This document discusses basic thermodynamics concepts. It begins by defining a perfect gas and stating Boyle's Law and Charles' Law, which describe the relationships between pressure, volume, and temperature in gases. It then defines specific heat capacity at constant volume (Cv) as the amount of heat required to raise the temperature of a gas by 1 degree Celsius while keeping its volume constant. The document provides equations relating heat transfer, temperature change, and internal energy for a constant volume process involving a perfect gas. It explains that for such a process, no work is done since the piston cannot move during constant volume heating or cooling.
1) The document discusses the three phases of matter - solid, liquid, and gas - using water as an example substance.
2) It explains that in solids, molecules are closely packed, in liquids they can move within a fixed volume, and in gases they are far apart and move randomly.
3) Various terms are defined regarding phase changes, including saturated and superheated states, and how heating water at constant pressure leads to transitions between these states.
The document defines key terms related to the properties of steam:
- Wet steam is a mixture of saturated liquid and saturated steam at a constant temperature as liquid vaporizes.
- Saturated steam is vapor that has vaporized from liquid at a constant pressure and temperature.
- Superheated steam is vapor whose temperature has increased above saturation temperature at constant pressure through continued heating.
The document discusses non-flow processes in thermodynamics, which occur when a fluid is sealed within a system and cannot cross the system boundary. It defines non-flow processes and differentiates them from flow processes. It then describes two important non-flow processes: [1] isothermal processes, where temperature remains constant, and [2] adiabatic processes, where there is no heat transfer. Equations are provided for calculating work and other properties for gases undergoing these reversible, non-flow processes. Examples are included to demonstrate applying the concepts and equations.
The document discusses the second law of thermodynamics. It defines the second law as stating that some heat must always be rejected by a system, even though the net heat supplied equals the net work done according to the first law. The second law implies that the thermal efficiency of heat engines must always be less than 100% because the gross heat supplied must be greater than the net work done. The document also discusses heat pumps and how they operate in the reverse of heat engines, requiring work input to transfer heat from a cold to hot reservoir.
This document provides an introduction to basic thermodynamics concepts. It defines key terms like system, boundary, surroundings, open and closed systems. It explains the differences between intensive and extensive properties, and defines state, process, and cycle. The document also covers the first law of thermodynamics, the differences between work and heat transfer, sign conventions, and the concept of internal energy. The objectives are to understand these fundamental concepts and the first law of thermodynamics.
The document discusses the steam power cycle. It begins by explaining that steam is commonly used as the working fluid in heat engine cycles due to its desirable properties. It then describes the ideal Carnot cycle, noting the four processes of heat addition, expansion, heat rejection, and compression. The thermal efficiency and work ratio of the Carnot cycle are defined. While theoretically efficient, the Carnot cycle is impractical. The document then introduces the Rankine cycle, which is the ideal cycle used in steam power plants as it overcomes the impracticalities of the Carnot cycle by fully condensing the steam.
The document defines and provides examples of non-flow processes in thermodynamics, specifically polytropic processes. It states that in a non-flow process, the change in internal energy of a fluid equals the net heat supplied minus the net work done. It then discusses polytropic processes, defining them by the equation pV^n = constant, and providing examples of indices for different types of compression processes. The document provides equations to calculate work, temperature, and pressure changes for a polytropic process on a perfect gas. It includes an example problem calculating these values.
The document discusses the application of the steady flow energy equation to various flow processes including turbines, nozzles, throttles, and pumps. It explains that for turbines, the steady flow energy equation relates the enthalpy drop of the fluid to the work produced. For nozzles, the equation shows the relationship between the enthalpy drop and the kinetic energy increase of the fluid. For throttles, the equation indicates that the enthalpy remains constant. And for pumps, the equation relates the enthalpy rise to the work input into the system. Examples are provided to demonstrate how to use the steady flow energy equation to analyze different flow processes.
1) The document discusses the three phases of matter - solid, liquid, and gas - using water as an example substance.
2) It explains that in solids, molecules are closely packed, in liquids they can move within a fixed volume, and in gases they are far apart and move randomly.
3) Various terms are defined regarding phase changes, including saturated and superheated states, and how heating water at constant pressure leads to transitions between these states.
The document defines key terms related to the properties of steam:
- Wet steam is a mixture of saturated liquid and saturated steam at a constant temperature as liquid vaporizes.
- Saturated steam is vapor that has vaporized from liquid at a constant pressure and temperature.
- Superheated steam is vapor whose temperature has increased above saturation temperature at constant pressure through continued heating.
The document discusses non-flow processes in thermodynamics, which occur when a fluid is sealed within a system and cannot cross the system boundary. It defines non-flow processes and differentiates them from flow processes. It then describes two important non-flow processes: [1] isothermal processes, where temperature remains constant, and [2] adiabatic processes, where there is no heat transfer. Equations are provided for calculating work and other properties for gases undergoing these reversible, non-flow processes. Examples are included to demonstrate applying the concepts and equations.
The document discusses the second law of thermodynamics. It defines the second law as stating that some heat must always be rejected by a system, even though the net heat supplied equals the net work done according to the first law. The second law implies that the thermal efficiency of heat engines must always be less than 100% because the gross heat supplied must be greater than the net work done. The document also discusses heat pumps and how they operate in the reverse of heat engines, requiring work input to transfer heat from a cold to hot reservoir.
This document provides an introduction to basic thermodynamics concepts. It defines key terms like system, boundary, surroundings, open and closed systems. It explains the differences between intensive and extensive properties, and defines state, process, and cycle. The document also covers the first law of thermodynamics, the differences between work and heat transfer, sign conventions, and the concept of internal energy. The objectives are to understand these fundamental concepts and the first law of thermodynamics.
The document discusses the steam power cycle. It begins by explaining that steam is commonly used as the working fluid in heat engine cycles due to its desirable properties. It then describes the ideal Carnot cycle, noting the four processes of heat addition, expansion, heat rejection, and compression. The thermal efficiency and work ratio of the Carnot cycle are defined. While theoretically efficient, the Carnot cycle is impractical. The document then introduces the Rankine cycle, which is the ideal cycle used in steam power plants as it overcomes the impracticalities of the Carnot cycle by fully condensing the steam.
The document defines and provides examples of non-flow processes in thermodynamics, specifically polytropic processes. It states that in a non-flow process, the change in internal energy of a fluid equals the net heat supplied minus the net work done. It then discusses polytropic processes, defining them by the equation pV^n = constant, and providing examples of indices for different types of compression processes. The document provides equations to calculate work, temperature, and pressure changes for a polytropic process on a perfect gas. It includes an example problem calculating these values.
The document discusses the application of the steady flow energy equation to various flow processes including turbines, nozzles, throttles, and pumps. It explains that for turbines, the steady flow energy equation relates the enthalpy drop of the fluid to the work produced. For nozzles, the equation shows the relationship between the enthalpy drop and the kinetic energy increase of the fluid. For throttles, the equation indicates that the enthalpy remains constant. And for pumps, the equation relates the enthalpy rise to the work input into the system. Examples are provided to demonstrate how to use the steady flow energy equation to analyze different flow processes.
The document describes the second law of thermodynamics and reversible processes involving perfect gases on temperature-entropy (T-s) diagrams. It discusses:
1) Constant pressure, volume, temperature, and adiabatic processes on T-s diagrams, with constant pressure lines sloping more steeply than constant volume lines.
2) Analyzing a example problem involving a constant pressure expansion of nitrogen gas, calculating work, heat, entropy change, and sketching the process on a T-s diagram.
3) The relationships between pressure, volume, temperature and entropy for perfect gases during various reversible thermodynamic processes.
