Question

A 300-W heat pump operates between the ground, whose temperature is 0°C, and the interior of a house at 22°C. What is the maximum amount of heat per hour that the heat pump can supply to the house?

a) 322 W
b) 300 W
c) 278 W
d) 250 W

Answer 1

The answer of the given statement that "the maximum amount of heat per hour that the heat pump can supply to the house" is c) 278 W.

Step-by-step explanation:

The efficiency
`(\( \eta \))` of a heat pump is given by the Carnot efficiency formula:

`\[ \eta = 1 - (T_C)/(T_H) \]`

Where:

-
`\( T_C \)` is the absolute temperature of the cold reservoir (in Kelvin),

-
`\( T_H \)`is the absolute temperature of the hot reservoir (in Kelvin).

To find the maximum amount of heat
`(\( Q_H \))` that the heat pump can supply to the house, we use the formula:

\[ Q_H = \eta \times \text{Input Power} \]

Given that the ground temperature is 0°C and the interior temperature is 22°C, we convert these temperatures to Kelvin:

`\[ T_C = 273 \, \text{K} \]`

`\[ T_H = 273 + 22 \, \text{K} \]`

Substitute these values into the Carnot efficiency formula:

`\[ \eta = 1 - (273)/(273 + 22) \]`

`\[ \eta \approx 0.92 \]`

Now, calculate the maximum heat supplied:

`\[ Q_H = 0.92 * 300 \, \text{W} \]`

`\[ Q_H \approx 276 \, \text{W} \]`

Therefore, the correct answer is not among the given options. The closest option is c) 278 W.