A HEAT ENGINE is a device that permits heat to flow from a hotter region to a colder region, extracting some of that heat as useful work in the process.

SECOND LAW OF THERMODYNAMICS: The ENTROPY of a thermally isolated system of objects NEVER decreases.

Moving heat from the hotter region to the colder region increases the total ENTROPY of the system. The SECOND LAW OF THERMODYNAMICS then allows some heat to be converted to work.

A heat engine's MAXIMUM EFFICIENCY is limited by the temperatures of the hot and cold regions. The hotter the hot region and the colder the cold region, the more EFFICIENT the heat pump can be. It's efficiency is the fraction of the thermal energy from the hot region that's converted into ordered energy.

COMPRESSING a gas requires WORK and results in an INCREASE in the TEMPERATURE of that gas.