Chapter 15=Thermodynamics

1. 1 CHAPTER 15: Thermodynamics

2. 15.1 Learning Outcome Remarks : Keypoint : Distinguish between thermodynamic work done on the system and work done by the system. State and use first law of thermodynamics , PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.1

3. 3 15.1.1 Signs for heat, Q and work, W Sign convention for heat, Q : Q = positive value Q = negative value Heat flow into the system Heat flow out of the system 3 Surroundings (environment) System (a) Surroundings (environment) System (b) PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.1

4. 4 Sign convention for work, W : W = positive value W = negative value Work done by the system Work done on the system Surroundings (environment) System Surroundings (environment) System PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.1

5. 5 Surroundings (environment) System Surroundings (environment) System Q = positive value Q = negative value W = positive value W = negative value PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.1

6. 6 Air Compression Air Expansion Air Initially Motion of piston Motion of piston Work done by gas (Expansion) When the air is expanded , the molecule loses kinetic energy and does positive work on piston. Work done on gas(Compression ) When the air is compressed , the molecule gains kinetic energy and does negative work on piston. PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.1

7. 15.1.2 Work done in the thermodynamics system 7 Consider the infinitesimal work done by the gas (system) during the small expansion, dx in a cylinder with a movable piston as shown in Figure 15.3. Suppose that the cylinder has a cross sectional area, A and the pressure exerted by the gas (system) at the piston face is P . Gas A A dx Initial Final Figure 15.3 PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.1

8. 15.1.3 First law of thermodynamics It states that : “ The heat ( Q ) supplied to a system is equal to the increase in the internal energy (  U ) of the system plus the work done ( W ) by the system on its surroundings .” where and (15.2) For infinitesimal change in the energy, PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.1

9. The first law of thermodynamics is a generalization of the principle of conservation of energy to include energy transfer through heat as well as mechanical work. The change in the internal energy (  U ) of a system during any thermodynamic process is independent of path . For example a thermodynamics system goes from state 1 to state 2 as shown in Figure 16.5. Figure 15.4 PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.1

10. 10 A vessel contains an ideal gas in condition A, as shown in Figure 16.6. When the condition of the gas changes from A to that of B, the gas system undergoes a heat transfer of 10.5 kJ. When the gas in condition B changes to condition C, there is a heat transfer of 3.2 kJ. Calculate a. the work done in the process ABC, b. the change in the internal energy of the gas in the process ABC, c. the work done in the process ADC, d. the total amount of heat transferred in the process ADC. Example 1 : Figure 15.6 PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.1

11. Calculate: a. the work done in the process ABC , b. the change in the internal energy of the gas in the process ABC , c. the work done in the process ADC , d. the total amount of heat transferred in the process ADC. a. The work done in the process ABC is given by : but PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.1 W = P.dV

12. b. By applying the 1 st law of thermodynamics for ABC, thus Calculate: a. the work done in the process ABC , b. the change in the internal energy of the gas in the process ABC , c. the work done in the process ADC , d. the total amount of heat transferred in the process ADC. PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.1

13. c. The work done in the process ADC is given by but Calculate: a. the work done in the process ABC , b. the change in the internal energy of the gas in the process ABC , c. the work done in the process ADC , d. the total amount of heat transferred in the process ADC. PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.1

14. d. By applying the 1 st law of thermodynamics for ADC, thus and Calculate: a. the work done in the process ABC , b. the change in the internal energy of the gas in the process ABC , c. the work done in the process ADC , d. the total amount of heat transferred in the process ADC. PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.1

15. 15 Thermodynamics processes (1 hours) Remarks : Keypoint : Define the following thermodynamics processes: i ) Isothermal, Δ U = 0 ii) Isovolumetric , W = 0 iii) Isobaric, Δ P = Adiabatic, Q = 0 Sketch P  V graph to distinguish between isothermal process and adiabatic process. 15.2 Learning Outcome PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.2

16. There are four specific kinds of thermodynamic processes. It is : Isothermal process Isovolumetric @ Isochoric process Isobaric process Adiabatic process PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.2

17. 15.2.1 Isothermal process is defined as a process that occurs at constant temperature . Thus, Isothermal changes When a gas expands or compresses isothermally (constant temperature) thus (16.3) Equation (16.3) can be expressed as If the gas expand isothermally , thus V 2 >V 1 If the gas compress isothermally , thus V 2 <V 1 W = positive W = negative PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.2

