A) \[273{}^\circ C\]
B) \[546{}^\circ C\]
C) \[1092{}^\circ C\]
D) \[819{}^\circ C\]
Correct Answer: D
Solution :
Velocity of sound in gas medium is given by \[v=\sqrt{\frac{\gamma RT}{M}}\] or \[v\propto \sqrt{T}\] or \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\] Here,\[{{v}_{1}}=332\,m/s,\,{{T}_{1}}=0+273=273\,K,\] \[{{v}_{2}}=664\,m/s\] Hence, \[\frac{332}{664}=\sqrt{\frac{273}{{{T}_{2}}}}\] or \[\frac{1}{2}=\sqrt{\frac{273}{{{T}_{2}}}}\] or \[{{T}_{2}}=4\times 273=1092\,K\] or \[{{T}_{2}}=1092-273=819{{\,}^{o}}C\]
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