Question

If the pressure of a gas increases upto nine times keeping the temperature constant, then its RMS velocity will become:
(A) 9 times
(B) 3 times
(C) Remains same
(D) $\dfrac{1}{3}$ times

Answer 1

Pressure is defined as the force a substance exerts on another substance per unit area. The force that the gas exerts on the container walls is known as the gas pressure. The gas molecules travel about in a random pattern throughout the given space. They collide with the surface as well as each other during this movement.

Complete answer:
The square root of the mean square (RMS or rms or rms) is known as the root mean square (RMS or rms) in mathematics and its applications (the arithmetic mean of the squares of a set of numbers). The quadratic mean, also known as the RMS, is a special case of the generalised mean with exponent 2. RMS can also be expressed as an integral of the squares of the instantaneous values over a loop for a continuously variable function.
The square root of the sum of the squares of the stacking velocity values separated by the number of values yields the root-mean square (RMS) velocity. The RMS velocity is the speed of a wave as it travels through subsurface layers at various intervals along a given ray line. The reason we use the rms velocity rather than the average is that the net velocity of a normal gas sample is zero since the particles are travelling in both directions. This is an important formula since particle velocity defines both diffusion and effusion speeds.
The square root of the mean of squares of the velocity of individual gas molecules is the root mean square velocity (RMS value).
${{\mathbf{V}}_r}_{{\text{ms}}} = \sqrt {\dfrac{{3{\text{RT}}}}{{\text{M}}}}$
${{\mathbf{V}}_r}_{{\text{ms}}}$ = Root-mean-square velocity
T = Temperature in Kelvin.
R= Molar gas constant
M = Molar mass of the gas (Kg/mole)
The RMS velocity stays stable since the temperature is constant. As can be shown, root mean square speed is unaffected by pressure and is only affected by temperature.
If the pressure of a gas is increased up to 9 times while the temperature remains constant, the root mean square speed would remain the same.
As a result, option C is right.

Note:
Each specific gas molecule has a very small effect that is difficult to imagine. The gas pressure, on the other hand, is the product of the combined effect of all the gas molecules. The strain would increase as the number of crashes increased.