A commercial refrigerator with refrigerant-134a as the

Chapter 6, Problem 101P

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QUESTION:

A commercial refrigerator with refrigerant-134a as the working fluid is used to keep the refrigerated space at \(-35^{\circ} \mathrm{C}\) by rejecting waste heat to cooling water that enters the condenser at \(18^{\circ} \mathrm{C}\) at a rate of \(0.25 \mathrm{~kg} / \mathrm{s}\) and leaves at \(26^{\circ} \mathrm{C}\). The refrigerant enters the condenser at \(1.2 \mathrm{MPa}\) and \(50^{\circ} \mathrm{C}\) and leaves at the same pressure subcooled by \(5^{\circ} \mathrm{C}\). If the compressor consumes \(3.3 \mathrm{~kW}\) of power, determine

(a) the mass flow rate of the refrigerant,

(b) the refrigeration load,

(c) the COP, and

(d) the minimum power input to the compressor for the same refrigeration load.

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QUESTION:

A commercial refrigerator with refrigerant-134a as the working fluid is used to keep the refrigerated space at \(-35^{\circ} \mathrm{C}\) by rejecting waste heat to cooling water that enters the condenser at \(18^{\circ} \mathrm{C}\) at a rate of \(0.25 \mathrm{~kg} / \mathrm{s}\) and leaves at \(26^{\circ} \mathrm{C}\). The refrigerant enters the condenser at \(1.2 \mathrm{MPa}\) and \(50^{\circ} \mathrm{C}\) and leaves at the same pressure subcooled by \(5^{\circ} \mathrm{C}\). If the compressor consumes \(3.3 \mathrm{~kW}\) of power, determine

(a) the mass flow rate of the refrigerant,

(b) the refrigeration load,

(c) the COP, and

(d) the minimum power input to the compressor for the same refrigeration load.

ANSWER:

Step 1 of 4

(a)

Obtain the enthalpy of the refrigerant, R134a entering into the condenser at 1.2 MP1 and

\(50^{\circ} \mathrm{C}\) from the table A-13.

\(h_{R_{1}}=278.27 \mathrm{~kJ} / \mathrm{kg}\)

Obtain the enthalpy of the saturated liquid refrigerant. R134a at 1.2 MP3 from the table A-12.

\(h_{\text {sat } @ 1.2 \mathrm{MPa}}=117.7 \mathrm{~kJ} / \mathrm{kg}\)

Calculate the enthalpy of the refrigerant, R134a at 1.2 MPa that is sub-cooled by \(50^{\circ} \mathrm{C}\) as

follows,

\(h_{R_{2}}=h_{\text {sat } @ 1.2 \mathrm{MPa}}-C_{P_{. \pi}} \Delta T\)

Here, \(h_{\text {sat } @ 1.2 \mathrm{MPa}}\) is the enthalpy of the saturated liquid refrigerant, R134a at 1.2 MPa. \(C_{P_{, R}}\) is

the specific heat capacity of the liquid refrigerant. R134a and \(\Delta T\) is the degree of sub-cooling done.

Substitute \(117.7 \mathrm{~kJ} / \mathrm{kg} \text { for } h_{\text {sat } @ 1.2} \mathrm{MPa}, 5^{\circ} \mathrm{C} \text { for } \Delta T\) and \(1.4944 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C} \text { for } C_{P_{\cdot, k}} \text {. }\)

\(\begin{aligned}
h_{R_{2}} & =117.7-1.4944 \times 5 \\
& =110.228 \mathrm{~kJ} / \mathrm{kg}
\end{aligned}\)

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