Question

A Carnot refrigerator exhausts heat to the air, which is at a temperature of 25°C. How much power is used by the refrigerator if it freezes 1.5 g of water per second? Assume the water is at 0°C.

a) 4.5 W
b) 5.5 W
c) 6.5 W
d) 7.5 W

Answer 1

To calculate the power used by the Carnot refrigerator, you need to calculate the heat transfer rate and the coefficient of performance. The heat transfer rate can be calculated using the mass of water, specific heat capacity, and change in temperature. The coefficient of performance can be calculated using the cold and hot temperatures. Substituting these values into the formula for power will give you the answer.

Step-by-step explanation:

The power used by the Carnot refrigerator can be calculated using the formula:

Power = Heat transfer rate / Coefficient of performance

The heat transfer rate can be calculated using the formula:

Heat transfer rate = mass of water x specific heat capacity x change in temperature

Given that the mass of water is 1.5 g, the specific heat capacity of water is 4.18 J/g°C, and the change in temperature is (0°C - 25°C) = -25°C, we can calculate the heat transfer rate. The coefficient of performance can be calculated using the formula:

Coefficient of performance = Tc / (Th - Tc)

Given that Tc = 0°C and Th = 25°C, we can calculate the coefficient of performance. Substituting these values into the formula for power, we can calculate the power used by the refrigerator.