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:
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, D U, D H, and D 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 D 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 DH and DS 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 DHfusion = 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-1. The heat capacities are 28.1 J K-1 mol-1 for the solid, and 30.2 J K-1 mol-1 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
Note: S° (CH3CHO, g) = 250.3 J K-1 mol-1; S° (O2, g) = 205.14 J K-1 mol-1; S° (CH3COOH, l) = 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, , where Sm is the absolute molar entropy.
14. The molar constant-pressure heat capacity of a certain solid at 10 K is 0.43 J K-1 mol-1. Calculate its molar entropy at 10 K relative to its molar entropy at zero kelvin.
15. Using Trouton's Rule, predict the standard molar enthalpy of vaporization of bromine given that it boils at 59.2° C.