One mole of an ideal monatomic gas undergoes a process described by the equation P V ^ 3 = constant. The heat capacity of the gas during this process is

Correct answer: D. R P V ^ 3 = constant polytropic process with n = 3 C = C _ v + R 1 - n For monoatomic gas : C _ v = 3R 2 C = 3R 2 + R 1 - 3 = 3R 2 - R 2 = 2R 2 C = R

NEET 2016

Exam: NEET
Year: 2016
Subject: Physics
Chapter: Thermodynamics

NEET 2016 · Physics · Thermodynamics

One mole of an ideal monatomic gas undergoes a process described by...

One mole of an ideal monatomic gas undergoes a process described by the equation

\text{P}{\text{V}}^{3} =

constant. The heat capacity of the gas during this process is

Options

A $\dfrac{3}{2}R$
B $\dfrac{5}{2}R$
C $2R$
D $R$

Correct answer

D. $R$

Step-by-step solution

\text{P}{\text{V}}^{3} =

constant polytropic process with

\text{n} = 3

\text{C} = {\text{C}}_{\text{v}} + \dfrac{\text{R}}{1 - \text{n}}

For monoatomic gas :

{\text{C}}_{\text{v}} = \dfrac{3\text{R}}{2}

\text{C} = \dfrac{3\text{R}}{2} + \dfrac{\text{R}}{1 - 3}

= \dfrac{3\text{R}}{2} - \dfrac{\text{R}}{2}

= \dfrac{2\text{R}}{2}

\text{C} = \text{R}

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