A heat 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 Tc

D) Qh > Qc and Th > Tc

For the heat engine to do work. The quantity of heat in the hot reservoir (Qh) must be greater than the quantity of heat in the cold reservoir (Qc). So also, the temperature of the hot reservoir (Th) is greater than the temperature of the cold reservoir (Tc).

Therefore the correct answer is option (D)

Qh > Qc and Th > Tc

Explanation:

One of the general ways to illustrate a heat engine is the energy reservoir model. The engine takes energy from a hot reservoir and uses part of it to do work, but is constrained by the second law of thermodynamics to exhaust part of the energy to a cold reservoir. In the case of the automobile engine, the hot reservoir is the burning fuel and the cold reservoir is the environment to which the combustion products are exhausted. The efficiency of the heat engine is given as:

(W/Qh) = (Qh - Qc) / Qh

Answer: B

Explanation:

Qh>Qc and Th>Tc is the right condition for heat engine to operate since it needs heat.

It obtains this heat input (Qh) through a high temperature heat reservoir (Th). It takes some of this heat and does work, and releases the rest of the heat (Qc) to a low temperature heat reservoir (Tc)

For energy balance on a heatbengine, we obtain the following equation

Qh=W+Qc

Therefore if Qh is less than Qc, we get negative work, meaning we have to put work into our engine (obviously not the purpose of a engine). So Qh>Qc. As for the temperature, the high temperature has to be higher than the low temp reservoir for heat to flow, as heat flows from high to low, and never the other way around (Clausius Second Law Statement).

In other words heat flows from a hotter body to a cooler body, that is the principle under which heat engine operate