An ideal gas is expanding such that {PT}^{3}= constant. coefficient of volume expansion of gas is:

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10-1.Thermometry, Thermal Expansion and Calorimetry

hard

An ideal gas is expanding such that ${PT}^{3}=$ constant. The coefficient of volume expansion of the gas is:

A

$\frac{1}{{T}}$

B

$\frac{2}{{T}}$

C

$\frac{4}{{T}}$

D

$\frac{3}{{T}}$

(JEE MAIN-2021)

Solution

${PT}^{3}={constant}$

$\left(\frac{{nRT}}{{v}}\right) {T}^{3}=$ constant

${T}^{4} {V}^{-1}=\text { constant }$

${T}^{4}={kV}$

$\Rightarrow 4 \frac{\Delta {T}}{{T}}=\frac{\Delta {V}}{{V}} \ldots . .(1)$

$\Delta {V}={V} \gamma \Delta {T} . \ldots \ldots \ldots .(2)$

comparing $(1)$ and $(2)$ we get

$\gamma=\frac{4}{{T}}$

Standard 11

Physics

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