An ideal monoatomic gas is taken around the cycle ABCDA as Shown in the P →V diagram. The work d

An ideal monoatomic gas is taken around the cycle ABCDA as...

An ideal monoatomic gas is taken around the cycle $\mathrm{ABCDA}$ as Shown in the $\mathrm{P} \rightarrow \mathrm{V}$ diagram. The work done during the cycle is given by
(A) PV
(B) $(1 / 2)$
(C) $2 \mathrm{PV}$
(D) $4 \mathrm{PV}$

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Key Concepts

Properties of a Monoatomic Gas

A monoatomic gas, consisting of single-atom molecules, has simpler thermodynamic behavior compared to polyatomic gases. Its internal energy and specific heats are well-defined, which simplifies the study of processes involving ideal gases in thermodynamic cycles.

Work in a P-V Diagram

This concept involves understanding that the work done by a gas during a thermodynamic process can be represented by the area under the curve in a pressure-volume diagram. For cyclic processes, the net work corresponds to the area enclosed by the cycle, which can be calculated using integration of pressure with respect to volume.

Thermodynamic Cycles

Thermodynamic cycles refer to a series of processes through which a system returns to its initial state. In these cycles, despite internal energy changes canceling out over the complete cycle, the net work done by the gas is determined by the path taken around the cycle on a P-V diagram.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental equation of state that relates pressure, volume, and temperature of an ideal gas. It is crucial for analyzing the behavior of gases in different thermodynamic processes and for determining the state variables at various points in a cycle.

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