A gas follows VT^2 = constant. coefficient of volume expansion of gas is

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10-1.Thermometry, Thermal Expansion and Calorimetry

hard

A gas follows $VT^2 =$ constant. The coefficient of volume expansion of the gas is

A

$\frac{2}{T}$

B

$ - \frac{2}{T}$

C

$\frac{3}{T}$

D

$ - \frac{3}{T}$

Solution

$V T^2=c$

$V(2 T)+T^2\left(\frac{d V}{d T}\right)=0$

$2 V=-T\left(\frac{dV}{d T}\right)$

$d V=V \gamma d T$

$\frac{d V}{V}=\gamma dT$

$\gamma=\frac{d V}{VdT}$

$\Rightarrow \gamma=-\frac{2}{T}$

Standard 11

Physics

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