Calculate the change in entropy for the system for each of the following cases. Explain the sign that you obtain by a physical argument.

(a) A gas undergoes a reversible, adiabatic expansion from an initial state at 500 K, 1 MPa, and 8.314 L to a fi nal volume of 16.628 L.

(b) One mole of methane vapor is condensed at its boiling point, 111 K; Δhvap 5 8.2[kJ/mol]

(c) One mole of liquid water is cooled from 100°C to 0°C. Take the average heat capacity of water to be 4.2 JK-1g-1.

(d) Two blocks of the same metal with equal mass are at different temperatures, 200°C and 100°C. These blocks are brought together and allowed to come to the same temperature. Assume that these blocks are isolated from their surroundings. The average heat capacity of the metal is 24 J K-1 mol-1.