Question

A refrigerator operates on Reversed Carnot cycle. What is the power required to drive the refrigerator between temperatures of 42°C and 4°C, if heat at the rate of 2 kJ/s is extracted from the low-temperature region?
1. 0.174 kW
2. 0.374 kW
3. 0.274 kW
4. 0.474 kW
5.

Answer 1

Correct Answer - Option 3 : 0.274 kW

Concept:

COP of Refrigerator:

\(\rm COP_{Ref}=\frac{Desired\;Effect}{Power\;Input}=\frac{Q_2}{Power\;Input}\)

For Reversible Refrigerator:

\(\rm COP_{Ref}=\frac{T_2}{T_1\;-\;T_2}\)

Calculation:

Given:

T₁ = 42°C ⇒ 315 K, and T₂ = 4°C ⇒ 277 K, Q₂ = 2 kJ/sec = 2 kW.

\(\rm COP_{Ref}=\frac{Desired\;Effect}{Power\;Input}=\frac{Q_2}{Power\;Input}\)

\(\rm COP_{Ref}=\frac{T_2}{T_1\;-\;T_2}\)

\(\rm \frac{Q_2}{Power\;Input}=\frac{T_2}{T_1\;-\;T_2}\)

\(\rm {Power\;Input}=\left(\frac{T_1\;-\;T_2}{T_2}\right)\times {Q_2}\;\)

\(\rm {Power\;Input}=\left(\frac{315\;-\;277}{277}\right)\times {2}=0.274\;kW\)