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)

$\frac{1}{T}$

Answer 2

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 E (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 ${{T}_{2}}-{{T}_{1}}=1K$ ) $\frac{{{V}_{2}}-{{V}_{1}}}{{{V}_{1}}}=\frac{1}{{{T}_{1}}}$