The document discusses steady flow processes and the steady flow energy equation. It provides the conditions that must be satisfied for a steady flow process, including constant mass flow rate, constant fluid properties over time, and uniform rates of work, heat, and energy transfer. It then derives the steady flow energy equation and discusses its various terms. Finally, it provides examples of applying the equation to boilers and condensers.
This experiment aims to determine the relationship between the saturated temperature and pressure of steam in equilibrium with water between 0 and 14 bars using a Marcet boiler. The measured slope of the temperature-pressure graph is compared to theoretical values from steam tables. Results show a direct proportional relationship between temperature and pressure, with the experimental slope deviating slightly from the theoretical slope due to measurement errors ranging from 0.3-44%. The Marcet boiler can be used to study this relationship and various thermodynamic applications that involve changes in steam properties with pressure and temperature.
The document describes the application of the steady flow energy equation to various fluid flow processes, including turbines, nozzles, throttling, and pumps. It explains that the steady flow energy equation can be applied provided certain conditions are met. For each type of process, it lists the key points and assumptions made in applying the equation. Examples are also provided to demonstrate how to set up and solve the steady flow energy equation for specific problems involving turbines, nozzles, and pumps.
This document discusses non-flow processes in thermodynamics. It defines non-flow processes as those that occur in a closed system where the working fluid does not cross the system boundary, unlike flow processes. Two main non-flow processes are described: isothermal (constant temperature) and adiabatic (no heat transfer) processes. Equations related to work, heat, and state properties are provided for analyzing these processes for ideal gases. Examples are included to demonstrate calculating work, heat, pressure, temperature and volume changes.
Liza anna jj309 fluid mechanics (buku kerjalizaannaseri
The document is a student workbook on fluid mechanics. It contains 11 units that cover topics like fluid properties, fluid statics, fluid dynamics, energy loss in pipelines, and nozzles. Example problems are provided throughout to demonstrate concepts like pressure measurements, fluid characteristics, buoyancy, hydraulic systems, and manometers. The objectives are to explain fluid mechanics concepts, solve related problems correctly, and explain their applications in engineering.
This document provides an introduction to basic thermodynamics concepts including units, dimensions, and conversions. It defines fundamental and derived physical quantities and their SI units. Examples are provided to demonstrate calculating force, pressure, work, power, and density using the appropriate units and conversion factors. The document also discusses dimensional homogeneity and using unit conversions and prefixes to change between units of the same physical quantity. Multiple practice problems are given for students to test their understanding of applying concepts of units, dimensions, and conversions.
This experiment aimed to determine the Reynolds number (NRe) as a function of flow rate for liquid flowing through a circular pipe. NRe was calculated for 6 trials with increasing flow rates. All trials had NRe below 2100, indicating laminar flow as observed by the smooth movement of dye in the pipe. As flow rate increased, NRe also increased but remained in the laminar flow regime. The results show that flow type depends on NRe, with laminar flow occurring at low velocities (NRe < 2100).
Thermodynamic Chapter 3 First Law Of ThermodynamicsMuhammad Surahman
This document provides an overview of the first law of thermodynamics for closed systems. It defines key terms like internal energy, kinetic energy, and potential energy. It presents the general energy balance equation for closed systems undergoing various processes like constant volume, constant pressure, or adiabatic. Example problems demonstrate applying the first law to calculate changes in internal energy or heat transfer. The document also discusses thermodynamic cycles and how the first law applies to systems that return to their initial state.
This experiment studied the effects of cooling load and inlet water temperature on a cooling tower's performance. In experiment 1, cooling load was varied at 0.5 kW, 1 kW, and 1.5 kW while water flow rate and air flow were held constant. Higher cooling loads resulted in larger cooling ranges between inlet and outlet water temperatures. Experiment 2 varied water flow rate from 0.8 LPM to 1.6 LPM at a 1 kW cooling load. Higher water flow rates produced smaller cooling ranges and lower heat loads transferred. The results show that increasing cooling load or decreasing water flow rate improves a cooling tower's heat removal capabilities.
Thermodynamic Chapter 4 Second Law Of ThermodynamicsMuhammad Surahman
This document provides an overview of the second law of thermodynamics. It discusses how the second law establishes conditions for equilibrium and determines theoretical performance limits. The document defines key concepts like thermal efficiency, the Carnot cycle, and entropy. It presents examples calculating efficiency and heat transfer for systems like power plants, refrigerators, and heat pumps operating between different temperature levels.
This document summarizes an experiment conducted using a Marcet boiler to determine the relationship between the pressure and temperature of saturated steam. The experiment measured pressure and temperature values over a range of approximately 0-14 bars. These measured values were then compared to theoretical values from steam tables. The results showed that pressure and temperature were directly proportional, though some measured values differed slightly from predicted values, possibly due to experimental errors. The document also lists the objectives, equipment used, calculations made, and discusses sources of error in the experiment.
This document discusses the boundary work done during various thermodynamic processes involving gases and liquids in closed systems. Several examples are provided to calculate the boundary work done during processes such as compression, expansion, heating and cooling of gases and liquids. The key steps involve using the ideal gas law, gas tables, process lines on P-V and T-s diagrams to determine initial and final states, and then integrating the work equation between these states. EES software is also used in one example to plot the variation of work with pressure for a constant-pressure heating process of R-134a refrigerant.
The document summarizes key concepts about thermodynamics cycles. It describes the processes that make up the Otto cycle used in spark-ignition engines, including isentropic compression, constant volume heat addition, isentropic expansion, and constant volume heat rejection. The thermal efficiency of the Otto cycle is defined. An example calculation illustrates determining temperatures, pressures, thermal efficiency, back work ratio, and mean effective pressure for an Otto cycle. The Diesel cycle used in compression ignition engines is also introduced.
The document provides information about piston engine processes and various engine cycles. It discusses the Otto, diesel, and dual/combined cycles. For each cycle it provides the pressure-volume and temperature-entropy diagrams. It also discusses air standard cycles and assumptions made in the analysis. Key points covered include defining the cycles, explaining the processes in each cycle (e.g. compression, combustion, expansion), and providing examples of calculating temperatures, pressures, efficiencies using the relationships between pressure, volume, and temperature.
The document provides an overview of basic thermodynamics concepts including:
- Defining systems, boundaries, surroundings, open and closed systems
- Explaining properties, states, and processes
- Stating the first law of thermodynamics that total energy is conserved
- Describing the differences between work and heat transfer
- Defining internal energy as the sum of all energy stored within a system
The document defines different phases of steam:
1) Wet steam is a mixture of liquid and vapor at saturation temperature;
2) Saturated steam is all vapor at saturation temperature;
3) Superheated steam is vapor with temperature above saturation.
Thermodynamic Chapter 2 Properties Of Pure SubstancesMuhammad Surahman
This document provides an overview of properties of pure substances and phase change processes. It defines a pure substance as having a fixed chemical composition throughout. Pure substances can exist in solid, liquid, or gas phases. Phase change processes like melting, boiling, and condensation occur at saturation conditions where two phases coexist in equilibrium. Properties like specific volume, internal energy, and enthalpy vary based on temperature, pressure, and quality (ratio of vapor mass to total mass) of mixtures. Property tables and interpolation are used to determine properties at given conditions for pure substances like water. Examples show how to apply these concepts to calculate properties like pressure, temperature, and enthalpy at different states.
The document discusses fluid pressure and its relationship to depth. It introduces Pascal's law and how it applies to hydraulic systems. Specifically:
1) Pressure increases with depth in fluids due to the weight of the fluid above pushing down. Pascal's law states that pressure increases are equal throughout a confined fluid.
2) Hydraulic systems use this principle to multiply forces. A small force applied to a piston with a small surface area can create a much larger force when transmitted through fluid to a piston with a larger surface area.
