Water’s Phase Diagram

1. Water’s Phase Diagram Source: P.W. Atkins, Physical Chemistry, 2 ed., 1978, p.193.

2. The Final • Monday, 1:15–3:15 PM, here • About 50% old and 50% new stuff • 300 points (double other tests) • MC, essay, worked problems • Calculators permitted, probably unneeded

3. Thermodynamic Processes molecular models § 19.5–19.7

4. Named Path Types Adiabatic Noheat transfer • Q = 0 • DU = –W Examples: • Rapid expansion or compression (piston engine) • Large system (atmospheric parcels)

5. Named Path Types Isochoric Constant volume • W = 0 • DU = Q Examples: • Rigid containers • Engine spark • Bomb calorimetry

6. Named Path Types Isobaric Constant pressure • W = pDV Examples: • Open-air processes • Most lab chemistry

7. Named Path Types Isothermal Constant temperature Examples: • Slow processes (thermal equilibrium) • Thermostatted systems If an ideal gas: • DU = 0 , so • Q = W • constant pV

8. Named Path Types Free Expansion Expansion at zero pressure • W = 0 • Q = 0 • DU = 0 Absolutely irreversible If Ideal Gas: • DT = 0 • No work done on individual molecules

9. Free Expansion of Real Gases DT < 0 • expand against mutual attraction of molecules DU = 0 anyway • Potential energy gain from separation of molecules, so they slow down

10. CPS Question Water ice melting at 0 °C is an example of a(n) process. (Add correct answers together and enter the sum.) 1. adiabatic 2. isochoric 4. isothermal 8. isobaric 16. free expansion

11. CPS Question A hot-air balloon expanding as it rises is an example of a(n) process. (Add correct answers together and enter the sum.) 1. adiabatic 2. isochoric 4. isothermal 8. isobaric 16. free expansion

12. CPS Question The crew of Soyuz-11 died during re-entry shortly after a pressure seal failed at an altitude of 168 km. This disaster was an example of a(n) process. (Add correct answers together and enter the sum.) 1. adiabatic 2. isochoric 4. isothermal 8. isobaric 16. free expansion Source: Wikimedia Commons

13. Ideal Gases U= f(T) and nothing else! • Monatomic ideal gas U = 3/2 NkT • Diatomic ideal gas U = 5/2 NkT • etc. DU = nCvDT No intermolecular potentials

14. Constant-Volume Heating dU = dK + pdV Ktr = 3/2 NkT dKtr = 3/2 NkdT dV= 0 nCv = dU/dT = 3/2 Nk = 3/2 nR Cv = 3/2 R Cv of a monatomic ideal gas

15. CPS Question To raise the temperature of a mole of ideal from T1 to T2 at constant pressure requires the same temperature increase at constant volume. less heat than the same amount of heat as more heat than The processes cannot be compared.

16. Constant-Pressure Heating Some internal energy becomes work Source: Young and Freedman, Fig. 19.4a

17. Constant-Pressure Heating dU = dK + pdV Ktr = 3/2 NkT V = NkT/p nCv= dU/dT = dK/dT + dV/dT = 3/2 Nk + pNk/p = 5/2 Nk = 5/2 nR Cv= 5/2 R Cp of a monatomic ideal gas

18. Any Ideal Gas Cp = Cv + R • Cv is energy to increase molecular K • 1/2 kT/molecule = 1/2 RT/mole per mode • R is work to expand against constant p • pDV = pD(NkT/p) = NkDT = nRDT/mole No complication from intermolecular interactions

19. Heat Capacity Ratio g g = Cp/Cv • g > 1 always • Useful for analyzing adiabatic processes (§19.8)

20. Group Work • Qualitatively sketch a pV plot for each described process AB. • System is heated at constant pressure until volume doubles, then cooled at constant volume to the initial temperature. • System is heated at constant volume until its absolute temperature doubles, allowed to expand at constant temperature to twice its volume, then cooled at constant volume to the initial temperature. • System is allowed to expand into a vacuum (free expansion) to twice its volume. • Volume is gradually doubled while maintaining a constant temperature.

21. Group Work • Give the formulas for W of each process. • Give the formulas for Qof each process.

22. Example Problem 19.38 A cylinder contains 0.1 moles of an ideal monatomic gas initially at pressure 1.0  105 Pa and volume2.5  10–3 m3. • Find the initial temperature of the gas. • If the gas is allowed to expand to twice its initial volume, find the final temperature and pressure if the expansion is • isothermal • isobaric • adiabatic

23. Otto Cycle Source: Young and Freedman, Fig. 20.5