Heat Engine

Heat engine is defined as a device that converts heat energy into mechanical energy or more exactly a system which operates continuously and only heatand work may pass across its boundaries. 
The operation of a heat engine can best be represented by a thermodynamic cycle. Some examples are: Otto, Diesel, Brayton, Stirling and Rankine cycles.

Forward Heat Engine

LTER= Low Temperature Energy Reservoir
HTER= High Temperature Energy Reservoir 

A forward heat engine has a positive work output such as Rankine or Brayton cycle. Applying the first law of thermodynamics to the cycle gives:

Q1 - Q2 - W = 0 

The second law of thermodynamics states that the thermal efficiency of the cycle, , has an upper limit (the thermal efficiency of the Carnot cycle), i.e.

It can be shown that:

Q1 > W

which means that it is impossible to convert the whole heat input to work and

Q2 > 0 

which means that a minimum of heat supply to the cold reservoir is necessary.

Reverse Heat Engine

LTER= Low Temperature Energy Reservoir
HTER= High Temperature Energy Reservoir 

A reverse heat engine has a positive work input such as heat pump and refrigerator. Applying the first law of thermodynamics to the cycle gives:

- Q1 + Q2 + W = 0 

In case of a reverse heat engine the second law of thermodynamics is as follows: It is impossible to transfer heat from a cooler body to a hotter body without any work input i.e.

W > 0 

which means that the coefficient of performance for a heat pump is greater than unity.