For an isothermal expansion of a Perfect gas, the value of (ΔP / P) is equal to (A) -γ^(1 / 2){(

step 1 Hello students in the question it is given that for an isothermal expansion of a perfect gas the

For an isothermal expansion of a Perfect gas, the value of...

For an isothermal expansion of a Perfect gas, the value of $(\Delta \mathrm{P} / \mathrm{P})$ is equal to (A) $-\gamma^{(1 / 2)}\{(\Delta \mathrm{V}) / \mathrm{V}\}$ (B) $-\gamma\{(\Delta \mathrm{V}) / \mathrm{V}\}$ (C) $-\gamma^{2}\{(\Delta \mathrm{V}) / \mathrm{V}\}$ $(\mathrm{D})-(\Delta \mathrm{V} / \mathrm{V})$

For an isothermal expansion of a Perfect gas, the value of $(\Delta \mathrm{P} / \mathrm{P})$ is equal to
(A) $-\gamma^{(1 / 2)}\{(\Delta \mathrm{V}) / \mathrm{V}\}$
(B) $-\gamma\{(\Delta \mathrm{V}) / \mathrm{V}\}$
(C) $-\gamma^{2}\{(\Delta \mathrm{V}) / \mathrm{V}\}$
$(\mathrm{D})-(\Delta \mathrm{V} / \mathrm{V})$

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Key Concepts

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant throughout the change. For ideal gases, this implies that the product of pressure and volume is constant, as dictated by the ideal gas law. This constancy of temperature is crucial in simplifying the analysis of the process, especially when using differential relations.

Ideal Gas Law

The ideal gas law, represented as PV = nRT, relates the pressure, volume, and temperature of an ideal gas. In an isothermal process, since the temperature (T) is constant, the product PV remains constant. This is a fundamental property that allows for the derivation of relationships between infinitesimal changes in pressure and volume.

Differential Relationships in Thermodynamics

Differential relationships are used when analyzing small changes in thermodynamic variables. By applying calculus to the product PV = constant during an isothermal process, one can derive that the relative change in pressure is equal in magnitude but opposite in sign to the relative change in volume. This differential relation provides insight into how the state variables interact during the process.

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