Carnot cycle for maximum convertibility of heat into work?

Question: Carnot cycle for maximum convertibility of heat into work?

The Carnot cycle is a theoretical model of an ideal heat engine that can achieve maximum efficiency in converting heat into work. It was proposed by Sadi Carnot, a French physicist, in 1824.

The Carnot cycle consists of four reversible processes: two isothermal and two adiabatic. In an isothermal process, the temperature of the system remains constant. In an adiabatic process, no heat is exchanged between the system and the surroundings.

The four processes of the Carnot cycle are:

1. Isothermal expansion: The system (a gas) absorbs heat from a high-temperature reservoir at temperature T1 and expands, doing work on the surroundings.

2. Adiabatic expansion: The system continues to expand without heat transfer, and its temperature drops to T2.

3. Isothermal compression: The system releases heat to a low-temperature reservoir at temperature T2 and is compressed by external work.

4. Adiabatic compression: The system continues to be compressed without heat transfer, and its temperature rises back to T1.

The net work done by the system in one cycle is equal to the net heat absorbed from the high-temperature reservoir. The efficiency of the Carnot cycle is given by:

efficiency = 1 - T2/T1

This shows that the efficiency depends only on the temperatures of the reservoirs and not on the nature of the working substance or the details of the processes. The Carnot cycle has the highest possible efficiency for any heat engine operating between two given temperatures.

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