3) An example is given of a hydraulic car lift, where 1 kg applied to a small piston creates enough pressure to lift 10 kg with a larger piston, multiplying the applied
Fluid tutorial 2_ans dr.waleed. 01004444149 dr walid
This document contains 11 multi-step physics problems involving fluid mechanics concepts like pressure, viscosity, density, and fluid flow. The problems are solved with relevant equations for ideal gases, compressible fluids, laminar flow, and viscometry. Detailed calculations are shown to determine values like mass, pressure, shear stress, drag force, velocity, and viscosity based on given variables like temperature, volume, pressure, velocity, dimensions, torque, and fluid properties.
This document summarizes a lecture on thermodynamics that discusses various topics:
1) The working fluid in a thermodynamic system can exist as a liquid, vapor, or gas. Water can be a liquid, vapor, or gas depending on temperature and pressure conditions.
2) Phase change points from liquid to vapor and vaporization are plotted on PV diagrams. The saturated liquid and vapor lines denote boiling and vaporization points.
3) Wet vapor is a mixture of liquid and dry vapor that exists at state points within the liquid-vapor dome on the PV diagram.
The document discusses various thermodynamic processes including constant temperature, isothermal, isobaric, and adiabatic processes. It provides the equations of state and relationships between pressure, volume, temperature, internal energy, enthalpy, entropy, and work for both closed and open systems undergoing these processes. The summary focuses on defining the key thermodynamic processes and relating the relevant process variables using mathematical equations.
The document describes the second law of thermodynamics and reversible processes involving perfect gases on temperature-entropy (T-s) diagrams. It discusses:
1) Constant pressure, volume, temperature, and adiabatic processes on T-s diagrams, with constant pressure lines sloping more steeply than constant volume lines.
2) Analyzing a example problem involving a constant pressure expansion of nitrogen gas, calculating work, heat, entropy change, and sketching the process on a T-s diagram.
3) The relationships between pressure, volume, temperature and entropy for perfect gases during various reversible thermodynamic processes.
The document discusses steady flow processes and the steady flow energy equation. It provides the conditions that must be satisfied for a steady flow process, including constant mass flow rate, constant fluid properties over time, and uniform rates of work, heat, and energy transfer. It then derives the steady flow energy equation and discusses its various terms. Finally, it provides examples of applying the equation to boilers and condensers.
This experiment aims to determine the relationship between the saturated temperature and pressure of steam in equilibrium with water between 0 and 14 bars using a Marcet boiler. The measured slope of the temperature-pressure graph is compared to theoretical values from steam tables. Results show a direct proportional relationship between temperature and pressure, with the experimental slope deviating slightly from the theoretical slope due to measurement errors ranging from 0.3-44%. The Marcet boiler can be used to study this relationship and various thermodynamic applications that involve changes in steam properties with pressure and temperature.
The document describes the application of the steady flow energy equation to various fluid flow processes, including turbines, nozzles, throttling, and pumps. It explains that the steady flow energy equation can be applied provided certain conditions are met. For each type of process, it lists the key points and assumptions made in applying the equation. Examples are also provided to demonstrate how to set up and solve the steady flow energy equation for specific problems involving turbines, nozzles, and pumps.
This document discusses non-flow processes in thermodynamics. It defines non-flow processes as those that occur in a closed system where the working fluid does not cross the system boundary, unlike flow processes. Two main non-flow processes are described: isothermal (constant temperature) and adiabatic (no heat transfer) processes. Equations related to work, heat, and state properties are provided for analyzing these processes for ideal gases. Examples are included to demonstrate calculating work, heat, pressure, temperature and volume changes.
Liza anna jj309 fluid mechanics (buku kerjalizaannaseri
The document is a student workbook on fluid mechanics. It contains 11 units that cover topics like fluid properties, fluid statics, fluid dynamics, energy loss in pipelines, and nozzles. Example problems are provided throughout to demonstrate concepts like pressure measurements, fluid characteristics, buoyancy, hydraulic systems, and manometers. The objectives are to explain fluid mechanics concepts, solve related problems correctly, and explain their applications in engineering.
This document provides an introduction to basic thermodynamics concepts including units, dimensions, and conversions. It defines fundamental and derived physical quantities and their SI units. Examples are provided to demonstrate calculating force, pressure, work, power, and density using the appropriate units and conversion factors. The document also discusses dimensional homogeneity and using unit conversions and prefixes to change between units of the same physical quantity. Multiple practice problems are given for students to test their understanding of applying concepts of units, dimensions, and conversions.
This experiment aimed to determine the Reynolds number (NRe) as a function of flow rate for liquid flowing through a circular pipe. NRe was calculated for 6 trials with increasing flow rates. All trials had NRe below 2100, indicating laminar flow as observed by the smooth movement of dye in the pipe. As flow rate increased, NRe also increased but remained in the laminar flow regime. The results show that flow type depends on NRe, with laminar flow occurring at low velocities (NRe < 2100).
Thermodynamic Chapter 3 First Law Of ThermodynamicsMuhammad Surahman
This document provides an overview of the first law of thermodynamics for closed systems. It defines key terms like internal energy, kinetic energy, and potential energy. It presents the general energy balance equation for closed systems undergoing various processes like constant volume, constant pressure, or adiabatic. Example problems demonstrate applying the first law to calculate changes in internal energy or heat transfer. The document also discusses thermodynamic cycles and how the first law applies to systems that return to their initial state.
This experiment studied the effects of cooling load and inlet water temperature on a cooling tower's performance. In experiment 1, cooling load was varied at 0.5 kW, 1 kW, and 1.5 kW while water flow rate and air flow were held constant. Higher cooling loads resulted in larger cooling ranges between inlet and outlet water temperatures. Experiment 2 varied water flow rate from 0.8 LPM to 1.6 LPM at a 1 kW cooling load. Higher water flow rates produced smaller cooling ranges and lower heat loads transferred. The results show that increasing cooling load or decreasing water flow rate improves a cooling tower's heat removal capabilities.
Thermodynamic Chapter 4 Second Law Of ThermodynamicsMuhammad Surahman
This document provides an overview of the second law of thermodynamics. It discusses how the second law establishes conditions for equilibrium and determines theoretical performance limits. The document defines key concepts like thermal efficiency, the Carnot cycle, and entropy. It presents examples calculating efficiency and heat transfer for systems like power plants, refrigerators, and heat pumps operating between different temperature levels.
This document summarizes an experiment conducted using a Marcet boiler to determine the relationship between the pressure and temperature of saturated steam. The experiment measured pressure and temperature values over a range of approximately 0-14 bars. These measured values were then compared to theoretical values from steam tables. The results showed that pressure and temperature were directly proportional, though some measured values differed slightly from predicted values, possibly due to experimental errors. The document also lists the objectives, equipment used, calculations made, and discusses sources of error in the experiment.
This document discusses the boundary work done during various thermodynamic processes involving gases and liquids in closed systems. Several examples are provided to calculate the boundary work done during processes such as compression, expansion, heating and cooling of gases and liquids. The key steps involve using the ideal gas law, gas tables, process lines on P-V and T-s diagrams to determine initial and final states, and then integrating the work equation between these states. EES software is also used in one example to plot the variation of work with pressure for a constant-pressure heating process of R-134a refrigerant.
The document summarizes key concepts about thermodynamics cycles. It describes the processes that make up the Otto cycle used in spark-ignition engines, including isentropic compression, constant volume heat addition, isentropic expansion, and constant volume heat rejection. The thermal efficiency of the Otto cycle is defined. An example calculation illustrates determining temperatures, pressures, thermal efficiency, back work ratio, and mean effective pressure for an Otto cycle. The Diesel cycle used in compression ignition engines is also introduced.
