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: (T = absolute temperature of the gas)

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

Answer 1

Answer: (C)

According to the ideal gas law $PV=RT$ or $V=\left(\frac{R}{P}\right)T$ or $V\propto T$ (at constant pressure) Hence, $\frac{V_1}{V_2}=\frac{T_1}{T_2}$ or $\frac{V_2}{V_1}=-\frac{T_2}{T_1}$ ?(i) (where $V_2$ is the final volume) Now, the ratio of change in volume to the original volume From Eq. (i) $\frac{V_2}{V_1}-1=\frac{T_2}{T_1}-1$ $\frac{V_2-V_1}{V_1}=\frac{T_2-T_1}{T_1}$ (given $T_2-T_1=1K$ ) $\frac{V_2-V_1}{V_1}=\frac{1}{T_1}$