# Peter Lux

## Using Energy and Thermal Efficiency

This is a follow on from my previous post – Energy and Temperature and looks at how we can extract and use energy from a system and what constraints there are in terms of efficiency.

## Energy Differences

Let us consider two water containers. We have just filled one with water and it connected by a small pipe to a second container. In the pipe we have a small turbine or water wheel that we can use to generate power. Figure 1

Initially the turbine will spin but as the water level in the second container reaches the level of the water in the first the turbine slows and eventually stops.

The energy in the system remains the same but we cannot extract that energy since to do this we need energy differences. We always need energy differences to be able to extract useful work.

If we were on the surface of the sun we would have enormous amounts of heat. However this would not provide us with any useful energy since there would be no energy differences. What we would need in this case would be a cold source.

## Heat Engines

We are now going to consider what is called a ‘heat engine’. We have two closed containers (Figure 2). We apply heat from some source – could be burning coal or gas, from a nuclear reactor of another power source. The heat turns water into steam which expands and turns a turbine as it goes into the chamber on the right.

Here the steam loses heat to the environment and turns back into liquid water. This water is then returned to the chamber on the left where is is heated and the cycle continues.

You will notice that we have to lose heat (i.e. energy) to environment so this system can never be 100% efficient. This is the reason why power plants either have large cooling towers or are next to the sea or large rivers.

## How Efficient Can We Be?

It is possible to calculate the maximum efficiency possible which is explained very well elsewhere1. It turns out the efficiency is where Th is the temperature of the hot container and Tc is the temperature of the cold container. The temperatures must be measured in Kelvin (see Energy and Temperature for an explanation of this).

If we have the hot source at 573K (300°C) and the cold source at 298K (25°C) this only gives us an efficiency of about 49%. It gets even worse since to achieve this you have to run things infinitely slowly – i.e. your power would be zero. Therefore real efficiencies are much lower than this theoretic maximum.

If you can run your heat engine at higher temperatures then you can increase your efficiency. For example modern gas power stations can operate at very high temperatures and can reach 60% efficiency whereas a nuclear power plant has to run at lower temperatures and has a much lower efficiency 33-41%.

Therfore there are two ways of rating the power/energy output of thermal power plant – either the total thermal output (MWth) or the Electricity output (MWe).

1 Feynman Lectures on Physics Volume 1 Chapter 44 (http://ebookbrowse.com/feynman-lectures-on-physics-volume-1-chapter-44-pdf-d255122059)