Question

A Carnot cycle working between 100°C and 30°C is used to drive a refrigerator between −10°C and 30°C. How much energy must the Carnot engine produce per second so that the refrigerator is able to discard 10 J of energy per second?

a) 3 J
b) 6 J
c) 9 J
d) 12 J

Answer 1

The energy produced by the Carnot engine per second is 0 J.

Step-by-step explanation:

The energy produced by the Carnot engine per second can be calculated using the formula:

Energy produced per second = (Energy discarded by the refrigerator per second) / (Coefficient of performance of the refrigerator)

In this case, the energy discarded by the refrigerator per second is 10 J and the coefficient of performance of the refrigerator can be calculated using the formula:

Coefficient of performance = (Temperature difference between the two reservoirs) / (Temperature of the cold reservoir)

Given that the temperature difference between the two reservoirs is 40 °C and the temperature of the cold reservoir is -10 °C, the coefficient of performance can be calculated as:

Coefficient of performance = 40 °C / (-10 °C - 30 °C) = -1

Now, plugging these values into the first formula:

Energy produced per second = 10 J / -1 = -10 J

Since energy can't be produced or consumed in negative quantities, the energy produced by the Carnot engine per second must be 0 J.