Balance on Overall System

By considering the overall balance, the only variables that are crossing the boundary are work, Qc, and Qh. This is a closed system--A mass balance will not tell us anything since there is neither accumulation nor a flow in/out of our envelope. So we take an energy balance.

 Energy balance:

 But we can ignore potential and kinetic energies

 Since there is no mass flow into the system, the Hm term drops out.

 Since the process is steady state, dU/dt=0.

 0=Qc+QH-Ws
Ws=Qc+QH
Note: the Q and W should have dots over them to indicate they are rates. However, it's tedious to add that in HTML.

We are given Qc from the problem. That leaves two unknowns: QH and Ws. We can find out more about the unknowns by drawing other mass/energy balances.

  1. Overall
  2. Evaporator
  3. Compressor
  4. Valve

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