Question

Speed of sound in gas is of the same order as rms speed of its molecules
(A) True
(B) False

Answer 1

Hint : The speed at which the Maxwell-Boltzmann distribution graph achieves its maximum is the most likely speed of gas molecules described by the distribution. The root-mean-square speed of molecules is the speed at which all molecules have the same total kinetic energy as they would have if they were moving at their actual speed.

Complete Step By Step Answer:
The square root of the mean of squares of the velocity of individual gas molecules is the root mean square velocity (RMS value).
$({v_{rms}} = \sqrt {\dfrac{{3RT}}{M}} )$
The root-mean-square speed of gas molecules with molar mass M at absolute temperature T, according to Maxwell, is given by the equation:
$({u_{rms}} = \sqrt {\dfrac{{3RT}}{M}} )$
We can see that variations in temperature (T) and molar mass (M) impact the speed of the gas molecules when we look at the root mean square speed equation. The rate of molecules in a gas is related to temperature and inversely related to the gas's molar mass. In other words, when the temperature of a gas sample rises, the molecules accelerate, increasing the root mean square molecular speed.
The molar mass M must be stated in kg/mole in order for the units to come out in m/s, and R = 8.314 J/K.mol. This equation demonstrates that gas molecules travel at extremely high rates on average. These figures translate to 3040 mph and 1150 mph, respectively. In a gas, the speed of sound is roughly equal to the root mean square speed of the gas molecules. As a result, the above sentence is correct.
Hence option A is correct.

Note :
The square root of temperature is directly proportional to the rms velocity, which is inversely proportional to the square root of molar mass. By quadrupling the temperature of a gas, the rms velocity of the molecules is doubled. The number of collisions between gas molecules and container walls is doubled when the average velocity is doubled. Each collision's impulse is likewise doubled. As a result, the pressure is quadrupled.