Wave Mechanics Question 52
Question: At which temperature the speed of sound in hydrogen will be same as that of speed of sound in oxygen at 100oC
[UPSEAT 1999]
Options:
A) ? 148oC
B) ? 212.5oC
C) ? 317.5oC
D) ? 249.7oC
Show Answer
Answer:
Correct Answer: D
Solution:
Speed of sound in gases is $ v=\sqrt{\frac{\gamma RT}{M}} $
Therefore $ T\propto M $ (Because v, g-constant). Hence $ \frac{{T _{H _{2}}}}{{T _{O _{2}}}}=\frac{{M _{H _{2}}}}{{M _{O _{2}}}} $
Therefore $ \frac{{T _{H _{2}}}}{(273+100)}=\frac{2}{32} $
Therefore $ {T _{H _{2}}}=23.2K=-249.7{}^\circ C $
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