Question

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

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

Answer 1

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

According to the ideal gas law,

$pV=RT$

$\Rightarrow V=\left[\frac{R}{p}\right]T$

$V\infty T$

$\Rightarrow \frac{V_1}{V_2}=\frac{T_1}{T_2}$

or $\frac{V_2}{V_1}-1=\frac{T_2}{T_1}-1$

$\frac{V_2-V_1}{V_1}=\frac{T_2-T_1}{T_1}$

$\frac{V_2-V_1}{V_1}=\frac{1}{T_1}=\frac{1}{T}$