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}}} $