If at NTP, velocity of sound in a gas is 1150 m / s, then the rms velocity of gas molecules at

step 1 Hello students in this question we have given that at the ntp the velocity of sound in a gas is

If at NTP, velocity of sound in a gas is 1150 m / s, then...

If at NTP, velocity of sound in a gas is $1150 \mathrm{~m} / \mathrm{s}$, then the rms velocity of gas molecules at NTP is : (Given: $R=8.3$ joule $\left./ \mathrm{mol} / \mathrm{K}, \mathrm{C}_{P}=4.8 \mathrm{cal} / \mathrm{mol} / \mathrm{K}\right)$ (a) $1600 \mathrm{~m} / \mathrm{s}$ (b) $1532.19 \mathrm{~m} / \mathrm{s}$ (c) $160 \mathrm{~m} / \mathrm{s}$ (d) $16 \mathrm{~m} / \mathrm{s}$

If at NTP, velocity of sound in a gas is $1150 \mathrm{~m} / \mathrm{s}$, then the rms velocity of gas molecules at NTP is :
(Given: $R=8.3$ joule $\left./ \mathrm{mol} / \mathrm{K}, \mathrm{C}_{P}=4.8 \mathrm{cal} / \mathrm{mol} / \mathrm{K}\right)$
(a) $1600 \mathrm{~m} / \mathrm{s}$
(b) $1532.19 \mathrm{~m} / \mathrm{s}$
(c) $160 \mathrm{~m} / \mathrm{s}$
(d) $16 \mathrm{~m} / \mathrm{s}$

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Key Concepts

Kinetic Theory of Gases

This theory explains how the microscopic motions of gas molecules relate to the macroscopic properties observed in gases. It provides the basis for understanding how the speeds of individual molecules, their collisions, and interactions give rise to pressure, temperature, and other thermodynamic characteristics.

Root Mean Square (rms) Velocity

The rms velocity is a measure of the average speed of gas molecules derived from the kinetic energy associated with their random motion. It is defined as the square root of the mean of the squares of the individual molecular speeds and is directly linked to the temperature and mass of the molecules in the gas.

Speed of Sound in Gases

The speed of sound in a gas is determined by how quickly pressure disturbances propagate through the medium. This speed depends on the gas's temperature, density, and the specific heats, and it provides information about the collective behavior of molecules under thermodynamic processes.

Specific Heat Ratio (?)

The specific heat ratio, also known as gamma (?), is the ratio of the specific heat at constant pressure to that at constant volume. It plays a critical role in characterizing adiabatic processes in gases and directly influences formulas related to both the speed of sound and the rms velocity of molecules.

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