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
Named Path Types
No heat transfer• Q = 0• U = –W
Examples:• Rapid expansion or compression (piston
engine)• Large system (atmospheric parcels)
Adiabatic
Named Path Types
Constant volume• W = 0• U = Q
Examples:• Rigid containers • Engine spark• Bomb calorimetry
Isochoric
Named Path Types
Constant pressure• W = pVExamples:• Open-air processes• Most lab chemistry
Isobaric
Named Path Types
Constant temperature
Examples:• Slow processes (thermal equilibrium)• Thermostatted systemsIf an ideal gas:• U = 0 , so• Q = W• constant pV
Isothermal
Named Path Types
Expansion at zero pressure• W = 0• Q = 0• U = 0
Absolutely irreversible
If Ideal Gas:• T = 0• No work done on individual molecules
Free Expansion
Free Expansion of Real Gases
T < 0
• expand against mutual attraction of molecules
U = 0 anyway
• Potential energy gain from separation of molecules, so they slow down
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
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
CPS QuestionThe 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 expansionSource: Wikimedia Commons
Ideal Gases
U = f(T) and nothing else!• Monatomic ideal gas U = 3/2 NkT• Diatomic ideal gas U = 5/2 NkT• etc.
U = nCvT
No intermolecular potentials
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
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.A. less heat than
B. the same amount of heat as
C. more heat than
D. The processes cannot be compared.
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
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 pV = p(NkT/p) = NkT = nRT/mole
No complication from intermolecular interactions
Group Work
1. Qualitatively sketch a pV plot for each described process AB.
a) System is heated at constant pressure until volume doubles, then cooled at constant volume to the initial temperature.
b) 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.
c) System is allowed to expand into a vacuum (free expansion) to twice its volume.
d) Volume is gradually doubled while maintaining a constant temperature.
Example Problem 19.38
A cylinder contains 0.1 moles of an ideal monatomic gas initially at pressure 1.0 105 Pa and volume 2.5 10–3 m3.a) Find the initial temperature of the gas.b) If the gas is allowed to expand to twice its
initial volume, find the final temperature and pressure if the expansion is
i. isothermal ii. isobaric iii. adiabatic