In the exam you are expected to know:
Need for an engine to operate between a source and a sink
Reasons for the lower efficiencies of practical engines
The Second Law of Thermodynamics states that it is impossible for any heat engine to be 100 % efficient:
No process is possible which results in the extraction of an amount of heat from a reservoir and its conversion to an equal amount of mechanical work.
The theory behind this is that entropy increases. In other words all processes tend towards chaos (which might explain my physics lessons). If you drop a pack of cards, they will scatter and the chances of them landing in a meaningful order are very small indeed.
Most energy is lost to the surroundings as low grade heat. We can show this in the diagram below:
In this diagram, called a Sankey Diagram, we can see that of 72 kW of power from the fuel, only 9 kW are used in actually driving a car along a road. The rest is lost as low grade heat. As we said before, getting energy out of heat is remarkably difficult.
All heat engines work by extracting mechanical energy from a temperature gradient. Heat flows from hot to cold, never the other way round:
Heat won't pass from a cooler to a hotter.
You can try it if you like,
But you far better notta,
Because the cold in the cooler
Will get hotter as a ruler,
And that's a physical law!
[Michael Flanders and Donald Swan]
We can show the heat flowing from a hot reservoir through a heat engine to a cold reservoir.
All heat engines give up their energy to a cold reservoir. We can define the terms used on the diagram:
Qin = the heat flow from the hot reservoir to the engine
Qout is the heat flow from the engine to the cold reservoir.
The work done by the heat engine is the difference between Qin and Qout.
We can write down an efficiency relationships from this:
Question 1 A car uses energy from the fuel at a rate of 72 kJ s-1. It uses 9 kJ s-1 to move along the road. How much heat is lost as waste? What is the efficiency? ANSWER
An ideal heat engine takes a quantity of heat Qin from a hot reservoir of temperature TH and sends a quantity of heat Qout as waste to a cold reservoir of temperature TC. It can be shown that:
We can rewrite the efficiency equation:
This can be rearranged to give us a useful relationship:
The temperature must always be in Kelvin. If we set TC at 0 K, we could have a heat engine that was 100 % efficient, but as we can't get down to 0 K, forget it! However we can make heat engines more efficient by making the difference between that hot reservoir and the cold reservoir as big as possible. In a power station, the steam coming from the boiler is at about 400 oC, while for the cold reservoir, water at about 10 oC is used.
Question 2 What is the maximum possible efficiency of an engine using steam at a temperature of 100 oC on a day when the temperature is 24 oC? ANSWER
The dipping duck in the photograph below is a heat engine:
Question 3 What do you think are the hot and cold reservoirs? ANSWER
There are limitations to the theoretical efficiency of any heat engine.
TH cannot be too high, otherwise components could melt;
TC will be in the normal range of atmospheric temperatures.
Careful analysis of the cycle of an engine can help improve efficiency;
Careful design of ports so that gas can get in and out with the minimum resistance.
Friction cannot be eliminated. Lubrication reduces friction in bearings, but there is some viscous drag with the oils themselves.
A small geothermal power station in Iceland pumps cold water into hot rock strata far below the Earth’s surface to be heated and returned at a constant temperature of 87 °C. The power station uses the hot water as the heat source for a heat engine which rejects energy to the much colder sea water near the station.
(a) When the temperature of the sea water is 7 °C the power output from the heat engine is 5.0MW. Calculate:
(i) the maximum theoretical efficiency of the heat engine,
(ii) the rate at which heat energy must be transferred from the hot water if the engine works at the maximum theoretical efficiency,
(iii) the rate at which energy must be transferred to the sea water under these conditions.
(b) The power station produces electrical power with an overall efficiency which is much lower than the maximum theoretical efficiency of the heat engine. Give two reasons for this lower efficiency.
(c) The overall efficiency of an oil-fired power plant of similar size to the geothermal station is over four times as great. Suggest one reason, other than less pollution, why the geothermal source was preferred for the power station.
(AQA Past question) ANSWER
| Summary
Heat engines need a source and a sink No heat engine can ever be 100 % efficient
Practical engines do not work at their theoretical efficiency. |