A mass of monoatomic gas is taken through a cycle as...

A mass of monoatomic gas is taken through a cycle as indicated in the diagram. The efficiency of the cycle is :
(a) $\frac{2}{12-\pi}$
(b) $\frac{2 \pi}{12+\pi}$
(c) $\frac{2 \pi}{24-\pi}$
(d) $\frac{1}{12-\pi}$

Key Concepts

First Law of Thermodynamics

The first law of thermodynamics is a statement of the conservation of energy, establishing that the change in a system's internal energy is equal to the heat added to the system minus the work done by the system. This fundamental principle is used to analyze energy exchanges in every stage of a thermodynamic cycle.

Specific Heat Capacities of Monoatomic Gases

Monoatomic gases have specific heat capacities that depend on their degrees of freedom, with typical values being Cv = (3/2)R at constant volume and Cp = (5/2)R at constant pressure. These parameters are essential when calculating changes in internal energy, heat transfer, and work done during thermodynamic processes involving ideal monoatomic gases.

Thermodynamic Cycles

A thermodynamic cycle involves a system undergoing a series of processes that eventually return it to its original state. In such cycles, the net work output is equivalent to the area enclosed by the cycle on a pressure–volume diagram, serving as a fundamental concept in understanding energy conversion processes.

Heat Engine Efficiency

Efficiency in a heat engine is defined as the ratio of the net work output of the cycle to the total heat input. This concept is central to thermodynamics as it quantifies how effectively a system converts heat into work, and it is bounded by the limitations imposed by the second law of thermodynamics.

Ideal Gas Behavior

The behavior of ideal gases is governed by the ideal gas law (PV = nRT), which provides a simple relationship between pressure, volume, and temperature. This law is critical in analyzing the state changes of gases during various thermodynamic processes and in determining work and heat exchanges in a cycle.

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