Solved: A vapor-compression air conditioning system

Chapter 10, Problem 26P

(choose chapter or problem)

A vapor-compression air conditioning system operates at steady state as shown in Fig. P10.26. The system maintains a cool region at \(60^{\circ} \mathrm{F}\) and discharges energy by heat transfer to the surroundings at \(90^{\circ} \mathrm{F}\). Refrigerant 134a enters the compressor as a saturated vapor at \(40^{\circ} \mathrm{F}\) and is compressed adiabatically to \(160 \mathrm{\ lbf} / \mathrm{in.}^{2}\) The isentropic compressor efficiency is 80%. Refrigerant exits the condenser as a saturated liquid at \(160 \mathrm{\ lbf} / \mathrm{in.}^{2}\) The mass flow rate of the refrigerant is 0.15 lb/s. Kinetic and potential energy changes are negligible as are changes in pressure for flow through the evaporator and condenser. Determine

(a) the power required by the compressor, in Btu/s.

(b) the coefficient of performance.

(c) the rates of exergy destruction in the compressor and expansion valve, each in Btu/s.

(d) the rates of exergy destruction and exergy transfer accompanying heat transfer, each in Btu/s, for a control volume comprising the evaporator and a portion of the cool region such that heat transfer takes place at \(T_{\mathrm{C}}=520^{\circ} \mathrm{R}\left(60^{\circ} \mathrm{F}\right)\).

(e) the rates of exergy destruction and exergy transfer accompanying heat transfer, each in Btu/s, for a control volume enclosing the condenser and a portion of the surroundings such that heat transfer takes place at \(T_{\mathrm{H}}=550^{\circ} \mathrm{R}\left(90^{\circ} \mathrm{F}\right)\).

Let \(T_{0}=550^{\circ} \mathrm{R}\).