An air-conditioning system operating on the reversed Carnot cycle is required to remove heat from the house at a rate of 32 kJ/s to maintain its temperature constant at 20 degrees C. If the temperature of the outdoors is 35 degrees C, the power required to operate this air-conditioning system isQuestion 5Select one:a.0.58 kWb.3.20 kWc.1.56 kWd.2.26 kWe.1.64 kW
Question
An air-conditioning system operating on the reversed Carnot cycle is required to remove heat from the house at a rate of 32 kJ/s to maintain its temperature constant at 20 degrees C. If the temperature of the outdoors is 35 degrees C, the power required to operate this air-conditioning system isQuestion 5Select one:a.0.58 kWb.3.20 kWc.1.56 kWd.2.26 kWe.1.64 kW
Solution
To solve this problem, we need to use the formula for the Carnot efficiency, which is:
Efficiency = 1 - (Tc/Th)
where Tc is the cold temperature (inside the house) and Th is the hot temperature (outside). These temperatures need to be in Kelvin.
First, convert the temperatures from Celsius to Kelvin. The formula to convert Celsius to Kelvin is K = C + 273.15.
Tc = 20C = 20 + 273.15 = 293.15 K Th = 35C = 35 + 273.15 = 308.15 K
Now, substitute these values into the efficiency formula:
Efficiency = 1 - (293.15/308.15) = 0.0486
The efficiency of the air-conditioning system is 0.0486, or 4.86%.
The power required to operate the system is the rate of heat removal divided by the efficiency. So:
Power = 32 kJ/s / 0.0486 = 658.43 kW
However, this value is not in the options. There might be a mistake in the problem or in the options provided.
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