An air conditioner based on the ideal vapor-compression refrigeration cycle uses

Question

An air conditioner based on the ideal vapor-compression refrigeration cycle uses R134a as the working fluid.  States and enthalpies are shown on the diagram.  The air conditoner is used to cool a 0.25kg/s stream of air from 50 to 20 degrees centigrade.  Heat transfer from the compressor can be neglected, and the changes in the kinetic and potential energies are negligible.  Find the rate of cooling the air conditioner must provide and the required mass flow rate of the R134a.  (ans:  7.54kW, 0.0630 kg/s)

P1=400kPa

x1=100%

h1=255.55 kj/kg

P2=1.6MPa

T2=62.9 centigrade

h2=284.27

P3=1.6MPa

x3= 0 %

h3= 135.93

P4=400kPa

Explanation / Answer

we know Cp of air = 1.006 kJ/kg

rate of cooling of air conditioner = m*cp* delta T = .25 * 1.006 * (50-20 ) = 7.545 kW

heat absorbed by the refrigerant = m*(h1-h3 )

this should be equal to rate of cooling of air conditioner

hence =>m*(h1-h3 ) = 7.545

m* (255.55-135.93 ) = 7.545

we get m = .06303 kg/s

mass flow rate of R134a = .06303 kg/s

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