A) \[{{8322}^{o}}C\]
B) \[{{3822}^{o}}C\]
C) \[{{1911}^{o}}C\]
D) \[{{4095}^{o}}C\]
Correct Answer: D
Solution :
From Laplaces equation, the velocity of sound is given by \[v=\sqrt{\frac{\gamma \,RT}{M}}\] where \[\gamma \] is ratio of specific heats, R is gas constant, T is temperature and M is molecular weight. Given,\[{{v}_{1}}=v,\,{{v}_{2}}=4v,\,{{T}_{1}}={{0}^{o}}C=0+273\] \[=273K\] \[\therefore \] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\] \[\frac{v}{4\,v}=\sqrt{\frac{273}{{{T}_{2}}}}\] \[\Rightarrow \] \[{{T}_{2}}=273\times 16=4368\,K\] \[\Rightarrow \] \[{{T}_{2}}=4368-273={{4095}^{o}}C\]
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