A refrigerator removes 1.5 kW from the cold space at -10 C using 750 W of power

Question

A refrigerator removes 1.5 kW from the cold space at -10 C using 750 W of power input while it rejects heat to the kitchen at 25 C. Find the rate of irreversibility. I am unsure of how to solve this problem. The entire concept of irreversibility and exergy and availability is very difficult for me to grasp, and I need to review this a billion more times! Thank you for your help! A refrigerator removes 1.5 kW from the cold space at -10 C using 750 W of power input while it rejects heat to the kitchen at 25 C. Find the rate of irreversibility. I am unsure of how to solve this problem. The entire concept of irreversibility and exergy and availability is very difficult for me to grasp, and I need to review this a billion more times! Thank you for your help!

Explanation / Answer

If there were no entropy generation inside the fridge (i.e. reversible), we would have Qh/Th = Qc/Tc. Whatever entropy it took out of the cold side, it would dump into the hot side. If the fridge generates entropy internally, it will need to sink the extra entropy into the hot side. (in a cyclic heat engine/ fridge, entropy neither accumulates nor depletes) So the entropy generated inside is the balance, (Qh/Th) - (Qc/Tc). We don't know Qh directly: however the first law states that Qh = Qc + W. Plugging in values, we get 1.85 Watt per degree Kelvin as the entropy generation rate. I assume rate of irreversibility means (internal) entropy generation rate.

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