18. is defined as a process that occurs without heat transfer into or out of a system i.e. For example, the compression stroke in an internal combustion engine is an approximately adiabatic process. thus Notes : For Adiabatic expansion ( V 2 > V 1 ), W = positive value but  U =negative value hence the internal energy of the system decreases . For Adiabatic compression ( V 2 < V 1 ), W = negative value but  U = positive value hence the internal energy of the system increases . 15.2.2 Adiabatic Process PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.2

19. 15.2.3 Iso volumetric @ Isochoric is defined as a process that occurs at constant volume i.e. In an isochoric process, all the energy added as heat remains in the system as an increase in the internal energy thus the temperature of the system increases . For example, heating a gas in a closed constant volume container is an isochoric process. thus 15.2.4 Iso bar ic is defined as a process that occurs at constant pressure i.e. For example, boiling water at constant pressure is an isobaric process. thus and PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.2

20. 15.2.4 Pressure-Volume diagram (graph) for thermodynamic processes Figure 15.5 shows a P  V diagram for each thermodynamic process for a constant amount of an ideal gas. Figure 16.8 Path A B Isothermal process ( T B= T A ) Path A C Path A D Path A E Adiabatic process ( T C< T A ) Isochoric process ( T D< T A ) Isobaric process ( T E> T A ) PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.2

21. From the Figure 15.5, For comparison between the isothermal ( A  B ) and adiabatic expansions ( A  C ): The temperature fall ( T C < T B ) which accompanies the adiabatic expansion results in a lower final pressure than that produced by the isothermal expansion ( P C < P B ) . The area under the isothermal is greater than that under the adiabatic , i.e. more work is done by the isothermal expansion than by the adiabatic expansion. The adiabatic through any point is steeper than the isothermal through that point. Figure 15.5 shows a P  V diagram for each thermodynamic process for a constant amount of an ideal gas. PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.2

22. Air is contained in a cylinder by a frictionless gas-tight piston . a. Calculate the work done by the air as it expands from a volume of 0.015 m 3 to a volume of 0.027 m 3 at a constant pressure of 2.0  10 5 Pa . b. Determine the final pressure of the air if it starts from the same initial conditions as in (a) and expanding by the same amount, the change occurs isothermally. Example 3 : PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.2

23. Air is contained in a cylinder by a frictionless gas-tight piston . a. Calculate the work done by the air as it expands from a volume of 0.015 m 3 to a volume of 0.027 m 3 at a constant pressure of 2.0  10 5 Pa . b . Determine the final pressure of the air if it starts from the same initial conditions as in (a) and expanding by the same amount, the change occurs isothermally Example 3 : Solution : a. Given The work done by the air is: PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.2

24. Example 3 : b. The final pressure for the isothermal process is PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.2 Air is contained in a cylinder by a frictionless gas-tight piston . a. Calculate the work done by the air as it expands from a volume of 0.015 m 3 to a volume of 0.027 m 3 at a constant pressure of 2.0  10 5 Pa . b . Determine the final pressure of the air if it starts from the same initial conditions as in (a) and expanding by the same amount, the change occurs isothermally

25. 25 Remarks : Keypoint : Derive expression for work, W = Determine work from the area under p-V graph. Derive the equation of work done in isothermal, isovolumetric and isobaric processes. Calculate work done in :- isothermal process and use isobaric process, use isovolumetric process, use Thermodynamics work (4 hour) PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3 15.3 Learning Outcome

26. 15.3.1 Work done in the thermodynamics system 26 Gas A A dx Initial Final Figure 15.6 The work, dW done by the gas is given by In a finite change of volume from V 1 to V 2 , where and and (15.3) where PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3

27. 15.3.2 Work done in the thermodynamics system 27 For a change in volume at constant pressure, P Work done at constant pressure For any process in the system which the volume is constant (no change in volume), the work done is Work done at constant volume PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3

28. Area under graph = work done by gas Compression Area under graph = work done on gas Expansion When a gas is expanded from V1 to V2 Work done by gas, When a gas is compressed from V1=> V2 Work done on gas, Since V2 < V1 the value of work done is (-) PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3

29. From the equation of state for an ideal gas, Therefore the work done in the isothermal process which change of volume from V 1 to V 2 , is given then (15.9) PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3 15.3.3 Work done in Isothermal Process

30. For isothermal process, the temperature of the system remains unchanged, thus (15.10) The equation (16.9) can be expressed as By applying the 1 st law of Thermodynamics,thus and PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3 15.3.3 Work done in Isothermal Process

