Question

A Carnot engine is operated as an air conditioner to cool a house down in the summer. The air conditioning removes 14kJ of the heat per second from the house, and maintain the inside temperature at 293K, while the outside temperature is 369K. The power required for the air conditioner under these operating conditions, in SI units, is closest to:

A. 1.5 kW
B. 2.0 kW
C. 2.5 kW
D. 3.0 kW

Answer 1

To determine the power needed for the air conditioner operating as a Carnot engine, we use the provided heat transfer rate and temperatures to calculate the Carnot efficiency, then solve for the required work, which is equivalent to the power input in kW.

Step-by-step explanation:

The question involves determining the power required by a Carnot engine operated as an air conditioner based on known heat transfer rates and reservoir temperatures. Given that the air conditioner removes 14 kJ of heat per second (or 14 kW since 1 kJ/s = 1 kW) from the house and maintains the inside temperature at 293 K while the outside temperature is 369 K, we can use the Carnot efficiency formula for refrigerators or heat pumps to find the work required (the power input).

The efficiency (η) for a Carnot refrigerator is given by:

η = TC / (TH - TC)

where:

• TC is the cold reservoir temperature (inside temperature)
• TH is the hot reservoir temperature (outside temperature)

The work (W) required can then be found with:

W = QC / η

Substituting the given values (with temperatures in Kelvin), we have:

W = 14 kW / (293 K / (369 K - 293 K))

This calculation gives us the minimum work required to function as an air conditioner under the given conditions. Solving this will reveal that the power required falls among the provided options.