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NEET 2022

Exam: NEET
Year: 2022
Subject: Physics
Chapter: Thermodynamics

NEET 2022 · Physics · Thermodynamics

An ideal gas follows a process described by the equation PV^2=C...

An ideal gas follows a process described by the equation

\mathrm{PV}^2=\mathrm{C}

from the initial \left(\mathrm{P}_1, \mathrm{~V}_1, \mathrm{~T}_1\right)

to final ( \left.\mathrm{P}_2, \mathrm{~V}_2, \mathrm{~T}_2\right)

thermodynamic states, where

\mathrm{C}

is a constant. Then:

Options

AIf $\mathrm{P}_1>{ }_2$ then $\mathrm{T}_1 < \mathrm{T}_2$
BIf $\mathrm{V}_2>\mathrm{V}_1$ then $\mathrm{T}_2>\mathrm{T}_1$
CIf $\mathrm{V}_2>\mathrm{V}_1$ then $\mathrm{T}_2 < \mathrm{T}_1$
DIf $\mathrm{P}_1>\mathrm{P}_2$ then $\mathrm{V}_1>\mathrm{V}_2$

Correct answer

C. If $\mathrm{V}_2>\mathrm{V}_1$ then $\mathrm{T}_2 < \mathrm{T}_1$

Step-by-step solution

As per question,

\mathrm{PV}^2=\mathrm{C}

And by ideal gas equation, we have;

\mathrm{PV}=n \mathrm{RT}

Hence,

\left(\frac{n \mathrm{RT}}{\mathrm{V}}\right) \mathrm{V}^2=\mathrm{C}

Hence, TV = constant

\mathrm{T} \propto \frac{1}{\mathrm{~V}} \therefore \mathrm{V}_2 > \mathrm{V}_1 \text{\text{ and } } \mathrm{T}_1 > \mathrm{T}_2

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