This problem is simply a reminder of the thermodynamic, as opposed to statistical, definition of entropy. However, to keep you aware of the connection between the thermodynamic and statistical definitions, all the entropies appearing in this particular homework problem are the dimensionless entropy s.

a) If J of energy is added to a huge object at °C (assume that the object is so big that you can ignore the change of its temperature) how much does its entropy change?

ds =

b) How much does the entropy of a huge object at °C change if xxxx J of energy is removed?

ds =

c) Two cups of water are at xx °C and xx °C, respectively. In order for them to both reach xx°C, xxxx J must flow from the hot cup to the cold one. Assume that the heat capacity C is constant. What is the heat capacity of each cup? (Don't worry about constant pressure vs constant volume, which isn't important for liquids.)

C = J/K

d) What is the entropy change of the cold cup as it is heated to xx °C ?

ds =

e) How much does the total entropy of the two cups change during the process in which their temperature equilibrates at xx°C?

ds =

f) The two cups would end up at the same final T, xx°C, if they were allowed to equilibrate with a reservoir at that T. How much would the Helmholtz free-energy, F, of the two-cup system change in that equilibration process in that environment?

DF = J

Comment
The point of the problem is that although DQ₁ = -DQ₂,    DS₁ ≠ -DS₂. That's why heat preferentially flows one way. In reaching equilibrium, total S increases and free-energy is lowered.