The document provides information about piston engine processes and various engine cycles. It discusses the Otto, diesel, and dual/combined cycles. For each cycle it provides the pressure-volume and temperature-entropy diagrams. It also discusses air standard cycles and assumptions made in the analysis. Key points covered include defining the cycles, explaining the processes in each cycle (e.g. compression, combustion, expansion), and providing examples of calculating temperatures, pressures, efficiencies using the relationships between pressure, volume, and temperature.
The document provides an overview of basic thermodynamics concepts including:
- Defining systems, boundaries, surroundings, open and closed systems
- Explaining properties, states, and processes
- Stating the first law of thermodynamics that total energy is conserved
- Describing the differences between work and heat transfer
- Defining internal energy as the sum of all energy stored within a system
The document defines different phases of steam:
1) Wet steam is a mixture of liquid and vapor at saturation temperature;
2) Saturated steam is all vapor at saturation temperature;
3) Superheated steam is vapor with temperature above saturation.
Thermodynamic Chapter 2 Properties Of Pure SubstancesMuhammad Surahman
This document provides an overview of properties of pure substances and phase change processes. It defines a pure substance as having a fixed chemical composition throughout. Pure substances can exist in solid, liquid, or gas phases. Phase change processes like melting, boiling, and condensation occur at saturation conditions where two phases coexist in equilibrium. Properties like specific volume, internal energy, and enthalpy vary based on temperature, pressure, and quality (ratio of vapor mass to total mass) of mixtures. Property tables and interpolation are used to determine properties at given conditions for pure substances like water. Examples show how to apply these concepts to calculate properties like pressure, temperature, and enthalpy at different states.
The document discusses fluid pressure and its relationship to depth. It introduces Pascal's law and how it applies to hydraulic systems. Specifically:
1) Pressure increases with depth in fluids due to the weight of the fluid above pushing down. Pascal's law states that pressure increases are equal throughout a confined fluid.
2) Hydraulic systems use this principle to multiply forces. A small force applied to a piston with a small surface area can create a much larger force when transmitted through fluid to a piston with a larger surface area.
3) An example is given of a hydraulic car lift, where 1 kg applied to a small piston creates enough pressure to lift 10 kg with a larger piston, multiplying the applied
Fluid tutorial 2_ans dr.waleed. 01004444149 dr walid
This document contains 11 multi-step physics problems involving fluid mechanics concepts like pressure, viscosity, density, and fluid flow. The problems are solved with relevant equations for ideal gases, compressible fluids, laminar flow, and viscometry. Detailed calculations are shown to determine values like mass, pressure, shear stress, drag force, velocity, and viscosity based on given variables like temperature, volume, pressure, velocity, dimensions, torque, and fluid properties.
This document summarizes a lecture on thermodynamics that discusses various topics:
1) The working fluid in a thermodynamic system can exist as a liquid, vapor, or gas. Water can be a liquid, vapor, or gas depending on temperature and pressure conditions.
2) Phase change points from liquid to vapor and vaporization are plotted on PV diagrams. The saturated liquid and vapor lines denote boiling and vaporization points.
3) Wet vapor is a mixture of liquid and dry vapor that exists at state points within the liquid-vapor dome on the PV diagram.
The document discusses various thermodynamic processes including constant temperature, isothermal, isobaric, and adiabatic processes. It provides the equations of state and relationships between pressure, volume, temperature, internal energy, enthalpy, entropy, and work for both closed and open systems undergoing these processes. The summary focuses on defining the key thermodynamic processes and relating the relevant process variables using mathematical equations.
The document provides an overview of thermodynamics and its applications. It discusses key concepts like the laws of thermodynamics, state functions, energy conservation, and entropy. Thermodynamics allows the energy requirements and extent of processes to be calculated using mathematical relationships between measurable quantities. Computer software can perform thermodynamic calculations and is a useful tool. Examples are given to illustrate applying the first law of thermodynamics to calculate energy balances for processes like melting iron and combustion reactions.
This document summarizes the work done by an ideal gas during isochoric and isobaric processes. It defines these two types of processes, showing that work is done during isobaric processes but not during isochoric processes. It also discusses molar specific heat at constant volume and how this relates to the temperature change and internal energy change of an ideal gas. The document was prepared by a mechanical engineering student as part of their coursework.
1. The document discusses entropy and the Clausius inequality which is a consequence of the second law of thermodynamics. It involves heat transfer (Q) to or from a system, absolute temperature (T) at the boundary, and a cyclic integral.
2. For a reversible heat engine or refrigeration cycle, the cyclic integral of Q/T is equal to zero, but it is always less than or greater than zero for irreversible cycles depending on whether it is a heat engine or refrigeration cycle.
3. Entropy change is calculated as the area under the T-S curve for a reversible process, but is always greater for an irreversible process between the same two states. Property diagrams like T-
The document discusses various concepts related to work and heat transfer in thermodynamic systems. It defines work as the product of force and distance, and explains that work is done by or on a system. It also defines heat as energy transferred due to temperature difference and describes different modes of heat transfer. The document then discusses various thermodynamic processes like isobaric, isochoric, isothermal, and adiabatic processes. It provides equations to calculate work done and related thermodynamic properties for these processes.
1. The document discusses a first week thermodynamics course covering measuring units like force and pressure, and terms like specific volume.
2. The second week covers thermodynamic terms like state and process, and classifications of systems as closed, open, or isolated.
3. The third week covers temperature measurement scales, pressure measurement units, and relations between them. It also discusses manometers and barometers.
4. The fourth week will cover work, its kinds, energy and its forms. The goal is for students to understand work and its types, and types and forms of energy.
Here are the answers to the tutorial questions:
1. TRUE (T) or FALSE (F)
i. F
ii. T
iii. F
iv. T
v. T
vi. T
vii. F
2. Thermal efficiency (η) = Work done/Heat supplied from hot reservoir
= 20 kW/3000 kJ/min
= 0.2 or 20%
Rate of heat rejection (Q2) = Heat supplied - Net work done
= 3000 kJ/min - (20 kW * 1000/60) kJ/min
= 3000 - 333.33 kJ/min
= 2666.67 kJ/min
3.
This document discusses Pascal's principle of fluid mechanics, which states that pressure changes in an enclosed fluid are transmitted equally in all directions. It then discusses applications of hydraulics including hydraulic lifts, elevators, and bridges which use Pascal's principle to transmit pressure through liquid and amplify force. Hydraulic systems use an incompressible fluid like oil to transfer pressure from a pump to actuators with advantages over other systems in withstanding heat and pressure.
This document provides an overview of a thermodynamics module for Malaysian polytechnics. It includes biographies of the two module writers, an evaluation form for students to provide feedback, a curriculum grid outlining the topics and hours for each unit, and summaries of the content and objectives covered in each of the 11 units. The units progress from basic thermodynamics concepts to properties of steam, the second law of thermodynamics, and the steam power cycle. Guidelines at the end instruct students to carefully complete all activities to maximize learning from the module.
This document provides information about constant volume (isochoric) processes and steady flow processes. It defines key concepts like work, heat, internal energy, enthalpy, and entropy for these processes. Equations of state and relationships between pressure, volume, temperature are presented. The document also discusses pumps, fans and example problems.
This document provides an introduction to the module on the Laws of Thermodynamics. It discusses the following key points:
1. The module will cover the historical background of thermodynamics, the first law of thermodynamics relating internal energy, heat and work, the second law regarding the direction of heat flow, and analyzing heat engines and refrigerators.
2. Students are expected to understand the historical development of thermodynamics, relate thermodynamic quantities, describe heat flow direction, and analyze thermodynamic processes.
3. Tips are provided for learning the module effectively, including taking time to understand concepts, not skipping lessons, being honest when answering, and asking for clarification when needed.
