Thermodynamics and Statistical Mechanics

1. Thermodynamics and Statistical Mechanics First Law of Thermodynamics

2. Review of van der Waals Critical Values Thermo & Stat Mech - Spring 2006 Class 3

3. van der Waals Results Thermo & Stat Mech - Spring 2006 Class 3

4. van der Waals Results Thermo & Stat Mech - Spring 2006 Class 3

5. Configuration Work • đW = PdV • Gas, Liquid, Solid: Thermo & Stat Mech - Spring 2006 Class 3

6. Kinds of Processes Often, something is held constant. Examples: dV = 0 isochoric or isovolumic process dQ = 0 adiabatic process dP = 0 isobaric process dT = 0 isothermal process Thermo & Stat Mech - Spring 2006 Class 3

7. Work done by a gas đW = PdV For isochoric process dV = 0, so W = 0 For isobaric process dP = 0, so W = PDV Thermo & Stat Mech - Spring 2006 Class 3

8. Work done by a gas Thermo & Stat Mech - Spring 2006 Class 3

9. Work done by an ideal gas For isothermal process dT = 0, so T = constant. Thermo & Stat Mech - Spring 2006 Class 3

10. Isothermal Process Thermo & Stat Mech - Spring 2006 Class 3

11. Heat Capacity • Heat capacity measures the amount of heat that must be added to a system to increase its temperature by a given amount. Its definition: • where y is a property of the system that is kept constant as heat is added. Thermo & Stat Mech - Spring 2006 Class 3

12. Heat Capacity • Properties that are usually kept constant for a hydrostatic system are volume or pressure. Then, Thermo & Stat Mech - Spring 2006 Class 3

13. Heat Capacity • Clearly, the heat capacity depends on the size of the system under consideration. To get rid of that effect, and have a heat capacity that depends only on the properties of the substance being studied, two other quantities are defined: specific heat capacity, and molar heat capacity. Thermo & Stat Mech - Spring 2006 Class 3

14. Specific Heat Capacity • Specific heat capacity is the heat capacity per mass of the system. A lower case letter is used to represent the specific heat capacity. Then, if m is the mass of the system, Thermo & Stat Mech - Spring 2006 Class 3

15. Molar Heat Capacity • Molar heat capacity is the heat capacity per mole of the system. A lower case letter is used to represent the molar heat capacity. Then, if there are n moles in the system, Thermo & Stat Mech - Spring 2006 Class 3

16. Shorter Version Use heat per mass. Thermo & Stat Mech - Spring 2006 Class 3

17. cP – cV đq = du + Pdv where u(T,v) Thermo & Stat Mech - Spring 2006 Class 3

18. Constant Volume Thermo & Stat Mech - Spring 2006 Class 3

19. Constant Pressure Thermo & Stat Mech - Spring 2006 Class 3

20. Ideal Gas u is not a function of v. Thermo & Stat Mech - Spring 2006 Class 3

21. Adiabatic Process • For an ideal gas, and most real gasses, • đQ = dU + PdV • đQ = CVdT + PdV,. • Then, when đQ = 0, Thermo & Stat Mech - Spring 2006 Class 3

22. Adiabatic Process For an ideal gas, PV=nRT, so Thermo & Stat Mech - Spring 2006 Class 3

23. Adiabatic Process Thermo & Stat Mech - Spring 2006 Class 3

24. Adiabatic Process Thermo & Stat Mech - Spring 2006 Class 3

25. Adiabatic Process Thermo & Stat Mech - Spring 2006 Class 3

26. Adiabatic Process Thermo & Stat Mech - Spring 2006 Class 3

27. gfor “Ideal Gasses” Thermo & Stat Mech - Spring 2006 Class 3