On a cold winter day,the outside temperature is -20°C and the inside temperature is maintained at 20°C.There is a net thermal energy flow to the outside through the walls,roof,etc.,of 25 kW.What is the rate of increase of the entropy of the universe as a result of this energy flow?

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Quizplus · Accepted Answer

The rate of increase of entropy in the universe due to the energy flow can be calculated using the formula ΔS = Q/T, where Q is the heat transferred and T is the temperature. However, since the process involves heat transfer across different temperatures, we must consider the entropy change for both the inside and outside environments. The heat lost by the inside (at 20°C or 293K) and gained by the outside (at -20°C or 253K) is the same in magnitude but will result in different entropy changes due to the different temperatures.For the inside, the decrease in entropy is ΔS_inside = -Q/T_inside = -25,000W / 293K.For the outside, the increase in entropy is ΔS_outside = Q/T_outside = 25,000W / 253K.The net entropy change is the sum of these two changes, which is positive, indicating an increase in the total entropy of the universe. The exact calculation gives a value close to 13 W/K, reflecting the irreversible nature of spontaneous heat flow from a warmer to a cooler body.

On a Cold Winter Day,the Outside Temperature Is -20°C and the Inside