Question

Is a temperature difference necessary to operate a heat engine? State why or why not.

Short answer

A difference in temperature is necessary for the heat engine to do its work.

Step-by-step solution

Explain the working principle of a heat engine

A heat engine is a machine that converts heat energy into useful work. The work done by the heat engine is equal to the difference between the heat taken from the source and released to the sink. It is mathematically expressed as:

\({\bf{W = }}{{\bf{Q}}_{\bf{h}}}{\bf{ - }}{{\bf{Q}}_{\bf{c}}}\).

Here,\({\bf{W}}\)is the work output,\({{\bf{Q}}_{\bf{h}}}\)is the heat in the hot reservoir and\({{\bf{Q}}_{\bf{c}}}\)is the heat in the cold reservoir.

Describe the role of the temperature difference in operating the heat engine.

The heat engine absorbs heat from the source at a higher temperature and releases some part of it into the sink which is at a lower temperature. The heat only transfers between those bodies that have a temperature difference between them. Thus, if needs to transfer from source to sink, the temperature difference is mandatory.