Question

Velocity of sound is minimum in which of the following gases:
A. Nitrogen
B. Hydrogen
C. Air
D. Carbon dioxide

Answer 1

Hint: The velocity of sound in any gas is given by$\sqrt{\dfrac{\gamma RT}{M}}$, to find the gas in which velocity of sound is minimum; we will put value of different variable for all gases and compare the value obtained by formula. The gas with minimum value of $\sqrt{\dfrac{\gamma RT}{M}}$ will be the one in which the velocity of sound is minimum.

Complete Step-by-Step solution:
Velocity of sound in any gas having heat capacity ratio$\gamma $, temperature T, and molar mass M is given by;
$\sqrt{\dfrac{\gamma RT}{M}}$
While finding the minimum velocity of sound in different gases we will assume that the temperature of all gases is the same.
Heat capacity of nitrogen gas is 1.4 and its molar mass is 28. So velocity of sound will be
$\sqrt{\dfrac{1.4RT}{28}}=\sqrt{\dfrac{RT}{20}}$
Heat capacity of hydrogen is 1.4 and its molar mass is 2. So velocity of sound will be
$\sqrt{\dfrac{1.4RT}{2}}=\sqrt{\dfrac{7RT}{10}}$
Heat capacity of air is 1.4 and its molar mass is approximately 29. So velocity of sound will be
$\sqrt{\dfrac{1.4RT}{29}}$
Heat capacity of carbon dioxide gas is $\dfrac{4}{3}$ and its molar mass is 44. So velocity of sound will be
$\sqrt{\dfrac{4RT}{3\times 44}}=\sqrt{\dfrac{RT}{33}}$
After comparing velocities of sound in all the gases we can say that velocity of sound is minimum in carbon dioxide.
Hence the correct option is D.

Note: We cannot draw a conclusion that the gas with highest molar mass will be the one with minimum velocity of sound, because velocity of sound depends on other factors too. The above statement will be true only if temperature and heat capacities of all the given gases are the same.