RAJASTHAN PMT Rajasthan - PMT Solved Paper-2003

  • question_answer At which temperature the speed of sound will be three times of its speed at \[0{}^\circ C\]?

    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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