# Episode 606: Heat engines and thermal efficiency

Lesson for 16-19

- Activity time 65 minutes
- Level Advanced

This material is only relevant to some specifications so check carefully before covering it.

Lesson Summary

- Discussion and demonstration: Steam engines (10 minutes)
- Student activity: Finding out about thermal efficiencies (20 minutes)
- Discussion: The Second Law and efficiency (15 minutes)
- Worked examples and student questions: Calculating efficiency (20 minutes)

## Discussion and demonstrations: Steam engines

If you have a model steam engine it would be excellent to show this and consider the changes to the way energy is stored when it is used. Emphasise that energy is dissipated (wasted

) when, for example, steam emitted from the chimney heats the surroundings. If you do not have a steam engine, try to find a video or other resources relating to a power station. In all cases there should be energy stored in the fuel (and oxygen) that (usually) generates steam.

The steam drives a turbine and then is condensed and returned to the boiler. A significant proportion of the energy stored thermally in the steam is not delivered to the turbines and it is then wasted

in heating up the coolant in the condenser. That coolant may then itself be used as a source of energy (in Combined Heat and Power stations) improving the overall efficiency of the power station.

## Student activity: Finding out about thermal efficiencies

Use the web or printed information from energy companies to find out about the efficiency of different types of power stations. Use these to discuss the meaning of the definition of efficiency = useful energy outtotal energy in × 100 %.

Clearly without the word useful

the efficiency would be 100% in all systems. (Why? Because energy is conserved

)

Can students think of a system that is 100% efficient? If not, lead them to thinking about systems where heating is the intended change – such as a radiator or electrical fire. How does a coal fire compare (energy loss up the chimney)?

Can they draw up a quantitative Sankey diagram for a power station?

Episode 606-1: Power station efficiencies (Word, 30 KB)

Episode 606-2: Sankey diagrams (Word, 158 KB)

## Discussion: The Second Law of Thermodynamics and efficiency

Ultimately, justification of the Second Law of Thermodynamics rests on an understanding of entropy. Without a full-blown mathematical proof, which is inappropriate at this level, it is necessary to rely on assertion and justification by reason. A simple statement of the Second Law is that you cannot have a process whose only effect is to use energy stored thermally to do work. If you could, you could build a car which extracted energy from the air and drive along without needing petrol. This limitation is fundamental, not merely a practical constraint.

In a power station the working fluid (water or steam) is allowed to expand through the turbines and so drive them. Afterwards the expanded steam needs to be returned at low pressure by cooling in order to complete a *cycle* – to put it back as it was before it entered the boiler. Hence the need to cool the steam in the condenser. This energy is not useful. Thus, although we can use *some* energy stored thermally to do work we cannot extract *all* of it.

Consideration of cycles like those in a power station (a *heat engine* ) shows that the maximum efficiency of such a device is given by
*T*_{hot} − *T*_{cold}*T*_{hot}. In this equation *T* is in K, the *absolute temperature* .

Finally, you may need to mention the heat pump. This is simply a heat engine operated in reverse. Work shifts energy stored thermally in a cold reservoir to energy stored thermally in a hot one. The details are not needed, but a refrigerator is an example. Heat pumps are sometimes used to heat houses in cold climates. They can be very effective.

## Worked examples: Calculating efficiency

*1* Calculate the maximum theoretical thermal efficiency of a coal-fired power station that heats steam to 510 ° C and cools it in a condenser at 30 ° C.

Answer:

Maximum efficiency = *T*_{hot} − *T*_{cold}*T*_{hot}

Maximum efficiency = (510+273) K − (30+273) K(510+273) K

Maximum efficiency = 0.61, or 61%.

*2* The temperature of the gases in a car engine during combustion is 1800 ° C. The exhaust is expelled at 80 ° C.

Calculate the maximum theoretical thermal efficiency of the engine.

Answer:

Maximum theoretical efficiency = *T*_{hot} − *T*_{cold}*T*_{hot}

Maximum theoretical efficiency = (1800+273) K − (80+273) K(1800+273) K

Maximum efficiency = 0.83, or 83%.

Of course, in both case, the actual efficiency will be smaller. Students should consider why.

Episode 606-3: Student questions; calculating efficiency (Word, 27 KB)