4
The document discusses processes involving ideal gases. It defines reversible and irreversible processes, and describes various types of processes including constant pressure (isobaric) processes. It provides equations to calculate heat, work, internal energy, enthalpy and entropy changes for ideal gases undergoing constant pressure processes in both closed and open/flow systems. Examples include piston-cylinder assemblies and heat exchangers like steam boilers and shell and tube heat exchangers. Practice problems at the end apply the concepts and equations to calculate various thermodynamic properties.
This document discusses ideal gases and their properties. It defines an ideal gas as a theoretical gas composed of point-like particles that obey gas laws perfectly. Some key properties of ideal gases are that they have negligible volume and mass and undergo perfectly elastic collisions. The document also covers gas laws such as Boyle's, Charles', and Gay-Lussac's laws. It provides the ideal gas equation of state and defines terms like molar mass, gas constant, pressure units and heat capacities. Several example problems applying the ideal gas law are also included.
The chapter discusses entropy, which is defined based on the Clausius inequality. Entropy is a state function that depends on the initial and final states, not the path between states. It is a measure of disorder or unavailable work in a thermodynamic system. The entropy change of a system is determined by the heat transfer and temperature. Entropy always increases for irreversible processes in an isolated system according to the second law of thermodynamics.
The document discusses thermodynamics, dimensions and units, and fundamental concepts of thermodynamics. It defines thermodynamics as the science of energy, and discusses the conservation of energy principle and the first law of thermodynamics. It also defines dimensions as characteristics of physical quantities, and primary and secondary dimensions. Finally, it provides examples of converting between different units for dimensions like length, mass, time, and others.
This document provides an overview of basic thermodynamics concepts including:
- The objectives of understanding the laws of thermodynamics and their constants.
- Definitions of perfect gases and their properties of pressure, volume, and temperature.
- Explanations of Boyle's Law, Charles' Law, and the Universal Gas Law.
- Introduction of specific heat capacity at constant volume and constant pressure.
- Examples demonstrating applications of the gas laws and calculations involving specific heat.
1. Pressure of a gas is caused by particle collisions with the container walls. Higher temperature means higher particle kinetic energy, causing more frequent and forceful collisions and higher pressure.
2. Boyle's law states that at constant temperature, pressure and volume of a gas are inversely proportional. Charles' law says volume and temperature are directly proportional at constant pressure. Gay-Lussac's law finds pressure and temperature directly proportional at constant volume.
3. These gas laws can be combined into the ideal gas law: pV = nRT, relating pressure, volume, amount of gas, temperature, and the universal gas constant. This law approximates gas behavior except at low temperatures or high pressures.
1. The document discusses the key gas laws including Boyle's law, Charles' law, Gay-Lussac's law, Avogadro's law, Dalton's law, and the kinetic molecular theory of gases.
2. It provides the mathematical equations for each gas law and describes their relationships. For example, Boyle's law states that at a constant temperature, the pressure and volume of a gas are inversely proportional.
3. The kinetic molecular theory of gases makes assumptions about gas particles and derives the ideal gas law from calculations of molecular kinetic energy. It explains gas properties at the atomic/molecular level.
Unit cells describe the repeating arrangements of atoms or molecules in crystalline solids. A unit cell contains the smallest group of particles that can be repeated to form the entire crystal structure. Common unit cell types include cubic, hexagonal, and body-centered cubic, with the specific arrangement depending on the bonding and packing of particles within the solid material.
Properties of gases: gas laws, ideal gas equation, dalton’s law of partial pressure, diffusion of gases, kinetic theory of gases, mean free path, deviation from ideal gas behavior, vander wails equation, critical constants, liquefaction of gases, determination of molecular weights, law of corresponding states and heat capacity
This document summarizes several gas laws including Boyle's law, Charles' law, Avogadro's law, the combined gas law, and the ideal gas law. Boyle's law states that for a fixed amount of gas at constant temperature, the volume is inversely proportional to the pressure. Charles' law states that for a fixed amount of gas at constant pressure, the volume is directly proportional to the temperature. Avogadro's law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. The combined gas law incorporates Boyle's, Charles's and Avogadro's laws. The ideal gas law relates the pressure, volume, quantity, and temperature of an ideal gas using the formula
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.
1. The document discusses gas laws, including Boyle's law relating volume and pressure at constant temperature, and Charles' law relating volume and temperature at constant pressure.
2. It provides examples of using the gas laws to calculate volume or pressure changes given initial and final conditions.
3. The kinetic molecular theory is described as explaining the gas laws based on the random motion and elastic collisions of gas molecules.
1) An equation of state relates macroscopic variables like pressure, volume, temperature, and number of moles that describe a substance. The ideal gas law is the equation of state for gases.
2) Standard temperature and pressure (STP) are defined as 0°C (273.15 K) and 1 atmosphere (101.3 kPa). At STP, 1 mole of any gas occupies 22.4 L of volume.
3) Experiments on gas behavior led to Boyle's, Charles', and Gay-Lussac's laws, which combined form the ideal gas law: PV=nRT, relating pressure, volume, moles, and temperature.
PHYSICAL CHEMISTRY - Gases
Is the branch of chemistry which deals with measurable quantities.
PARTS OF PHYSICAL CHEMISTRY
The physical chemistry is studied under the following sub topics. These are
1. States of matter
2. Chemical equilibrium
3. Thermochemistry/ Energetics
4. Electrochemistry
5. Chemical kinetics
The document discusses the characteristics and properties of gases. It defines the gaseous state as the state where intermolecular forces are at a minimum. Some key characteristics of gases include having low density, high compressibility, diffusibility, and filling their container uniformly. The document also discusses various gas laws including Boyle's law, Charles' law, Gay-Lussac's law, Avogadro's law, and the ideal gas equation. It provides the mathematical relationships and graphical representations for each gas law.
Charles' law describes how gas volume changes with temperature. It states that the volume of a gas is directly proportional to its temperature when pressure is kept constant. The document provides the formula for Charles' law and shows examples of using it to calculate unknown volumes or temperatures given other variables like initial and final volumes and temperatures. It also discusses the limitations of Charles' law and provides sample problems and solutions demonstrating how to apply the law to calculate unknown values.
This document discusses properties of natural gases that are important for engineers to understand when designing equipment for natural gas production, processing, and transportation. It covers topics such as the molecular theory of gases and liquids, equations of state including the ideal gas law and real gas behavior, viscosity, thermodynamic properties including specific heat and heating values, and limits of flammability and safety considerations. Key equations of state and models for predicting properties like compressibility factor, viscosity, and specific heat are presented.
The document discusses the kinetic molecular theory of gases and properties of gases. Some key points:
1) Gases are composed of molecules that are in constant random motion and interact through perfectly elastic collisions. The average kinetic energy is proportional to temperature.
2) Gas pressure is caused by molecular collisions with container walls. Pressure increases with higher temperature or lower volume based on the gas laws.
3) The kinetic molecular theory explains gas properties and laws such as Boyle's, Charles', Avogadro's, and Dalton's through consideration of molecular motion and collisions.
4) Gas density, pressure, volume, temperature, and amount relationships can be described using the ideal gas law. Real gases deviate from
1. The document discusses the kinetic theory of gases and the gas laws. It explains that gas pressure is due to particle collisions with the container walls and increases with temperature as the particle speed and collision rate increases.
2. The gas laws of Boyle, Charles, and Gay-Lussac are summarized. Boyle's law states that at constant temperature, pressure and volume are inversely related. Charles' law specifies that at constant pressure, volume and temperature are directly related. Gay-Lussac's law indicates that at constant volume, pressure and temperature are directly related.
3. Experiments are described that verify each gas law through varying one property while holding the others constant. Graphs illustrate the mathematical relationships between pressure
The document discusses the three states of matter - solid, liquid, and gas. It explains the properties of gases and how gas particles are in constant random motion. The gas laws including Boyle's law, Charles' law, Avogadro's law, and the ideal gas equation are described. It also covers gas pressure, measurement of pressure using barometers and manometers, gas density calculations, and sample problems involving the gas laws.
