Refrigerant r-12 is used in a carnot refrigerator
operatingbetween saturated liquid and vapor during the heat
rejectionprocess. if the cycle has a high temperature of 50 deg c
and a lowtemperature of -20 deg c, find the heat transferred from
therefrigerated space, the work required, the coefficient
ofperformance and the quality at the beginning of the heat
additioncycle.

Heat transferred from  the refrigerated space = 95.93 kJ/kg

Work required = 18.45 kJ/kg

Coefficient  of performance = 3.61

Quality at the beginning of the heat  addition cycle = 0.37

Explanation:

From figure  

is heat rejection process

is heat transferred from the refrigerated space

is high temperature = 50 °C + 273 = 323 K

is low temperature = -20 °C + 273 = 253 K  

is net work of the cycle (the difference between compressor's work and turbine's work)

Coefficient of performance of a Carnot refrigerator is calculated as

From figure it can be seen that heat rejection is latent heat of vaporisation of R-12 at 50 °C. From table

From coefficient of performance definition

Energy balance gives

Vapor quality at the beginning of the heat addition cycle is calculated as (f and g refer to saturated liquid and saturated gas respectively)

From figure

Replacing with table values

Quality can be computed by other properties, for example, specific enthalpy. Rearrenging quality equation we get

By energy balance, turbine's work is

Finally, compressor's work is

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