The Carnot efficiency is
where and are the low and high temperatures in . So, in this case,
The efficiency is defined as the ratio of the work
where is the work done by the Carnot engine and is the heat input to the engine. In this problem, the engine is being run in reverse as a heat pump, so the work is the work done to the engine and the denominator of is the heat output by the heat pump.
So, the minimum amount of work required to put out of heat is
Therefore, answer (B) is correct.