Gases are highly compressible and expand to fill their containers, with pressure inversely proportional to volume according to Boyle's Law. The properties and behavior of gases can be explained by the kinetic molecular theory, which models gases as large numbers of molecules in random motion. Real gases deviate from ideal gas behavior at high pressures and low temperatures due to intermolecular forces and molecular volumes.
Gases are highly compressible and expand to fill their containers, with pressure inversely proportional to volume according to Boyle's Law. The properties and behavior of gases can be explained by the kinetic molecular theory, which models gases as large numbers of molecules in random motion. Real gases deviate from ideal gas behavior at high pressures and low temperatures due to intermolecular forces and molecular volumes.
1. This document discusses the kinetic molecular theory and properties of ideal gases. It introduces concepts such as average kinetic energy, Maxwell speed distribution curves, and the ideal gas law.
2. Several gas laws are described, including Boyle's law, Charles' law, Avogadro's law, and Dalton's law of partial pressures. Standard temperature and pressure is defined.
3. Deviations from ideal gas behavior occur at high pressures due to intermolecular forces and the non-negligible volume of gas particles. Real gases behave more ideally at lower pressures.
The document discusses the three states of matter - solid, liquid, and gas. It focuses on the gaseous state and properties of gases. Some key points:
- Gases have molecules that are separated by large distances and move freely and independently of each other.
- Many substances can exist as gases under normal conditions, including elements like hydrogen, nitrogen, oxygen as well as compounds like carbon dioxide and ammonia.
- Gases exert pressure uniformly on all surfaces. Gas pressure is measured using instruments like barometers and manometers.
- The behavior of gases is described by gas laws including Boyle's law, Charles' law, Avogadro's law, and the ideal gas equation.
Monitoring and Managing Anomaly Detection on OpenShift.pdfTosin Akinosho
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HCL Notes and Domino License Cost Reduction in the World of DLAU
Unit3
1. BASIC THERMODYNAMICS J2006/3/1
UNIT 3
BASIC THERMODYNAMICS
OBJECTIVES
General Objective : To understand the laws of thermodynamics and its constants.
Specific Objectives : At the end of the unit you will be able to:
define the definitions of Boyle’s Law, Charles’ Law and
Universal Gases Law
define and show the application of the specific heat capacity at
constant pressure
define and apply the specific heat capacity at constant volume
2. BASIC THERMODYNAMICS J2006/3/2
INPUT
3.0 Definition Of Perfect Gases
Did you know, one important type of fluid that has many applications in
thermodynamics is the type in which the working temperature of the fluid remains
well above the critical temperature of the fluid? In this case, the fluid cannot be
liquefied by an isothermal compression, i.e. if it is required to condense the fluid,
then cooling of the fluid must first be carried out. In the simple treatment of such
fluids, their behavior is likened to that a perfect gas. Although, strictly speaking, a
perfect gas is an ideal which can never be realized in practice. The behavior of many
‘permanent’ gases, e.g. hydrogen, oxygen, air etc is very similar to the behavior of a
perfect gas to a first approximation.
A perfect gas is a collection of particles that:
are in constant, random motion,
have no intermolecular attractions (which leads to elastic collisions in which no
energy is exchanged or lost),
are considered to be volume-less points.
You are more familiar with the term ‘ideal’ gas. There is actually a distinction
between these two terms but for our purposes, you may consider them
interchangeable. The principle properties used to define the state of a gaseous system
are pressure (P), volume (V) and temperature (T). SI units (Systems International)
for these properties are Pascal (Pa) for pressure, m3 for volume (although liters and
cm3 are often substituted), and the absolute scale of temperature or Kelvin (K).
Two of the laws describing the behavior of a perfect gas are Boyle’s Law and
Charles’ Law.
3. BASIC THERMODYNAMICS J2006/3/3
3.1 Boyle’s Law
The Boyle’s Law may be stated as follows:
Provided the temperature T of a perfect gas remains constant, then volume, V of a
given mass of gas is inversely proportional to the pressure P of the gas, i.e. P ∝ 1/V
(as shown in Fig. 3.1-1), or P x V = constant if temperature remains constant.
P
P ∝ 1/V
1/V
Figure 3.1-1 Graph P ∝ 1/V
If a gas changes from state 1 to state 2 during an isothermal process, then
P1 V1 = P2 V2 = constant (3.1)
If the process is represented on a graph having axes of pressure P and volume V, the
results will be as shown in Fig. 3.1-2. The curve is known as a rectangular
hyperbola, having the mathematical equation xy = constant.
P
P1 1
P2 2
3
P3
V1 V2 V3 V
PV = constant
Figure 3.1-2 P-V graph for constant temperature
4. BASIC THERMODYNAMICS J2006/3/4
Example 3.1
A quantity of a certain perfect gas is heated at a constant temperature from an
initial state of 0.22 m3 and 325 kN/m2 to a final state of 170 kN/m2. Calculate
the final pressure of the gas.
Solution to Example 3.1
From equation P1V1 = P2V2
325 kN/m 2
= ( 0.22 m 3 )
P1
∴V2 = V1 x 170 kN/m 2 = 0.421 m 3
P2
3.2 Charles’ Law
The Charles’s Law may be stated as follows:
Provided the pressure P of a given mass of gas remains constant, then the volume V
of the gas will be directly proportional to the absolute temperature T of the gas, i.e.
V ∝ T, or V = constant x T. Therefore V/T = constant, for constant pressure P.
If gas changes from state 1 to state 2 during a constant pressure process, then
V1 V2
= = constant (3.2)
T1 T2
If the process is represented on a P – V diagram as before, the result will be as shown
in Fig. 3.2.
P
1 2
0 V
V1 V2
Figure 3.2 P-V graph for constant pressure process
5. BASIC THERMODYNAMICS J2006/3/5
Example 3.2
A quantity of gas at 0.54 m3 and 345 oC undergoes a constant pressure process
that causes the volume of the gas to decreases to 0.32 m3. Calculate the
temperature of the gas at the end of the process.
Solution to Example 3.2
From the question
V1 = 0.54 m3
T1 = 345 + 273 K = 618 K
V2 = 0.32 m3
V1 V2
=
T1 T2
V2
∴ T2 = T1 x
V1
0.32 m 3
= ( 618 K )
0.54 m 3
= 366 K
3.3 Universal Gases Law
Charles’ Law gives us the change in volume of a gas with temperature when the
pressure remains constant. Boyle’s Law gives us the change in volume of a gas with
pressure if the temperature remains constant.
The relation which gives the volume of a gas when both temperature and the
pressure are changed is stated as equation 3.3 below.
PV
= constant = R (3.3)
T
i.e. P1V1 P2V2 (3.4)
=
T1 T2
6. BASIC THERMODYNAMICS J2006/3/6
No gases in practice obey this law rigidly, but many gases tend towards it. An
PV
imaginary ideal that obeys the law is called a perfect gas, and the equation =R
T
is called the characteristic equation of state of a perfect gas.
The constant, R, is called the gas constant. The unit of R is Nm/kg K or J/kg K.
Each perfect gas has a different gas constant.
The characteristic equation is usually written
PV = RT (3.5)
or for m kg, occupying V m3,
PV = mRT (3.6)
Another form of the characteristic equation can be derived using the kilogram-mole
as a unit. The kilogram-mole is defined as a quantity of a gas equivalent to m kg of
the gas, where M is the molecular weight of the gas (e.g. since the molecular weight
of oxygen is 32, then 1 kg mole of oxygen is equivalent to 32 kg of oxygen).
From the definition of the kilogram-mole, for m kg of a gas we have,
m = nM (3.7)
(where n is the number of moles).
