A) \[1100{}^\circ C\]
B) \[1284{}^\circ C\]
C) \[1500{}^\circ C\]
D) \[2184{}^\circ C\]
Correct Answer: D
Solution :
Speed of sound, \[\upsilon =\sqrt{\left\{ \frac{\gamma RT}{M} \right\}\propto }\sqrt{T}\] \[\therefore \] \[\frac{{{\upsilon }_{2}}}{{{\upsilon }_{1}}}=\sqrt{\frac{{{T}_{2}}}{{{T}_{1}}}}\] Given \[\frac{{{v}_{2}}}{{{v}_{1}}}=3\] \[\therefore \] \[3=\sqrt{\frac{{{T}_{2}}}{{{T}_{1}}}}or\frac{{{T}_{2}}}{{{T}_{1}}}=9\] \[\Rightarrow \] \[{{T}_{2}}=9{{T}_{1}}\] Here \[{{T}_{1}}=0{}^\circ C=273K\] \[\therefore \] \[{{T}_{2}}=9K\times 273K\] \[=2457K\] \[=(2457-273){}^\circ C\] \[=2184{}^\circ C\]
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