A refrigerator uses refrigerant-134a as the working fluid and operates on the ideal vapor-compression refrigeration cycle except for the compression process. The refrigerant enters the evaporator at 120 kPa with a quality of 34 percent and leaves the compressor at 70°C. If the compressor consumes 450 W of power, determine (a) the mass flow rate of the refrigerant, (b) the condenser pressure, and (c) the COP of the refrigerator

Answer:

(a) 0.0064 kg/s

(b) 800 KPa

(c) 2.03

Explanation:

The ideal vapor compression cycle consists of following processes:

Process  1-2 Isentropic compression in a compressor

Process 2-3 Constant-pressure heat rejection in a condenser

Process 3-4 Throttling in an expansion device

Process 4-1 Constant-pressure heat absorption in an evaporator

For state 4 (while entering compressor):

x₄ = 34% = 0.34

P₄ = 120 KPa

from saturated table:

h₄ = hf + x hfg = 22.4 KJ/kg + (0.34)(214.52 KJ/kg)

h₄ = 95.34 KJ/kg

For State 1 (Entering Compressor):

h₁ = hg at 120 KPa

h₁ = 236.99 KJ/kg

s₁ = sg at 120 KPa = 0.94789 KJ/kg.k

For State 3 (Entering Expansion Valve)

Since 3 - 4 is an isenthalpic process.

Therefore,

h₃ = h₄ = 95.34 KJ/kg

Since this state lies at liquid side of saturation line, therefore, h₃ must be hf. Hence from saturation table we find the pressure by interpolation.

P₃ = 800 KPa

For State 2 (Leaving Compressor)

Since, process 2-3 is at constant pressure. Therefore,

P₂ = P₃ = 800 KPa

T₂ = 70°C (given)

Saturation temperature at 800 KPa is 31.31°C, which is less than T₂. Thus, this is super heated state. From super heated property table:

h₂ = 306.9 KJ/kg

(a)

Compressor Power = m(h₂ - h₁)

where,

m = mass flow rate of refrigerant.

m = Compressor Power/(h₂ - h₁)

m = (0.450 KJ/s)/(306.9 KJ/kg - 236.99 KJ/kg)

m = 0.0064 kg/s

(b)

Condenser Pressure = P₂ = P₃ = 800 KPa

(c)

The COP of ideal vapor compression cycle is given as:

COP = (h₁ - h₄)/(h₂ - h₁)

COP = (236.99 - 95.34)/(306.9 - 236.99)

COP = 2.03

The Ph diagram is attached