Note: Since the standard of mass is the kg, kilogram-mole will be written simply as
mole.
Substituting for m from equation 3.7 in equation 3.6,
PV
PV = nMRT or MR = (3.8)
nT
7. BASIC THERMODYNAMICS J2006/3/7
Now Avogadro’s hypothesis states that the volume of 1 mole of any gas is the same
as the volume of 1 mole of any other gas, when the gases are at the same temperature
and pressure. Therefore V/n is the same for all gases at the same value of P and T.
That is the quantity PV/nT is constant for all gases. This constant is called the
universal gas constant, and is given the symbol Ro.
i.e. PV (3.9)
MR = Ro = or PV = nRo T
nT
or since MR = Ro then,
Ro
R= (3.10)
M
Experiment has shown that the volume of 1 mole of any perfect gas at 1 bar and 1 oC
is approximately 22.71 m3. Therefore from equation 3.8
PV 1 x 10 5 x 22.71
R0 = = = 8314.4 J/mole K
nT 1 x 273.15
From equation 3.10 the gas constant for any gas can be found when the molecular
weight is known, e.g. for oxygen of molecular weight 32, the gas constant is
Ro 8314.4
R= = = 259.8 J/kg K
M 32
Example 3.3
0.046 m3 of gas are contained in a sealed cylinder at a pressure of 300 kN/m2
and a temperature of 45 oC. The gas is compressed until the pressure reaches
1.27 MN/m2 and the temperature is 83oC. If the gas is assumed to be a perfect
gas, determine:
a) the mass of gas (kg)
b) the final volume of gas (m3)
Given:
R = 0.29 kJ/kg K
8. BASIC THERMODYNAMICS J2006/3/8
Solution to Example 3.3
From the question
V1 = 0.046 m3
P1 = 300 kN/m2
T1 = 45 + 273 K = 318 K
P2 = 1.27 MN/m2 = 1.27 x 103 kN/m2
T2 = 83 + 273 K = 356 K
R = 0.29 kJ/kg K
From equation 3.6
PV = mRT
P1V1 300 x 0.046
m= = = 0.1496 kg
RT1 0.29 x 318
From equation 3.4, the constant volume process i.e. V1 = V2
P1 P2
=
T1 T2
P 1.27 x 10 3
T2 = ( T1 ) 2
P = ( 318)
300 = 1346 K
1
9. BASIC THERMODYNAMICS J2006/3/9
Activity 3A
TEST YOUR UNDERSTANDING BEFORE YOU CONTINUE WITH THE
NEXT INPUT…!
3.1 Study the statements in the table below. Mark the answers as TRUE or
FALSE.
STATEMENT TRUE or FALSE
i. Charles’ Law gives us the change in volume
of a gas with temperature when the
temperature remains constant.
ii. Boyle’s Law gives us the change in volume of
a gas with pressure if the pressure remains
constant.
iii. The characteristic equation of state of a
perfect gas is PV = R .
T
iv. Ro is the symbol for universal gas constant.
v. The constant R is called the gas constant.
vi. The unit of R is Nm/kg or J/kg.
3.2 0.04 kg of a certain perfect gas occupies a volume of 0.0072 m3 at a pressure
6.76 bar and a temperature of 127 oC. Calculate the molecular weight of the
gas (M). When the gas is allowed to expand until the pressure is 2.12 bar the
final volume is 0.065 m3. Calculate the final temperature.
10. BASIC THERMODYNAMICS J2006/3/10
Feedback To Activity 3A
3.1 i. False
ii. False
iii. True
iv. True
v. True
vi. False
3.2 From the question,
m = 0.04 kg
V1 = 0.072 m3 V2 = 0.072 m3
P1 = 6.76 bar = 6.76 x 102 kN/m2 P2 = 2.12 bar = 2.12 x 102 kN/m2
T1 = 127 + 273 K = 400 K
From equation 3.6
P1V1 = mRT1
P1V1 6.76 x 10 2 x 0.0072
∴R = = = 0.3042 kJ/kg K
mT1 0.04 x 400
Then from equation 3.10
R
R= o
M
Ro 8.3144
∴M = = = 27 kg/kmol
R 0.3042
i.e. Molecular weight = 27
11. BASIC THERMODYNAMICS J2006/3/11
From equation 3.6
P2V2 = mRT2
P2V2 2.12 x 10 2 x 0.065
∴ T2 = = = 1132.5 K
mR 0.04 x 0.3042
i.e. Final temperature = 1132.5 – 273 = 859.5 oC.
CONGRATULATIONS, IF YOUR ANSWERS ARE CORRECT YOU CAN
PROCEED TO THE NEXT INPUT…..
12. BASIC THERMODYNAMICS J2006/3/12
INPUT
3.4 Specific Heat Capacity at Constant Volume (Cv)
The specific heat capacities of any substance is defined as the amount of heat energy
required to raise the unit mass through one degree temperature raise. In
thermodynamics, two specified conditions are used, those of constant volume and
constant pressure. The two specific heat capacities do not have the same value and it
is essential to distinguish them.
If 1 kg of a gas is supplied with an amount of heat energy sufficient to raise the
temperature of the gas by 1 degree whilst the volume of the gas remains constant,
then the amount of heat energy supplied is known as the specific heat capacity at
constant volume, and is denoted by Cv. The unit of Cv is J/kg K or kJ/kg K.
For a reversible non-flow process at constant volume, we have
dQ = mCvdT (3.11)
For a perfect gas the values of Cv are constant for any one gas at all pressures and
temperatures. Equations (3.11) can then be expanded as follows :
Heat flow in a constant volume process, Q12 = mCv(T2 – T1) (3.12)
Also, from the non-flow energy equation
Q – W = (U2 – U1)
mcv(T2 – T1) – 0 = (U2 – U1)
∴ (U2 – U1) = mCv(T2 – T1) (3.13)
i.e. dU = Q
Note:
In a reversible constant volume process, no work energy transfer can take
place since the piston will be unable to move i.e. W = 0.
13. BASIC THERMODYNAMICS J2006/3/13
The reversible constant volume process is shown on a P-V diagram in Fig. 3.4.
P
P2 2
P1 1
V
V1 = V2
Figure 3.4 P-V diagram for reversible constant volume process
Example 3.4
3.4 kg of gas is heated at a constant volume of 0.92 m 3 and temperature 17 oC
until the temperature rose to 147 oC. If the gas is assumed to be a perfect gas,
determine:
c) the heat flow during the process
d) the beginning pressure of gas
e) the final pressure of gas
Given
Cv = 0.72 kJ/kg K
R = 0.287 kJ/kg K
Solution to Example 3.4
From the question
m = 3.4 kg
V1 = V2 = 0.92 m3
T1 = 17 + 273 K = 290 K
T2 = 147 + 273 K = 420 K
Cv = 0.72 kJ/kg K
R = 0.287 kJ/kg K
14. BASIC THERMODYNAMICS J2006/3/14
a) From equation 3.13,
Q12 = mCv(T2 – T1)
= 3.4 x 0.72(420 – 290)
= 318.24 kJ
b) From equation 3.6,
PV = mRT
Hence for state 1,
P1V1 = mRT1
mRT1 3.4 kg x 0.287 kJ/kgK x 290 K
P1 = = 3
= 307.6 kN/m 2
V1 0.92 m
c) For state 2,
P2V2 = mRT2
mRT2 3.4 kg x 0.287 kJ/kgK x 420 K
P2 = = 3
= 445.5 kN/m 2
V2 0.92 m
3.5 Specific Heat Capacity at Constant Pressure (Cp)
If 1 kg of a gas is supplied with an amount of heat energy sufficient to raise the
temperature of the gas by 1 degree whilst the pressure of the gas remains constant,
then the amount of heat energy supplied is known as the specific heat capacity at
constant pressure, and is denoted by Cp. The unit of Cp is J/kg K or kJ/kg K.
