Reversible Heat Engine with Monatomic Gas Molecules

A reversible heat engine, also known as a Carnot engine, is an idealized heat engine that operates between two heat reservoirs. The working substance in a Carnot engine undergoes a series of reversible processes, including isothermal expansion and compression and adiabatic expansion and compression. The efficiency of a Carnot engine is given by the formula:

Efficiency = 1 - (Tc/Th)

where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.

In the case of a monatomic gas, the gas molecules consist of a single atom. These atoms do not have any internal degrees of freedom (such as rotational or vibrational modes), and their energy is solely determined by their translational kinetic energy. Therefore, the temperature of a monatomic gas is directly proportional to the average kinetic energy of its atoms.

Efficiency of a Carnot Engine with Diatomic Gas Molecules

In the case of a diatomic gas, the gas molecules consist of two atoms bound together. These molecules have additional internal degrees of freedom, namely, rotational and vibrational modes. As a result, the energy of a diatomic gas is distributed among both its translational and internal degrees of freedom.

When a diatomic gas is used as the working substance in a Carnot engine, the temperature of the gas is not solely determined by the average translational kinetic energy of its molecules. Instead, it is determined by the sum of the translational, rotational, and vibrational kinetic energies.

However, the efficiency of a Carnot engine is dependent only on the temperatures of the heat reservoirs and not on the specific properties of the working substance. This is because the efficiency is determined by the temperature difference between the hot and cold reservoirs, not by the internal energy or specific heat capacity of the working substance.

Therefore, regardless of whether the working substance is a monatomic gas or a diatomic gas, the efficiency of the Carnot engine remains the same. The efficiency is solely determined by the temperatures of the heat reservoirs and is independent of the specific gas used as the working substance.

Hence, the correct answer is option 'C' - the efficiency remains the same.