Subtopic: Refrigeration and cold storage basics and applications
Question Statement:
A refrigeration system based on the 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 the atmosphere (hot reservoir), in kW, is nearest to
Options:
(A) 84.40
(B) 14.41
(C) 186.67
(D) 116.67
Official Answer Key:
A
Step-by-Step Solution & Explanation
Step 1 — absolute temperatures:
T_L = −30 + 273.15 = 243.15 K
T_H = 20 + 273.15 = 293.15 K
Step 2 — Carnot COP for refrigeration:
COP = T_L/(T_H − T_L) = 243.15/(293.15 − 243.15) = 243.15/50 = 4.863
Step 3 — work input:
W = Q_L/COP = 70/4.863 = 14.40 kW
Step 4 — heat rejected (energy balance on the cycle):
Q_H = Q_L + W = 70 + 14.40 = 84.40 kW
(Option (B) 14.41 is the work input alone — a common misread of the question.)
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