Question

At constant pressure, the ratio of increase in volume of an ideal gas per degree rise in kelvin temperature to its original volume is :

• A. $T^2$
• B. $\frac{1}{T}$
• C. $T^3$
• D. $T$

Answer 1

The correct option is B $\frac{1}{T}$

According to ideal gas law,
$PV=RT\Rightarrow V=\left(\frac{R}{P}\right)T$
$V\propto T$ (at constant pressure).
Hence, $\frac{V_1}{V_2}=\frac{T_1}{T_2}$
$\Rightarrow \frac{V_2}{V_1}=\frac{T_2}{T_1}$ .....(i)
where, $V_2$ is the final volume.
$\frac{V_2}{V_1}-1=\frac{T_2}{T_1}-1$
$\Rightarrow \frac{V_2-V_1}{V_1}=\frac{T_2-T_1}{T_1}$ $[\because T_2-T_1=1K]$
$\Rightarrow \frac{V_2-V_1}{V_1}=\frac{1}{T_1}=\frac{1}{T}$