A) \[\frac{T}{2}\]
B) \[2T\]
C) \[\sqrt{2}T\]
D) \[\frac{T}{\sqrt{2}}\]
Correct Answer: C
Solution :
Additional law of ideal gas is \[{{P}^{2}}V=\] constant \[\because \] \[PV=nRT\] \[P=\frac{nRT}{V}\] \[\therefore \] \[{{\left( \frac{nRT}{V} \right)}^{2}}V=\]constant \[\frac{{{n}^{2}}{{R}^{2}}{{T}^{2}}}{V}=\] constant \[\frac{T_{1}^{2}}{{{V}_{1}}}=\frac{T_{2}^{2}}{{{V}_{2}}}\] [\[{{(nR)}^{2}}=\]constant, K] \[\because \] \[{{T}_{1}}=T,\,\,{{V}_{1}}=V\] \[{{T}_{2}}=?,\,\,{{V}_{2}}=2V\] \[\frac{{{T}^{2}}}{V}=\frac{T_{2}^{2}}{2V}\] \[T_{2}^{2}={{T}^{2}}2\] \[{{T}_{2}}=\sqrt{2}T\]
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