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