Reversible Heat Engine and Heat Pump

A reversible heat engine is an idealized thermodynamic engine that operates in a cycle and has the ability to convert all supplied heat energy into work. In a reversible heat engine, the heat supplied during a cycle is partially converted into work, while the remaining heat is rejected to the surroundings.

A heat pump, on the other hand, is a device that uses mechanical work to transfer heat from a low-temperature source to a high-temperature sink. It operates in reverse to a heat engine, as it extracts heat from a colder reservoir and transfers it to a hotter reservoir.

Given Information

According to the given information, the reversible heat engine rejects 50% of the heat supplied during a cycle. This implies that only half of the heat energy supplied is converted into work, while the other half is rejected.

Coefficient of Performance (COP)

The coefficient of performance (COP) is a measure of the efficiency of a heat pump or a refrigeration system. It is defined as the ratio of the desired output (heat transferred) to the required input (work supplied).

Mathematically, the COP of a heat pump is given by:

COP = Qc / W

Where Qc is the heat transferred from the low-temperature source and W is the work supplied to the heat pump.

In this case, since the reversible heat engine is operating as a heat pump, the COP can be calculated using the given information.

Solution

Since the reversible heat engine rejects 50% of the heat supplied during a cycle, it means that only half of the supplied heat (Qh) is converted into work (W), while the remaining half (Qr) is rejected.

Therefore, Qr = 0.5 * Qh

Since the heat pump operates in reverse, the heat transferred (Qc) is equal to the rejected heat (Qr).

Qc = Qr = 0.5 * Qh

Substituting this value of Qc into the COP equation, we get:

COP = Qc / W = (0.5 * Qh) / W

Since we know that W is equal to half of Qh, we can substitute this value into the equation:

COP = (0.5 * Qh) / (0.5 * Qh) = 1

Therefore, the coefficient of performance (COP) of the reversible heat engine operating as a heat pump is 1.

Conclusion

The correct answer is option (a) 1.0. The coefficient of performance of the reversible heat engine operating as a heat pump is 1, indicating that for every unit of work supplied, an equal amount of heat is transferred.