CHEM 341. Fall 2000. Next PS Previous PS Answers PS#4.doc (Word 97)
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: C_{p,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 V_{1} to V_{2} 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 C_{p,m}(ice) = 37 J K^{1} mol^{1}, C_{p,m}(water) = 76 J K^{1} mol^{1}; and DH_{fusion} = 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° (CH_{3}CHO, g) = 250.3 J K^{1} mol^{1}; S° (O_{2}, g) = 205.14 J K^{1} mol^{1}; S° (CH_{3}COOH, l) = 159.8 J K^{1} mol^{1}.
The Debye Law 13. Prove that at any temperature for which the Debye Law (C_{v,m} = aT^{3}) is obeyed, , where S_{m} is the absolute molar entropy. 14. The molar constantpressure 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. 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. PLEASE NOTE

