If at same temperature and pressure, the densities for two diatomic gases are d1 and d2 respectively, then the ratio of velocities of sound in these gases will be

Question

If at same temperature and pressure, the densities for two diatomic gases are d1 and d2 respectively, then the ratio of velocities of sound in these gases will be (A) √(d2/2d1) (B) √(d2/d1) (C) √(2d1/d2) (D) √(d1/d2)

Tardigrade Admin · Accepted Answer

The velocity of sound in a gas is given by

v = \frac{γ p}{d}

where

γ = \frac{C _{P}}{C _{V}}

p =

pressure

d =

density

∴

For two gases at constant pressure,

\frac{v _{1}}{v _{2}} = \frac{d _{2} γ _{1}}{d _{1} γ _{2}}

For a diatomic gas

γ_{1} = γ_{2} = \frac{7}{5}

∴ \frac{v _{l}}{v _{2}} = \frac{d _{2}}{d _{1}}

Q. If at same temperature and pressure, the densities for two diatomic gases are $d_{1}$ and $d_{2}$ respectively, then the ratio of velocities of sound in these gases will be

$\frac{d _{2}}{2 d _{1}}$

$\frac{d _{2}}{d _{1}}$

$\frac{2 d _{1}}{d _{2}}$

$\frac{d _{1}}{d _{2}}$

Q. If at same temperature and pressure, the densities for two diatomic gases are d1​ and d2​ respectively, then the ratio of velocities of sound in these gases will be

2d1​d2​​​

d1​d2​​​

d2​2d1​​​

d2​d1​​​

The velocity of sound in a gas is given by v=dγp​​ where γ=CV​CP​​ p= pressure d= density ∴ For two gases at constant pressure, v2​v1​​=d1​γ2​d2​γ1​​​ For a diatomic gas γ1​=γ2​=57​ ∴v2​vl​​=d1​d2​​​

Q. If at same temperature and pressure, the densities for two diatomic gases are $d_{1}$ and $d_{2}$ respectively, then the ratio of velocities of sound in these gases will be

$\frac{d _{2}}{2 d _{1}}$

$\frac{d _{2}}{d _{1}}$

$\frac{2 d _{1}}{d _{2}}$

$\frac{d _{1}}{d _{2}}$