# Heat Engines

### Heat Engines

Heat is a form of energy that can be easily transferred from one body to another. Heat engine is a kind of heat exchanger that converts heat into thermal and chemical energy. This energy is used to perform mechanical work. Real heat engines are complex and there are many ways of converting heat energy into useful work. We can generalise the workings of any heat engine into three parts:

Hot Reservoir: Heat energy is created by some process such as combustion of fuel to provide the heat energy.

Working body: Converts the heat energy into work. In real heat engines, the conversion process is never 100% efficient, so the work output is always less than the heat energy supplied. However, we frequently idealise and assume reversibility.

Cold Reservoir: The energy that cannot be turned into work is dumped and goes to heat up the cold reservoir. In practice, the cold reservoir is usually the atmosphere. We also assume that the temperature of the cold reservoir does not increase, it has an infinite heat capacity. Assume that a heat engine starts with a certain internal energy U, intakes ΔQᵢ heat from a heat source at temperature Tᵢ does work ΔW and exhausts heat ΔQf into the cooler heat reservoir with temperature Tf with a typical heat engine, we only want to use heat intake, not internal energy of the engine, to do work. So, ΔU = 0.

Now, the first law of thermodynamics tells that:

ΔU = 0 = ΔQᵢ – ΔQf – ΔW.

To determine how effectively an engine turn heat to work, we define the efficiency (η) as the ratio of work done to heat input.

$$\eta \,=\,\frac{\Delta W}{\Delta {{Q}_{i}}}\,=\,\frac{(\Delta {{Q}_{i}}\,-\,\Delta {{Q}_{f}})}{\Delta {{Q}_{i}}}$$.

$$\eta \,=\,1\,-\,\frac{\Delta {{Q}_{f}}}{\Delta {{Q}_{i}}}$$.

Because the engine is doing work. We know that ΔW > 0, so we can conclude that ΔQ > 0. Both are positive, so the efficiency is always between 0 and 1.