The 3rd step of the Carnot cycle is:

Correct option is D

The correct answer is (d) Reversible isothermal compression

• The Carnot cycle consists of four steps:

  1. Reversible isothermal expansion: The gas absorbs heat from a hot reservoir at a constant high temperature.

  2. Reversible adiabatic expansion: The gas expands without heat exchange, causing its temperature to decrease.

  3. Reversible isothermal compression: The gas is compressed at a constant low temperature, releasing heat to a cold reservoir. This is the 3rd step of the cycle.

  4. Reversible adiabatic compression: The gas is compressed adiabatically, increasing its temperature back to the initial high temperature.

• In the 3rd step, the gas undergoes isothermal compression at the low temperature, where the gas releases heat to the cold reservoir, and its volume decreases while its temperature remains constant.

Why other options are incorrect:

• (A) Reversible isothermal expansion: This is the 1st step of the Carnot cycle where the gas absorbs heat from a hot reservoir at a constant temperature.

• (B) Reversible adiabatic expansion: This is the 2nd step of the Carnot cycle, where the gas expands without exchanging heat, causing its temperature to decrease.

• (C) Reversible adiabatic compression: This is the 4th step of the Carnot cycle, where the gas is compressed without heat exchange, and its temperature increases.

Information Booster:
• Adiabatic processes (expansion or compression) involve no heat exchange with the surroundings, and the temperature of the gas changes due to work done on or by the gas.
• Isothermal processes occur at constant temperature, where heat is exchanged with the surroundings to maintain that temperature.

Additional Information:

• The Carnot cycle is the most efficient thermodynamic cycle, and its efficiency is determined by the temperatures of the hot and cold reservoirs: $$\eta = 1 - \frac{T_C}{T_H}$$

• where TCT_CTC​ is the temperature of the cold reservoir and THT_HTH​ is the temperature of the hot reservoir.

• The Carnot efficiency sets an upper limit on the efficiency of any heat engine.