1. The work of Reversible Adiabatic change for an ideal gas.

3. What if the final temperature is not available.

6. Work done in an Isothermal Expansion/compression of an ideal gas.
Free expansion
pex=0, w=0
(b) Expansion against constant pressure
(Expansion of a gas formed in a chemical reaction)
w =P2(V2-V1)
© Reversible isothermal Expansion/contr

7. Internal Energy Change in an Isothermal Expansion/compression of an ideal Gas

8. Thermodynamics changes in an adiabatic process of an ideal gas.

10. Thermodynamic changes for a real gas
Free expansion
pex=0, w=0
(b) Expansion against constant pressure
w =P2(V2-V1)
© Reversible isothermal Expansion/contr

11. Internal energy change in an isothermal process for a real gas.

12. Unfamiliar Quantities
Quantities that can be recognized, interpreted, or measured.

13. Change of volume with temperature.
EXPANSION COEFFICIENT ()
Thermal expansion is also used in mechanical applications to fit parts over one another.
There exist some alloys with a very small CTE, used in applications that demand very small changes in physical dimension over a range of temperatures. One of these is invar 36, with a coefficient in the range. These alloys are useful in aerospace applications where wide temperature swings may occur.

14. Change of volume with Pressure
ISOTHERMAL COMPRESSIBILITY (T)
Oxygen compresses more than helium. Therefore, if two cylinders with the same internal volume are filled to the same pressure, one with oxygen and the other with helium, the oxygen cylinder will hold more cubic feet of gas than the helium cylinder.
Change of pressure with Temperature

15. Test of a state Function
Change of internal energy with Volume
Test of a state Function
(e.g. p=f(V,T)

18. Internal energy change in an isothermal process for a real gas.

19. Internal energy change in an adiabatic process for a real gas.

20. Enthalpy changes in a thermodynamic Processes.

21. Changes in enthalpy with pressure

23. Changes in Internal energy with temperature at constant pressure

24. H P T

25. How to impose the constraint of constant enthalpy.
pi,,Vi,Ti
pf,Vf,Tf

26. For an ideal gas,
Real gases have non-zero Joule-Thompson coefficient. Since p is always –ve in a Joule Thompson experiment, a positive  corresponds to cooling on expansion, a negative  , to warming.

28. The sign of  depends on conditions
The sign of  depends on conditions.The temperature corresponding to the boundary at a given pressure is the ‘inversion temperature’ of the gas at that pressure.

30. Changes in enthalpy with temperature at constant volume.

32. Relation between Cp and CV