A) \[2d{{m}^{3}}\]
B) \[3d{{m}^{3}}\]
C) \[4d{{m}^{3}}\]
D) \[8d{{m}^{3}}\]
Correct Answer: C
Solution :
Given \[\frac{{{p}_{2}}}{{{p}_{1}}}=2,\frac{{{T}_{2}}}{{{T}_{1}}}=2,\,{{V}_{1}}=4d{{m}^{3}},{{V}_{2}}=?\] From gas equation, \[\frac{{{p}_{1}}{{V}_{1}}}{{{T}_{1}}}=\frac{{{p}_{2}}{{V}_{2}}}{{{T}_{2}}}\] or \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{{{p}_{2}}}{{{p}_{1}}}\times \frac{{{T}_{1}}}{{{T}_{2}}}\] \[\therefore \] \[\frac{4}{{{V}^{2}}}=2\times \frac{1}{2}=1\] \[\therefore \] \[{{V}_{2}}=4d{{m}^{3}}\]
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