Question

A one mole of an ideal gas expands adiabatically at constant pressure such that its temperature T$\propto \frac{1}{\sqrt{V}}$. The value of the adiabatic constant of gas is:

• A. 1.3
• B. 1.5
• C. q1.67
• D. 2

Answer 1

The correct option is B 1.5

In adiabatic process,

$P{V}^{\gamma }=k\left(constant\right)$. . . . . .(1)

From ideal gas equation,

$PV=nRT$

$P=\frac{nRT}{V}$

From equation (1),

$\frac{2RT}{V}{V}^{\gamma }=k$

$T{V}^{\gamma -1}=k^{\prime }\left(constant\right)$. . . . . .(2)

Given,

$T\propto \frac{1}{\sqrt{V}}$

$T{V}^{1/2}=constant$. . . . . . .(3)

By comparing equation (2) and (3), we get

$\gamma -1=\frac{1}{2}=0.5$

The value of adiabatic constant of gas is $1.5$.

$\gamma =1+0.5=1.5$

The correct option is B.