## Heat Engines and Water Wheels

Trevithick pumping engine (Cornish system). It is an example of 'heat engine', a device that converts heat energy into mechanical work. Figure from Wikipedia:

The culture around science is obsessed with novelty. This is understandable, but in my view regrettable. And nowhere is this clearer than in that most unfashionable of scientific fields: thermodynamics. The name combines thermo – to do with temperature and heat – and dynamics – to do with forces. So very roughly, thermodynamics is the study of what causes heat to move.

Thermodynamics emerged in the early to mid-nineteenth century as scientists around Europe struggled to understand the limits of steam engines. In the latter part of the 18th Century, just getting any amount of mechanical work ‘for free’ was a benefit, but as the miracle of steam became more workaday, engineers struggled to optimise the devices and get the most work output for the least coal input. It must have frustrated engine-owners that they could see hot water and steam leaving their machines – so clearly some energy was not being utilised!

After several years a solution emerged, generally credited to the french engineer Nicolas Léonard Sadi Carnot – even though his work was essentially ignored druing his short life. His conclusion was that despite all the astonishing complexity of heat engines – the maximum possible efficiency was determined by one simple formulae that depended only on the relative temperatures of the hot and cold parts of the engine. And absolutely nothing else.  No clever device, new fuel, or intricate design could overcome this limit.

I want to write lots of things for completeness, but since I have to go bed shortly, I will restrict myself to just one aspect of his description of how heat engines work: they work like a water mills.

The first result of Sadi Carnot’s analysis is that ‘waste’ heat is not ‘wasted’. In fact it is essential to the operation of the device.

• In a watermill – it is the flow of water which generates mechanical power. Reducing the amount of”waste’ water by preventing water leaving the mill causes the ‘water level’ at the output to rise and eventually no water would flow.
• In a heat engine – it is the flow of heat which generates mechanical power. Reducing the amount of”waste’ heat by preventing heat leaving the engine cause the ‘heat level’ – or temperature – at the output to rise and eventually no heat would flow

The second result of his analysis concerns the maximum possible efficiency.

• In a water mill – the maximum amount of mechanical work per litre of water flow that may be extracted is determined just by the difference in ‘water levels’ between the input and the output i.e. the height difference between the input and the output.
• In a heat engine – the maximum amount of mechanical work per joule of heat flow that may be extracted is determined just by the difference in ‘heat levels’ between the input and the output i.e. the temperature difference between the hot part and the cold part.

This is astonishing. It says that no matter how clever a device one builds: whether it is a steam engine, a gas turbine or a nano-engineered thermoelectric generator, the maximum achievable efficiency doesn’t depend on any details of the device. For sure it it is possible to have one design that is better than another, but nothing can beat Sadi Carnot’s limit

love results like this: simple insights that transcend the particular details of their discovery. And the law that Sadi Carnot discovered? It is called the Second law of Thermodynamics.

The maximum possible fraction of heat flow through a device that may be turned into useful work – mechanical or electrical. The calculation assumes that heat leaves the device at 20 °C and the calculation depends on the temperature of the hottest part of the device.

### 3 Responses to “Heat Engines and Water Wheels”

1. Steve Lawless Says:

This is fascinating and thanks. I understand that turning coal into electricity is only 35% efficient. A lot of people argue for combined heat and power to improve this efficiency at power stations. Is this possible because the power station is operating below maximum possible efficiency or is at that the second law gets reapplied to the difference in temperature of the cooling fluids etc?

• protonsforbreakfast Says:

35% is probably about right for old coal. More modern plant is better, approaching, but not quite reaching the efficiency of a ‘combined cycle gas turbine’ (CCGT) . A CCGT is two heat engines in series, each one optimised for a particular temperature. The gas is burned in a high temperature turbine (= high efficiency) and the waste heat runs a steam turbine. In this way I have heard that more the 50% of the methane’s chemical energy can be turned into electrical power.

Heat engines convert random molecular motion into ordered molecular motion. Using the ‘waste heat’ to heat houses just makes perfect sense and because it is not a conversion process it is not limited by the second law – you can ‘have it all’! (if your house is insulated). In the Netherlands I have read that they heat greenhouses with the waste power and enhance the atmosphere in the greenhouses with the CO2.

Finally note that energy conversion in general is not limited by the second law. SO fuel cells can convert chemical energy into electricity with, in principle, 100% efficiency because they don’t have to convert heat into work. Hope that helps.

All the best: M

2. Happy Birthday Andrew Hanson | Protons for Breakfast Blog Says:

[…] And it was this concern that inspired my gift. I was thinking about  the way Andrew is able to draw energy from his environment – when I realised that he was at heart a heat engine. […]