Problem # p017

Entropy, heat transfer between two solids

We have a solid piece of metal with a total mass of 4 kg. Initially, 1/4 thereof is at a temperature T1 = 200 K, while the other 3/4 is at the temperature T2 = 300 K.
The entire piece of metal is perfectly insulated against the surrounding as heat is flowing from the hot to the cold part until the entire piece reaches an equilibrium temperature.
  1. What is this final temperature of the piece of metal assuming that it has a temperature-independent specific heat ?

  2. Determine the change in entropy of the 1/4 piece of metal (mass = 1 kg) during the heat transfer process assuming that it has a specific heat c= 2 kJ/(kg K). The change in entropy of a solid body of mass mbody can be determined according to :

    Sb - Sa = mbody c ln(Tb/Ta)

    when its temperature changes from Ta to Tb.

  3. Determine the change in entropy of the 3/4 piece of metal (3 kg).

  4. What is the change in entropy of the entire 4 kg of mass during the heat transfer process ?