10-20 0.15
20-30 0.25
30-40 0.35
40-60 0.46
60-80 0.59
80-100 0.70
Water, unlike almost all other
liquids, expands when cooling from
4°C to freezing. It also has a highly
variable coefficient of expansion
over its whole temperature range:
17. Clicker Question
• A manufacturer of mercury in glass thermometers
decides to upgrade his product to Pyrex glass, which
holds up better to high heat because it has a lower
coefficient of expansion. He makes the new
thermometers identical to the old in all dimensions.
• To check his product, he puts a new one and an old
one together in water, and heats the water slowly.
What does he see?
A. The mercury in the new one rises faster.
B. The mercury in the old one rises faster.
C. They both rise at the same rate.
18. Boyle’s Law
• Boyle (born in 1627, the 14th child
of the Earl of Cork) discovered his
Law himself. He used a U-shaped
glass tube, closed at one end, open
at the other. He first carefully
poured in mercury, with the tube
almost horizontal so the trapped air
was at atmospheric pressure: the
levels in the two arms were equal.
• He then poured in thirty inches
more of mercury, that’s one
atmosphere, and found the
trapped air now had half the
original volume.
• m
19. Boyle’s Law
• Boyle knew that fast compression heats a
gas, so before measuring the volume at
the higher pressure, he waited for the air
to cool back down. He repeated the
experiment at different added pressures.
• He found that at constant temperature T,
pressure x volume = constant.
• m
P
V
20. Expansion Coefficient for Gases
• Charles’s Law
• A century after Boyle, Charles
discovered that at constant
pressure, and far from
liquefaction, all gases have the
same expansion coefficient, in
fact
V(T °C) = V(0 °C)(1 + T/273)
• This suggests the gas volume
shrinks to zero at −273, but of
course it liquefies first.
• The Kelvin temperature scale:
• T (K) = T (°C) + 273.15
• a V
0°C 100°C T
V
T
V ∝ T in kelvins
400 K
200 K
0 K
21. The Ideal Gas Law
• We can combine Boyle’s law and Charles’s law
to find PV ∝ T for gases well away from
liquefaction. Note this also implies that at
constant volume, P ∝ T.
• The standard notation for this Ideal Gas Law is:
PV = nRT
for n moles of gas, R = 8.314 J/(mol.K) is the
universal gas constant.
22. Gas Law Exercise
• 100.0 L of oxygen at 27.0°C and absolute pressure
10 atm are compressed to 50.0 L. The gas is
subsequently taken to 177.0°C. What is the final
pressure?
• P1V1/T1 = P2V2/T2: so P2 = P1(V1/V2)(T2/T1)
P2 = 10x(100/50)x(450/300) = 30 atm.
On homework: (1) watch out for gauge pressure and absolute
pressure! (2) the gas law always has T in kelvins. (3) for given
volume of gas and temperature, the pressure is determined by the
total number of molecules (which could be single atoms, for
example He) and not by the masses of the atoms. 1022 He atoms
will exert the same pressure as 1022 oxygen molecules at given T, V.