Water’s Phase Diagram

Source: P.W. Atkins, Physical Chemistry, 2 ed., 1978, p.193.

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

Thermodynamic Processes

molecular models

§ 19.5–19.7

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 HeatingSome internal energy becomes work

Source: Young and Freedman, Fig. 19.4a

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

Heat Capacity Ratio

= Cp/Cv

• > 1 always

• Useful for analyzing adiabatic processes (§19.8)

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.

Group Work

2. Give the formulas for W of each process.3. Give the formulas for Q of each process.

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

Otto Cycle

Source: Young and Freedman, Fig. 20.5