AP EAPCET 24-Aug-2021 Shift 1 Paper

For Oxygen,
Molar mass, M1=32
Heat capacity ratio at constant pressure to that at constant volume,
γ1=

Cp

CV

=

7

5

[for diatomic gas]
Speed of sound, v1=460m∕s
For Helium,
Molar mass, M2=4
Heat capacity ratio (

Cp

Cv

),
γ2=

5

3

[for monoatomic gas]
Let speed of sound =v2
Using the expression of speed of sound in an ideal gas at certain temperature (T) is
v=√

γRT

M

∴ v1=√γ1‌RT‌/M1 ...(i)
and v2=√

γ2‌RT

M2

...(ii)
Dividing Eq. (i) by Eq. (ii), we get

v1

v2

=√

γ1‌RT

M1

×√

M2

γ2‌RT

=√

γ1

γ2

×

M2

M1

Substituting the values, we get

460

v2

=√

7

5

×

4

32

×

3

5

⇒v2=1420m∕s
Hence, speed of sound in helium gas at the same temperature is 1420m∕s.