31. 15.3.3 Work done in iso bar ic process The work done during the isobaric process which change of volume from V 1 to V 2 is given by and OR (15.10) 15.3.3 Work done in isovol umetric process Since the volume of the system in isovolumetric process remains unchanged, thus Therefore the work done in the isovolumetric process is (15.11) PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3

32. A quantity of ideal gas whose ratio of molar heat capacities is  5/3 has a temperature of 300 K, volume of 64  10 3 m 3 and pressure of 243 kPa . It is made to undergo the following three changes in order: 1 : adiabatic compression to a volume 27  10 3 m 3 , 2 : isothermal expansion to 64  10 3 m 3 , 3 : a return to its original state. Example 4 : a. Describe the process 3. b. Sketch and label a graph of pressure against volume for the changes described. a. Process 3 is a process at constant volume known as isovolumetric (isochoric) . b. The graph of gas pressure ( P ) against gas volume ( V ) for the changes described is sh own in Figure 15.7. Process 2 Process 3 Process 1 Figure 15.7 PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3

33. A vessel of volume 8.00  10 3 m 3 contains an ideal gas at a pressure of 1.14  10 5 Pa. A stopcock in the vessel is opened and the gas expands adiabatically, expelling some of its original mass until its pressure is equal to that outside the vessel (1.01  10 5 Pa). The stopcock is then closed and the vessel is allowed to stand until the temperature returns to its original value. In this equilibrium state, the pressure is 1.06  10 5 Pa. Explain why there was a temperature change as a result of the adiabatic expansion? Example 5 : Solution : Adiabatic expansion Isochoric process Initial Final PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3

34. Solution : When the gas expands adiabatically, it does positive work . Thus The internal energy of the gas is reduced to provide the necessary energy to do work. Since the internal energy is proportional to the absolute temperature hence the temperature decreases and resulting a temperature change. and PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3 A vessel of volume 8.00  10 3 m 3 contains an ideal gas at a pressure of 1.14  10 5 Pa. A stopcock in the vessel is opened and the gas expands adiabatically, expelling some of its original mass until its pressure is equal to that outside the vessel (1.01  10 5 Pa). The stopcock is then closed and the vessel is allowed to stand until the temperature returns to its original value. In this equilibrium state, the pressure is 1.06  10 5 Pa. Explain why there was a temperature change as a result of the adiabatic expansion? Example 5 :

35. a. Write an expression representing i . the 1 st law of thermodynamics and state the meaning of all the symbols. ii. the work done by an ideal gas at variable pressure. [3 marks] b. Sketch a graph of pressure P versus volume V of 1 mole of ideal gas. Label and show clearly the four thermodynamics process. [ 5 marks] c. A monatomic ideal gas at pressure P and volume V is compressed isothermally until its new pressure is 3 P . The gas is then allowed to expand adiabatically until its new volume is 9 V . If P , V and  for the gas is 1.2  10 5 Pa,1.0  10 2 m 3 and 5/3 respectively, calculate i . the final pressure of the gas. ii. the work done on the gas during isothermal compression. ( Examination Question Intake 2003/2004) [ 7 marks] Example 6 : PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3

36. a. Write an expression representing i . the 1 st law of thermodynamics and state the meaning of all the symbols. ii. the work done by an ideal gas at variable pressure. [3 marks] Example 6 : Solution : a. i . 1 st law of thermodynamics: ii. Work done at variable pressure: where OR PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3

37. Example 6 : Solution : b. Sketch a graph of pressure P versus volume V of 1 mole of ideal gas. Label and show clearly the four thermodynamics process. [5 marks] b . PV diagram below represents four thermodynamic processes: Isobaric process Isochoric process Isothermal process adiabatic process PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3

38. Example 6 : Solution : c. A monatomic ideal gas at pressure P and volume V is compressed isothermally until its new pressure is 3 P . The gas is then allowed to expand adiabatically until its new volume is 9 V . If P , V and  for the gas is 1.2  10 5 Pa,1.0  10 2 m 3 and 5/3 respectively, calculate i . the work done on the gas during isothermal compression. [7 marks] and i . The work done during the isothermal compression is PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS Subtopic: 15.3

39. THE END… Good luck For Second Semester Examination PHYSICS DF 025 CHAPTER 15 :THERMODYNAMICS PDT STUDENTS, DO YOUR BEST, BEAT THE REST PHYSICS ‘A’, INSYAALLAH ...