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

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.

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.