Assertion Speed of sound in O2 gas at temperature T is v. If temperature is increased to 2T, the molecular…
Assertion Speed of sound in O2 gas at temperature T is v. If temperature is increased to 2T, the molecular oxygen breaks into atomic oxygen. Then, speed of sound under these conditions will become 2v.
Reason With increase in humidity in air, speed of sound increases.
(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.
Solution
Speed of sound $v\propto\sqrt{\dfrac{T}{M}}$ where $T$ is absolute temperature and $M$ the molar mass.
If $T$ becomes double and $M$ becomes half then
$v\propto\sqrt{\dfrac{2T_0}{(M_0/2)}}=\sqrt{4}\;v_0=2v_0$.
Also, increasing humidity replaces heavier air molecules by lighter water vapour, reducing effective molar mass (or density) and so increasing the speed of sound.
Thus the statements given are correct and the reasoning shown justifies the conclusions.