A commercial refrigerator with refrigerant-134a as the working fluid is used to keep the refrigerated space at 2300C by rejecting its waste heat to cooling water that enters the condenser at 180C at a rate of 0.25 kg/s and leaves at 260C. The refrigerant enters the condenser at 1.2 MPa and 650C and leaves at 420C. The inlet state of the compressor is 60 kPa and -340C and the compressor is estimated to gain a net heat of 450 W from the surroundings. Determine (a) the quality of the refrigerant at the evaporator inlet, (b) the mass flow rate of the refrigerant.

Correct question is;

A commercial refrigerator with refrigerant-134a as the working fluid is used to keep the refrigerated space at −30°C by rejecting its waste heat to cooling water that enters the condenser at 18°C at a rate of 0.25 kg/s and leaves at 26°C. The refrigerant enters the condenser at 1.2 MPa and 65°C and leaves at 42°C. The inlet state of the compressor is 60 kPa and −34°C and the compressor is estimated to gain a net heat of 450 W from the surroundings. Determine (a) the quality of the refrigerant at the evaporator inlet, (b) the mass flow rate of the refrigerant.

A) Quality = 0.48

B) Mass flow rate; m' = 0.0455 kg/s

Explanation:

A) From the refrigerant R-144 table I attached,

At P=60kpa and interpolating at - 34°C,we obtain enthalpy;

h1 = 230.03 Kj/kg

Also at P= 1.2MPa which is 1200kpa and interpolating at 65°C,we obtain enthalpy ;

h2 = 295.16 Kj/Kg

Also at P= 1.2MPa which is 1200kpa and interpolating at 42°C,we obtain enthalpy ;

h3 = 111.23 Kj/Kg

h4 is equal to h3 and thus h4 = 111.23 Kj/kg

We want to find the refrigerant quality at the evaporation inlet which is state 4 and P= 60 Kpa.

Thus, from the table attached, we see that hf = 3.84 at that pressure and hg = 227.8

Now, to find the quality of the refrigerant, we'll use the formula,

x4 = (h4 - hg) /(hf - hg)

Where x4 is the quality of the refrigerant. Thus;

x4 = (111.23 - 3.84)/(227.8 - 3.84) = 0.48

B) The mass flow rate of the refrigerant can be determined by applying a 1st law energy balance across the condenser. Thus, the water properties can be obtained by using a saturated liquid at the given temperatures;

So using the first table in the image i attached; interpolating at 18°C; hw1 = hf = 75.54 kJ/kg

Also interpolating at 26°C; hw2 = hf = 109.01 kJ/kg

Now;

(m')(h2 − h3)= (m_w)(hw2 − hw1)

m' is mass flow rate

Making m' the subject, we get;

m' = [(m_w)(hw2 − hw1)]/(h2 − h3)

m' = [(0.25 kg/s)(109.01 − 75.54) kJ/kg] /(295.13 − 111.37) kJ/kg

m' = 8.3675/183.76

m' = 0.0455 kg/s

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explanation: