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 100C if the condenser is at 20C.
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 1000C (a) at constant pressure; (b) at constant volume. Given:
5. Calculate the entropy changewhen 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 K1 mol1 and the atomic weight of argon is 39.948 g mol1.
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 (10C) to water (+10C) at 1 atm. Assume that all relevant heat capacities are constant over this range of temperatures, and that Cp,m(ice) = 37 J K1 mol1, Cp,m(water) = 76 J K1 mol1; and Hfusion = 6000 J mol1 (at 0C).
10. The normal melting point of tin is 231.9C, 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 231.9C.
(b) Calculate the entropy change when tin, supercooled 55C 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 K1 mol1; S(O2, g) = 205.14 J K1 mol1;
S(CH3CHO, g) = 159.8 J K1 mol1.
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 K1 mol1. 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 59.2C.
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