For a reversible non-flow process at constant pressure, we have
dQ = mCpdT (3.14)
For a perfect gas the values of Cp are constant for any one gas at all pressures and
temperatures. Equation (3.14) can then be expanded as follows:
Heat flow in a reversible constant pressure process Q = mCp(T2 – T1) (3.15)
15. BASIC THERMODYNAMICS J2006/3/15
3.6 Relationship Between The Specific Heats
Let a perfect gas be heated at constant pressure from T1 to T2. With reference to the
non-flow equation Q = U2 – U1 + W, and the equation for a perfect gas
U2 – U1 = mCv(T2 – T1), hence,
Q = mCv(T2 – T1) + W
In a constant pressure process, the work done by the fluid is given by the pressure
times the change in volume, i.e. W = P(V2 – V1). Then using equation PV = mRT,
we have
W = mR(T2 – T1)
Therefore substituting,
Q = mCv(T2 – T1) + mR(T2 – T1) = m(Cv + R)(T2 – T1)
But for a constant pressure process from equation 3.15,
Q = mCp(T2 – T1)
Hence, by equating the two expressions for the heat flow Q, we have
mCp(T2 – T1) = m(Cv + R)(T2 – T1)
∴Cp = Cv + R
Alternatively, it is usually written as
R = Cp - C v 3.16
3.7 Specific Heat Ratio (γ)
The ratio of the specific heat at constant pressure to the specific heat at constant
volume is given the symbol γ (gamma),
Cp
i.e. γ= (3.17)
Cv
Note that since Cp - Cv= R, from equation 3.16, it is clear that Cp must be greater than
Cv for any perfect gas. It follows therefore that the ratio Cp/Cv = γ , is always greater
than unity. In general, γ is about 1.4 for diatomic gases such as carbon monoxide
(CO), hydrogen (H2), nitrogen (N2), and oxygen (O2). For monatomic gases such as
16. BASIC THERMODYNAMICS J2006/3/16
argon (A), and helium (He), γ is about 1.6, and for triatomic gases such as carbon
dioxide (CO2), and sulphur dioxide (SO2), γ is about 1.3. For some hydro-carbons the
value of γ is quite low (e.g. for ethane (C2H6), γ = 1.22, and for iso-butane (C4H10), γ
= 1.11.
Some useful relationships between Cp , Cv , R, and γ can be derived.
From equation 3.17
Cp - Cv= R
Dividing through by Cv
Cp R
−1 =
Cv Cv
Cp
Therefore using equation 3.17, γ = , then,
Cv
R
γ −1 =
Cv
R
Cv = 3.18
(γ − 1)
Also from equation 3.17, Cp = γCv hence substituting in equation 3.18,
γR
Cp = γ Cv =
(γ − 1)
γR
Cp = 3.19
(γ − 1)
17. BASIC THERMODYNAMICS J2006/3/17
Example 3.5
A certain perfect gas has specific heat as follows
Cp = 0.846 kJ/kg K and Cv = 0.657 kJ/kg K
Find the gas constant and the molecular weight of the gas.
Solution to Example 3.5
From equation 3.16
R = Cp - C v
i.e. R = 0.846 – 0.657 = 0.189 kJ/kg K
or R = 189 Nm/kg K
From equation 3.10
R0
M=
R
8314
i.e. M= = 44
189
18. BASIC THERMODYNAMICS J2006/3/18
Activity 3B
TEST YOUR UNDERSTANDING BEFORE YOU CONTINUE WITH THE
NEXT INPUT…!
3.3 Two kilograms of a gas receive 200 kJ as heat at constant volume process. If
the temperature of the gas increases by 100 oC, determine the Cv of the
process.
3.4 A perfect gas is contained in a rigid vessel at 3 bar and 315 oC. The gas is
then cooled until the pressure falls to 1.5 bar. Calculate the heat rejected per
kg of gas.
Given:
M = 26 kg/kmol and γ = 1.26.
3.5 A mass of 0.18 kg gas is at a temperature of 15 oC and pressure 130 kN/m2.
If the gas has a value of Cv = 720 J/kg K, calculate the:
i. gas constant
ii. molecular weight
iii. specific heat at constant pressure
iv. specific heat ratio
19. BASIC THERMODYNAMICS J2006/3/19
Feedback To Activity 3B
3.3 From the question,
m = 2 kg
Q = 200 kJ
(T2 – T1) = 100 oC = 373 K
Q = mCv(T2 – T1)
Q 200
Cv = = = 0.268 kJ/kgK
m( T2 − T1 ) 2(373)
3.4 From the question,
P1 = 3 bar
T1 = 315 oC = 588 K
P2 = 1.5 bar
M = 26 kg/kmol
γ = 1.26
From equation 3.10,
R 8314
R= o = = 319.8 J/kg K
M 26
From equation 3.18,
R 319.8
Cv = = = 1230 J/kg K = 1.230 kJ/kg K
(γ − 1) 1.26 − 1
During the process, the volume remains constant (i.e. rigid vessel) for the
mass of gas present, and from equation 3.4,
20. BASIC THERMODYNAMICS J2006/3/20
P1V1 P2V2
=
T1 T2
Therefore since V1 = V2,
P 1.5
T2 = T1 2 = 588 x = 294 K
P1 3
Then from equation 3.12,
Heat rejected per kg gas, Q = Cv(T2 – T1)
= 1.230(588 – 294)
= 361.6 kJ/kg
3.5 From the question
m = 0.18 kg
T = 15 oC = 288 K
V = 0.17 m3
Cv = 720 J/kg K = 0.720 kJ/kg K
i. From equation 3.6,
PV = mRT
PV 130 x 0.17
R= = = 0.426 kJ/kgK
mT 0.18 x 288
ii. From equation 3.10,
R
R= o
M
R 8.3144
M = o = = 19.52 kg/kmol
R 0.426
iii. From equation 3.16,
R = Cp - C v
Cp = R + Cv = 0.426 + 0.720 = 1.146 kJ/kg K
iv. From equation 3.17,
C p 1.146
γ = = = 1.59
C v 0.720
21. BASIC THERMODYNAMICS J2006/3/21
SELF-ASSESSMENT
You are approaching success. Try all the questions in this self-assessment
section and check your answers with those given in the Feedback to Self-
Assessment on the next page. If you face any problem, discuss it with your lecturer.
Good luck.
1. 1 m3 of air at 8 bar and 120 oC is cooled at constant pressure process until the
temperature drops to 27 oC.
Given R = 0.287 kJ/kg K and Cp = 1.005 kJ/kg K, calculate the:
i. mass of air
ii. heat rejected in the process
iii. volume of the air after cooling.
2. A system undergoes a process in which 42 kJ of heat is rejected. If the
pressure is kept constant at 125 kN/m2 while the volume changes from
0.20 m3 to 0.006 m3, determine the work done and the change in internal
energy.
3. Heat is supplied to a gas in a rigid container.The mass of the container is 1 kg
and the volume of gas is 0.6 m3. 100 kJ is added as heat. If gas has
Cv = 0.7186 kJ/kg K during a process, determine the:
i. change in temperature
ii. change in internal energy
22. BASIC THERMODYNAMICS J2006/3/22
Feedback To Self-Assessment
Have you tried the questions????? If “YES”, check your answers now.
1. i. m = 7.093 kg
ii. Q = 663 kJ
iii. V2 = 0.763 m3
2. W = -24.25 kJ
(U2 – U1) = -17.75 kJ
3. i. (T2 – T1) = 139.2 K
ii. (U2 – U1) = 100 kJ
CONGRATULATIONS!!!!
…..May success be with
you always….