Question

Two flows of air both at 200 kPa, one has 1 kg/s at 400 K and the other has 2 kg/s at 290 K. The two lines exchange energy through a number of ideal heat engines taking energy from the hot line and rejecting it to the colder line. The two flows then leave at the same temperature. Assume the whole setup is reversible and find the exit temperature and the total power out of the heat engines. 

Answer 1

C.V. Total setup 

Assume the exit flow has the same pressure as the inlet flow then the pressure part of the entropy cancels out and we have 

Exit same T, P => h₃ = h₄ = he; s₃ = s₄ = s_e

Note: The solution using constant heat capacity writes the entropy  the pressure terms cancel out so we get