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 when I worked in schools). If you drop a pack of cards, they will scatter and the chances of their landing in a meaningful order are very small indeed.
Heat is work and work's a curse,
And all the heat in the Universe
Is gonna cool down.
That will mean no more work,
And there'll be perfect peace.
That's entropy, man!
[Michael Flanders and Donald Swan]
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.
Therefore:
W = Qin - Qout
We can write down an efficiency relationships from this:
We can reverse the process, pumping energy from the cold side to the hot side:
In a refrigerator, a motor pumps and compresses a coolant. The compressed coolant goes to a heat exchanger outside on the back, where heat is transferred by convection into the room. The coolant then is sprayed into an expansion chamber in the ice compartment of the fridge. The liquid evaporates, which requires energy as latent heat. The energy required is taken from the inside of the cabinet, which is heavily insulated to prevent heat flowing from the room. The coolant gas is taken back to the pump.
| 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? |
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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.
The picture below shows the condenser of a steam turbine:
| 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? |
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The dipping duck in the photograph below is a heat engine:
| What do you think are the hot and cold reservoirs? |
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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.
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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)
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A real engine does less work for a given heat transfer Qin. Additionally, if we do a job of work on the real engine, we would not get Qin back. The real engine is much less efficient than the reversible engine. If you are driving a car downhill in gear, the engine acts as a brake. It will not produce the same heat flow as it would if driving the car along a level road. Just as well, otherwise you would boil the engine going downhill. Not a good idea.
| 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. |
