1. Heat Engines

2. Heat Energy → Work Energy
When heat is added to a contained gas, the gas molecules start to move faster, increasing both the temperature (T) and pressure (P) of the gas.
If the lid of the container is able to move freely, it will be forced upward by an increased number of gas molecules colliding with it from below.

3. Heat Energy → Work Energy
We can harness this upward force by placing something on top of the lid that we want to lift upward.
When we do this, we basically are converting thermal energy (which we add to the gas in the form of heat flow) into work energy.

4. Work
Technically speaking, we say that work (W) is done whenever a force (F) causes an object to be displaced (Δx). When work is done, it adds to either the kinetic or potential energy of the object that the force is acting on.
The amount of work done (energy added) can be determine using the equation

5. How Energy Leaves a Heat Engine
Ideally, ALL of the energy added to the gas in the form of heat flow would leave the gas in the form of work.
In reality, some energy always flows back out of the gas in the form of heat (since the inside of the heat engine always ends up with a higher temperature than its surroundings, after heat is added).

6. The Heat Engine Equation
To summarize, energy enters a heat engine in the form of heat (we symbolize this input energy as QH).
Energy leaves a heat engine in two ways; either as work (W) or heat outflow (QL).
Since energy must be conserved in a heat engine, the input energy (QH) must be equal to the output energy (W + QL).

7. Schematic Diagram of a Heat Engine

8. Heat Engines
Example 1: A heat engine absorbs 250 J of energy in the form of heat, and does 170 J of work per cycle. How much energy per cycle is returned to the surroundings in the form of heat?

9. Heat Engines
Example 2: An engine absorbs 300 J of heat energy and expels 110 J of heat back to the environment. How much work does this engine do?

10. Heat Engines
Example 3: A heat engine does 65 J of work and gives off 15 J of heat per cycle. How much heat does it take in per cycle?