Question

a) Consider an ideal gas in a container with a frictionless piston. The gas is isothermally compressed at 26 degrees

Celsius as 940 Joules of work is done on it. Determine the resulting change in entropy of the gas, the change in entropy

of the environment and the universe. (assume the temperature of the environment is a constant 22 Celsius)

b) 20 grams of ice at 0 Celsius melt while being left at room temperature of 22 Celsius. After melting, its temperature

rises to 22 Celsius. Determine the resulting change in entropy of the gas, the change in entropy of the environment and

the universe.

c) If you are rolling a pair of dice, what is the entropy of the mactrostate 2, macrostate 5, and macrostate 7? Imagine a

pair of dice starts with a macrostate of 2 and then you roll it 5 times and get the following results: 5, 9, 7, 3, 8. What is

the resulting change of the entropy of the universe for each roll and for all 5 rolls put together?

Answers should be:

a) ΔSgas = -3.14 Joule/K, ΔSenvironment = +3.18 Joule/K, ΔSuniverse = +.04 Joule/K

b) ΔSice = +30.9 Joule/K, ΔSenvironment = -28.8 Joule/K, ΔSuniverse = +2.1 Joule/K

c) S2 = 0, S5 = kln4, S7 = kln6

ΔS1 = kln4, ΔS2 = 0, ΔS3 = kln(1.5), ΔS4 = -kln3, ΔS5 = kln(2.5), ΔStot = kln5

Answer 1