Aheat engine is designed to do work. this is possible only if certain relationships between the heats and temperatures at the input and output hold true. which of the following sets of statements must apply for the heat engine to do work?

a) qh < qc and th < tc
b) qh > qc and th < tc
c) qh < qc and th > tc
d) qh > qc and th > tc

Heat at the input must be greater than heat at the output for a heat engine to do work. Similarly the temperature at the input must be higher than the temperature at the output. Therefore, the right option is D.

Explanation:

Heat engines are designed to convert heat absorbed by a system to do work. Most times, there is an amount of heat lost from the system, thus, the amount of energy available to do work becomes lower than the heat gained.

...... (1)

Equation 1 shows that the heat at the input (hotter region) must be greater than heat at the output (colder region) for the system to do work.

The ratio of the work done by the engine to the heat gained from the hotter region is known as the Coefficient of Performance (C.o.P).

..... (2)

Heat pumps and refrigerators are typical examples of heat engines. For heat pumps, the hotter region is the major concern that determines the performance of the engine, while the colder region determines the performance of the engine in refrigerators.

the answer is b ) square root of 5