Standard content

A petrol engine, a diesel lorry and a jet engine all turn heat into work, and no two of them follow the same cycle. Here we follow gases along paths that lie between the four standard ones, work out the efficiency of real engine cycles, and find the entropy of an ideal gas. The level is that of JEE Advanced, A-Level Further Physics and IB Higher Level, and the course ends with a full timed paper.

What's inside

1. Polytropic processes and gas mixtures: Many real processes follow none of the four standard curves. A polytropic process keeps $pV^x$ constant, and it covers all four as special cases. Its molar heat capacity can even be negative. Gas mixtures and changing degrees of freedom change the heat capacity in the same way.
2. Otto, Diesel and Brayton cycles: Real engines follow cycles with adiabatic steps and steps at constant volume or constant pressure. Their efficiency depends on the compression ratio or the pressure ratio, and it never reaches the Carnot limit. We also find the heat taken in by a loop of any shape, where a trap waits for the careless.
3. Entropy of an ideal gas and the T-S diagram: The entropy of an ideal gas follows from the first law and the gas equation. It depends on the temperature ratio and the volume ratio and not on the path. A graph of temperature against entropy shows heat as an area, and it gives the quickest proof of the Carnot efficiency.