A monoatomic gas is used in a Carnot engine as the working...

A monoatomic gas is used in a Carnot engine as the working substance, If during the adiabatic expansion part of the cycle the volume of the gas increases from $\mathrm{V}$ to $8 \mathrm{~V}_{1}$ the efficiency of the engine is..
(A) $60 \%$
(B) $50 \%$
(C) $75 \%$
(D) $25 \%$

Key Concepts

Carnot Cycle

The Carnot cycle is an idealized thermodynamic cycle that provides the maximum possible efficiency for any heat engine operating between two thermal reservoirs. It consists of two isothermal processes where heat transfer takes place at constant temperature, and two adiabatic processes in which the system is insulated from heat exchange, meaning all the work done results in temperature change.

Carnot Efficiency

Carnot efficiency is the theoretical upper limit on the efficiency of a heat engine operating between two reservoirs, and it is determined solely by the temperatures of those reservoirs. It is given by the formula ? = 1 - (T_c/T_h), where T_h and T_c are the absolute temperatures of the hot and cold reservoirs, respectively.

Adiabatic Process

An adiabatic process in thermodynamics is one during which no heat is exchanged with the surroundings. In such a process, any change in the internal energy of a system is due entirely to work done by or on the system, often leading to a change in temperature as described by adiabatic relations.

Adiabatic Relations in Ideal Gases

For an ideal gas undergoing an adiabatic process, the relationship between pressure, volume, and temperature is governed by the adiabatic condition. Specifically, for temperature and volume, the relation T·V^(?-1) = constant holds, where ? (the specific heat ratio) depends on the nature of the gas. This relation allows one to determine how the temperature changes with volume during an adiabatic expansion or compression.

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