In each cycle of its operation or refrigerator removes 17 J of heat from the inside of the refrigerator and releases 40 J of heat into the room how much work per cycle is required to operate this refrigerator?

23 J

Explanation:

According to the law of conservation of energy, the total heat given off to the surroundings by a refrigerator is equal to the work done by the refrigerator and the heat removed from the inside of the refrigerator.

So we can write:

where

is the heat removed from the cold reservoir (the inside of the refrigerator)

W is the work  done

is the work released into the hot reservoir (the surroundings)

Here we have:

(heat removed from the inside of the refrigerator)

(heat released into the surroundings)

Solving the equation for W, we find the work done: