A) \[{{10}^{5}}N/{{m}^{2}}\]
B) \[2\times {{10}^{5}}N/{{m}^{2}}\]
C) \[0.5\times {{10}^{5}}N/{{m}^{2}}\]
D) \[4\times {{10}^{5}}N/{{m}^{2}}\]
Correct Answer: A
Solution :
From ideal gas equation \[PV=nRT\] \[\Rightarrow \] \[PV\propto T\] \[\therefore \] \[\frac{{{P}_{1}}{{V}_{1}}}{{{T}_{1}}}=\frac{{{P}_{2}}{{V}_{2}}}{{{T}_{2}}}\Rightarrow {{P}_{2}}\frac{{{P}_{1}}{{V}_{1}}{{T}_{2}}}{{{V}_{2}}{{T}_{1}}}\] Here : \[{{P}_{1}}=1\times {{10}^{5}}\,N/{{m}^{2}},\,{{V}_{1}}=1{{m}^{3}}\] \[{{T}_{1}},=300K,\,{{V}_{2}}=2{{V}_{1}}=2\,{{m}^{3}},\] \[{{T}_{2}}=2{{T}_{2}}=600\,K\] Putting given values in eq. (1) \[{{P}_{2}}=\frac{1\times {{10}^{-5}}\times 1\times 600}{2\times 300}={{10}^{5}}\,N/{{m}^{2}}\]
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