Refrigerant R-134a vaporizes in the evaporator and absorbs heat from the cooled space. Entropy changes of the Refrigerant R-134a, the cooled space and the whole process need to be determined.

Refrigerant R-134a enters the evaporator as a saturated liquid-vapor mixture and leaves the evaporator as saturated vapor. Hence the temperature in the evaporator remains constant at the saturation temperature of 200 kPa, which is,

      T_{sat. @ 200 kPa} = -10.09^oC

(1) Determine the entropy change of refrigerant R-134a

Take refrigerant R-134a as a system (system A). It enters the evaporator as a saturated liquid-vapor mixture, which is state 1.

      P₁ = 200 kPa
      T₁ = T_{sat. @ 200 kPa} = -10.09^oC

Refrigerant R-134a leaves the evaporator as saturated vapor, which is state 2.

      P₂ = 200 kPa
      T₂ = T_{sat. @ 200 kPa} = -10.09^oC

During this process, refrigerant R-134 absorbs 150 kJ heat.

      Q = 150 kJ

Hence, the entropy change for refrigerant R-134a from process 1-2 is

Temperature T is a constant in this case, and the above equation can be integrated as

Substituting Q and T into the above equation yields,

      ΔS_A = 150(1000)/(-10.09 + 273) = 570.56 J/K

(2) Determine the entropy change of the cooled space

Take the cooled space as a system (system B). During the heat transfer process, the space is maintained at -4^oC and it dissipates 150 kJ heat to refrigerant R-134a. The entropy change of the cooled space can be determined as

      ΔS_B =Q/T = -150(1000)/(-4 + 273) = -557.6 J/K

(3) Determine the total entropy change of the process

Take refrigerant R-134a and the cooled space together as a system (system C). Then refrigerant R-134a and the cooled space are subsystems of system C. The entropy change of system C is the sum of the entropy changes of its two subsystems.

      ΔS_C = ΔS_A+ ΔS_B
             = 570.56 + (-557.6) = 12.44 J/K

System C is an isolated system since no heat and mass transfer out of its boundaries. The entropy change of system C is greater than 0, which satisfies the increase of entropy principle.