A small vapor-compression refrigeration unit is to be built into a recreational

Question

A small vapor-compression refrigeration unit is to be built into a recreational vehicle and is designed to operate on a 12-volt electrical system. The refrigerator has a cooling capacity of 500 W and uses R-134a. The refrigerant enters the compressor as a saturated vapor and leaves at 1600 kPa, 100oC. The evaporator and condenser are constant pressure devices. The refrigerant leaves the condenser as a saturated liquid and the evaporator pressure is 400 kPa. Determine the following:
a) the mass flow rate of the refrigerant (in kg/s),
b) the rate at which heat is added to the environment of the recreational vehicle,
c) the power required to operate the compressor,
d) the COP of the cycle, and
e) the current flow through the recreational vehicle electrical system required to operate the
compressor (assume 100% electrical efficiency).

Explanation / Answer

STATE 1 (COMPRESSOR INLET = EVAPORATOR OUTLET)

Given

P1 = 400 kPa (since Evaporator pressure is constant)

Also the state is SATURATED VAPOR
So SATURATED VAPOR Properties of R134a at P1 = 400 kPa are

h1 = 403.7 kJ/kg

T1 = Tsat = 8.93 Deg

v1 = 0.05121 m^3/kg

STATE 2 ( COMPRESSOR EXIT = CONDENSER INLET)

Given

T2 = 100 C

P2 = 1600 kPa

The state is SUPERHEATED VAPOR

The properties at P2 and T2 are

h2 = 475.9 kJ/kg

v2 = 0.01601 m^3/kg

STATE 3 (CONDENSER OUTLET = TROTTLE INLET)

Given the state is SATURATED LIQUID

Also P3 = 1600 kPa (Becuase Pressure is constant in the condenser)

The SATURATED LIQUID Properties at P3 are

v3 = 0.00094 m^3/kg

h3 = 284.1 kJ/kg

STATE 4 (TROTTLE OUTLET = EVAPORATOR INLET)

This is Iso- enthalpy Process

h4 = h3 = 284.1 kJ/kg

P4 = P1 = 400 kPa

T4 = T1 = Tsat = 8.93 C

a)

Cooling Capacity = m*(h1-h4) = 500

m*(403.7 - 284.1)*1000 = 500

m = 4.186*10^-3 kg/s

b)

Qout = m*(h2-h3) = 4.186*10^-3*(475.9-284.1)*1000

Qout = 802.87 W

c)

Pcomp = m*(h2-h1) = 4.186*10^-3*(475.9-403.7)*1000

Pcomp = 302.23 W

d)

COP = Cooling Capacity/Pcomp = 500/302.23 = 1.654

e)

Pcomp = V*I

302.23 = 12*I

I = 25.2 A

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