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## University of Liverpool

Skip to 0 minutes and 6 seconds Last week, I talked about the Boulton and Watt steam engine. Today, we’re at Quarry Bank Mill, about an hour’s drive from Liverpool. Samuel Greg built this factory in 1784 to spin cotton. When he retired in 1832, it was the largest business of its kind in the UK. Originally, it was powered by a water wheel, but in 1810, they installed a Boulton and Watt steam engine to supplement the power, like the one behind me here. It was only a 10 horsepower engine. That compares to my car engine, which is about 90 horsepower. And one horsepower is about 3/4 of a kilowatt. In 1836, they installed a 20 horsepower steam engine, and in 1871, a 60 horsepower horizontal condensing engine.

Skip to 0 minutes and 55 seconds So by then, they had as much power as my car. Those original engines no longer exist. And during the restoration, the museum here, run by the National Trust, bought similar engines to replace them. [ENGINE NOISES] I’d like to talk about how we can idealise these engines and, for instance, a beating heart like this little one here, so that we can analyse their energy flows. By the way, just to give you a sense of scale, the mechanical power output from a human heart is between one and two watts. The problem with an engine or a pump is that the piston moves up and down at very high speeds.

Skip to 1 minute and 43 seconds The gas is not maintained equilibrium, and so the states through which the gas passes can’t be specified. Add to that, the fact that work is a path function. It depends on what states we go through as to how much work we need or how much work we get out. And so we can’t specify analytically the amount of work we get out of our engine or out of our pump. So what we do is assume a quasi-equilibrium process, or really a quasi-static process, in which we assume that everything is stationary for a snap shot. And when we approximate this in an engine, we can get an answer out.

Skip to 2 minutes and 20 seconds That assumption results in the maximum possible work out for an engine, and the minimum work input for a pump or a compressor. So our assumptions have some effect on our calculations. And as long as we understand that, it’s fine. We can go ahead and do some analysis.

# Cycles that work

At Quarry Bank Mill Eann compares early steam engines to his car and heart while discussing how these dynamic systems can be idealised to allow some simple analysis.