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Chapter 17 Heat & The First Law of Thermodynamics

Chapter 17 Heat & The First Law of Thermodynamics. 1. P. . 2. V. Thermal processes. Breaking of equilibrium. changing of state. If the process is extremely slow, or quasi-statical. system always at equilibrium state in the process. Shown in PV diagram. Point: equilibrium state.

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Chapter 17 Heat & The First Law of Thermodynamics

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  1. Chapter 17 Heat & The First Law of Thermodynamics

  2. 1 P  2 V Thermal processes Breaking of equilibrium changing of state If the process is extremely slow, or quasi-statical system always at equilibrium state in the process Shown in PV diagram Point: equilibrium state Curve: quasi-statical process 2

  3. Heat as energy transfer Heat is not a fluid substance and not even a form of energy calorie: amount of heat to raise 1g water by 1℃ Joule’s theory & mechanical equivalent of heat Heat is energy that transferred from one body to another because of a difference in temperature

  4. Internal energy The sum total of all the energy of all molecules —— thermal energy / internal energy Temperature, heat and internal energy Internal energy of monatomic (1-atom) ideal gases: n-atoms molecule, real gases, liquids & solids 4

  5. The first law of thermodynamics The change in internal energy of a closed system, will be equal to the heat added to the system minus the work done by the system. This is the first law of thermodynamics where Q is the net heat added to the system and W is the net work done by the system U is a state variable, but Q and W are not 5

  6. dx . . . . . . . . . S P A P B V Calculating the work Consider the gas in a cylinder with a piston Work done by the gas to move the piston dx: dV For a finite change in volume from VA to VB : 6

  7. P b c a d V Heat in process Example1: In process abc, 800J heat flow into the system, and 500J work done by system. In process cda, 300J work done to system, What’s the heat? Solution: First law ΔU is different! 7

  8. VB VA A B A P P C VB VA B V V 3 simple processes Isothermal process: ( constant T ) Isobaric process: ( constant P ) Isochoric process: ( constant V ) 8

  9. A P isothermal C B adiabatic V Adiabatic process Adiabatic process: ( Q = 0 ) No heat is allowed to flow into or out of system Well insulated or process happens too quickly Adiabatic curve is steeper than an isothermal curve Temperature decreases as well 9

  10. P(105Pa) c 3 b a 1 o 4V(l) 2 Cyclic process Example2: An monatomic (1-atom) gas system goes through processes ab, bc, ca. Determine Q, W and ΔUin each process. Solution: Inprocess ab: 10

  11. P(105Pa) c 3 b a 1 o 4V(l) 2 In process bc: In process ca: Q, W and ΔU in process abca? 11

  12. Specific heat Heat transfer in → temperature rises c is called the specific heat of material For water at 15℃ and 1atm: one of the highest specific heats of all substance c as constant (P407, T17-1) except for gases 12

  13. Molar specific heat c for gases depend on how the process goes on Heat required to raise 1mol gas by 1℃ (conditions) Isochoric(constant V)CV: Isobaric(constant P)CP: For CV of monatomic (1-atom) ideal gas, W = 0 13

  14. Degrees of freedom What is CV of diatomic or triatomic gas? Degrees of freedom: number of independent ways molecules can possess energy. monatomic: i = 3 diatomic: i = 5 triatomic: i = 6 14

  15. Equipartition of energy Principle of Equipartition of energy: Energy is shared equally among the active degrees of freedom, each degree of freedom of a molecule has on the average energy equal to kT/2. Average energy of a molecule: Internal energy: 15

  16. Active DoF & CV CV of diatomic gases by experiments: Active degrees of freedom at different T Translational motion; Rotation; Vibration i = 3, 5, 6 for 1, 2, n-atoms Isochoric molar specific heat: 16

  17. Energy in gas system Example3: Determine the internal energy of (a) 2lO2 gas system at 1atm; (b) same system at same T but O2 is dissociated to 2O. Solution: (a) Active degrees of freedom: i = 5 (b) O2dissociate to 2O: i = 3 17

  18. Isobaric molar specific heat CP In an isobaric process (constant P): Isobaric molar specific heat: Adiabatic coefficient 18

  19. A P isothermal C B adiabatic V Adiabatic equation Equation for adiabatic curve? Equation of quasi-static adiabatic process 19

  20. 2) Why 3) Monatomic / diatomic / triatomic gas A P P B C adiabatic D V V Some questions 1) Isothermal / adiabatic C ? 4) Process AC is adiabatic then does heat flow inor out in process AB and AD? 20

  21. B A P P isothermal ? C V 3V V Isobaric & adiabatic Example4: N2 system compresses isobarically in process AB, and then expands adiabatically to C. (a) Q in process AB; (b) PC ; (c) W in process BC. Solution: (a) (b) (c) 21

  22. PA , TA , V V Free expansion Example5: 2 well-insulated container. A is filled with gas and B is empty. Open the valve, there is an adiabatic free expansion. What is the final P, T ? Solution: No heat flows in or out → Q = 0 No work is done → W = 0 U doesn’t change in free expansion! Not quasi-static, no PV diagram 22

  23. *Heat transfer Conduction: Convection: Radiation: 23

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