CHEM 341. Fall 2000. Problem Set #4.
Carnot Heat Engine
1. What is the maximum work that can be obtained from 100 J of heat supplied to a water
boiler at 100C if the condenser is at 20C.
2. Draw a diagram of a Carnot cycle on a T vs. S plot.
Entropy Changes for Adiabatic, Isothermal, Isobaric, or Isochoric Processes
3. The pressure of a mole of perfect gas is increased from 1 bar to 10 bar at constant
temperature. What is the change in entropy?
4. Calculate the increase in entropy of nitrogen when it is heated from 25 to 1000C (a) at
constant pressure; (b) at constant volume. Given:
C p  26.9835  5.9622  10 3 T  3.377  10 7 T 2
5. Calculate the entropy change when 100 g of argon is heated and compressed from 300
K, 1.0 atm, to 900 K, 17 atm, assuming ideal gas behavior. Note: Cp,m = 20.93 J K1 mol1 and
the atomic weight of argon is 39.948 g mol1.
6. One mole of an ideal, monatomic gas undergoes an adiabatic expansion from 1.15 L to
4.65 L starting at 400 K. Calculate the final temperature, q, w, U, H, and S if the process is
(a) reversible; (b) irreversible into a vacuum (Joule expansion).
7. One mole of an ideal, monatomic gas undergoes the following sequence of steps, all
reversible, starting at 400 K, 1 bar.
(a) Expanded adiabatically until its volume is doubled.
(b) Heated at constant volume until the temperature returns to 400 K.
(c) Pressure is adjusted isothermally until it is 1 bar.
Calculate S for each step and for the entire sequence.
8. Derive the expression for the entropy change of a van der Waals gas that expands from
a volume of V1 to V2 at constant temperature.
Entropy Changes for Reversible and Irreversible (e.g. supercooling) Phase Changes
9. Calculate H and S for heating ice (10C) to water (+10C) at 1 atm. Assume that
all relevant heat capacities are constant over this range of temperatures, and that Cp,m(ice) = 37 J
K1 mol1, Cp,m(water) = 76 J K1 mol1; and Hfusion = 6000 J mol1 (at 0C).
10. The normal melting point of tin is 231.9C, with a heat of fusion of 7070 J mol. The
heat capacities are 28.1 J K mol for the solid, and 30.2 J K mol for the liquid.
(a) Calculate the change in entropy when tin melts at 231.9C.
(b) Calculate the entropy change when tin, supercooled 55C below its normal melting
temperature, is frozen.
Entropy Changes for Mixing of Ideal Gases
11. Calculate the entropy change when 3 moles of ideal gas #1 are mixed with 4 moles of
ideal gas #2 at constant T, P.
Entropy Changes for Chemical Reactions
12. Calculate the standard reaction entropy at 298 K of
2CH 3CHOg   O2 g   2CH 3COOH l 
Note: S(CH3CHO, g) = 250.3 J K1 mol1; S(O2, g) = 205.14 J K1 mol1;
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CHEM 341. Fall 2000. Problem Set #4.
S(CH3CHO, g) = 159.8 J K1 mol1.
The Debye Law
13. Prove that at any temperature for which the Debye Law (Cv,m = aT3) is obeyed,
C v,m
, where Sm is the absolute molar entropy.
Sm 
3
14. The molar constant-pressure heat capacity of a certain solid at 10 K is 0.43 J K1
1

mol . Calculate its molar entropy at 10 K relative to its molar entropy at zero kelvin.
Trouton's Rule
15. Using Trouton's Rule, predict the standard molar enthalpy of vaporization of bromine
given that it boils at 59.2C.
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