Discussion
A refrigeration system based on reverse Carnot cycle operates between −30 °C and 20 °C. The refrigeration capacity of the system is 70 kW. Heat rejected at the condenser to atmosphere (hot reservoir), in kW, is nearest to
Answer: A
The heat rejected is about 84.40 kW.
A reversed Carnot cycle must use absolute temperatures: \(T_{L} = 243\) K and \(T_{H} = 293\) K.
\[ \begin{aligned} COP &= \frac{T_{L}}{T_{H} - T_{L}} = \frac{243}{50} = 4.86 \\ W &= \frac{70}{4.86} = 14.40\ \text{kW} \\ Q_{H} &= Q_{L} + W = 84.40\ \text{kW} \end{aligned} \]
14.41 kW is the compressor work, not the heat rejected. 116.67 kW is what the work comes to if the temperatures are left in degrees Celsius (COP = 30/50 = 0.6), and 186.67 kW is 70 plus that wrong work. Heat rejected must always be the refrigeration load plus the work input.
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