A) \[{{7}^{2}}\]
B) \[\frac{1}{T}\]
C) \[{{T}^{3}}\]
D) T
Correct Answer: B
Solution :
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. \[\frac{{{V}_{2}}}{{{V}_{1}}}-1=\frac{{{T}_{2}}}{{{T}_{1}}}-1\] \[\Rightarrow \] \[\frac{{{V}_{2}}-{{V}_{1}}}{{{V}_{1}}}=\frac{{{T}_{2}}-{{T}_{1}}}{{{T}_{1}}}\] \[[\because {{T}_{2}}-{{T}_{1}}=1\,K]\] \[\Rightarrow \] \[\frac{{{V}_{2}}-{{V}_{1}}}{{{V}_{1}}}=\frac{1}{{{T}_{1}}}=\frac{1}{T}\]
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