Past exam of the mathematics course of the University of Cambridge 2017 ii Paper 3 34D a Solution Created 2026-09-24 Updated 2026-10-05
A clockwise engine Carnot cycle has four reversible steps. At hot temperature , isothermal expansion absorbs and does positive work by the gas. Adiabatic expansion then cools it to , with zero heat and positive work by the gas. Isothermal compression at emits and requires work on the gas. Finally adiabatic compression returns it to , with zero heat and work on the gas.
For an ideal gas, the isotherms obey and the adiabats , the latter being steeper. In the plane, the isotherms are horizontal and the adiabats vertical, forming a clockwise rectangle. Heat occurs only on the horizontal legs, while work occurs on all four legs.Reversing the arrows gives a refrigerator, reversing the heat and work signs.
