Carnot Cycle and Efficiency

The second law of thermodynamics states that no engine can be 100% efficient.

Sadi Carnot explored the maximum theoretical efficiency allowed by this law by constructing the Carnot cycle of an ideal heat engine.

The cycle begins with an ideal gas absorbing heat from a hot reservoir at temperature T_h and undergoing isothermal expansion while doing work.

The gas is then isolated from the hot reservoir and undergoes reversible adiabatic expansion. As the gas does work, its temperature drops to T_c.

When the gas contacts the cold reservoir, it undergoes isothermal compression. Heat is released to the cold reservoir as work is done on the gas. Finally, removing the cold reservoir causes adiabatic compression. As work continues on the gas, it returns to its initial state.

Because the system returns to its initial state, its internal energy remains constant, and the net work produced equals the net heat transferred during the cycle.

The efficiency of the engine is defined as the ratio of work performed to heat absorbed from the hot reservoir. Efficiency can also be expressed solely in terms of the temperatures of the cold and hot reservoirs.