A completely reversible heat pump produces heat at a rate of 300 kW to warm a house maintained at 24°C. The exterior air, which is at 7°C, serves as the source. Calculate the rate of entropy change of the high temperature energy reservoir.Group of answer choices1.01 kW/KNo answer text provided.-1.01 kW/K0
Question
A completely reversible heat pump produces heat at a rate of 300 kW to warm a house maintained at 24°C. The exterior air, which is at 7°C, serves as the source. Calculate the rate of entropy change of the high temperature energy reservoir.Group of answer choices1.01 kW/KNo answer text provided.-1.01 kW/K0
Solution 1
The rate of entropy change for the high temperature energy reservoir (the house) can be calculated using the formula:
ΔS = Q/T
where: ΔS is the change in entropy, Q is the heat transferred, and T is the absolute temperature.
First, we need to convert the temperatures from Celsius to Kelvin. The Kelvin temperature is found by adding 273.15 to the Celsius temperature. So, the temperature of the house in Kelvin is 24°C + 273.15 = 297.15 K.
Next, we substitute the given values into the formula:
ΔS = 300 kW / 297.15 K = 1.01 kW/K
Therefore, the rate of entropy change of the high temperature energy reservoir is 1.01 kW/K.
Solution 2
The rate of entropy change for the high temperature energy reservoir (the house) can be calculated using the formula:
ΔS = Q/T
where: ΔS is the change in entropy, Q is the heat transferred, and T is the absolute temperature.
First, we need to convert the temperatures from Celsius to Kelvin. The Kelvin temperature is found by adding 273.15 to the Celsius temperature. So, the temperature of the house in Kelvin is 24°C + 273.15 = 297.15 K.
Next, we substitute the given values into the formula:
ΔS = 300 kW / 297.15 K = 1.01 kW/K
Therefore, the rate of entropy change of the high temperature energy reservoir is 1.01 kW/K.
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