Question

An ideal gas on heating from 100 $K$ to 109 $K$ shows an increase by $a$ % in its volume at constant $P$. The value of $a$ is .....

Answer 1

The ideal gas equation is $PV=nRT$
$P,n$ and $R$ are constant.
Hence,
$\frac{V^{\prime }}{V}=\frac{T^{\prime }}{T}$
Here, $V$ and $V^{\prime }$ are initial and final volumes and $T$ and $T^{\prime }$ are initial and final temperatures.
$\frac{V^{\prime }}{V}=\frac{109}{100}$
The percentage increase in the volume is
$a=\frac{V^{\prime }-V}{V}\times 100=\frac{109-100}{100}\times 100=9$ %
Hence, $a=9$