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Specific Heat Capacity

Thermodynamic...

Question

Thermodynamic process is shown below on a $P - V$ diagram for one mole of an ideal gas . If $V_{2}$ $=$ $2 V_{1}$ , then the ratio of temperature $\frac{T_{2}}{T_{1}}$ is :

\frac{1}{\sqrt{2}}

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\frac{1}{2}

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2

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\sqrt{2}

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Solution

The correct option is D $\sqrt{2}$

Given , $P V^{\frac{1}{2}} = constant . . . . . . . (1)$

We know that $P V = n R T$

$P$ $\propto$ $\frac{T}{V} . . . . (2)$ [ For one mole of gas ]

Using $(1)$ and $(2)$ we get :

$(\frac{T}{V})$ $V^{\frac{1}{2}} = constant$

$\frac{T_{2}}{T_{1}}$ $=$ ${(\frac{V_{2}}{V_{1}})}^{\frac{1}{2}}$ $=$ ${(\frac{2 V_{1}}{V_{1}})}^{\frac{1}{2}}$

$\frac{T_{2}}{T_{1}}$ $=$ $\sqrt{2}$

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