BITSAT 2024 Shift 1 Paper

In a mixture of gases where the average number of degrees of freedom per molecule is 6 , the velocity of sound in the gas can be determined using the following relationships:
The root mean square (rms) speed vrms is given by:
vrms=√‌

3RT

M

The velocity of sound v‌sound ‌ is given by:
v sound=√‌

γRT

M

The ratio of the velocity of sound to the rms speed is:
‌

v sound

vrms

=√‌

γ

3

Given that the degrees of freedom f=6, we calculate the adiabatic index γ as follows:
γ=1+‌

2

f

=1+‌

2

6

=‌

4

3

Substituting γ=‌

4

3

into the equation for the velocity of sound:
v sound=√‌

4∕3

3

vrms=‌

2

3

vrms
Therefore, the velocity of sound in the gas is:
‌

2c

3