Question

Calculate the ratio of the speed of sound in neon to that in water vapour at any temperature. Given that the molecular weight of neon gas $=2.02\times 10^{-2}kgmol{e}^{-1}$ and molecular weight of water vapour $=1.8\times 10^{-2}kgmol{e}^{-1}$ . ${\gamma }_{\text{neon}}=\frac{5}{3}$ and $\gamma$ for water vapour $=\frac{4}{3}$ .

• A. $1.1$
• B. $1.7$
• C. $1.9$
• D. $1.3$

Answer 1

Answer: (A)

Let v₁ and v₂ be the speeds of sound in neon and water vapour respectively. Suppose that M₁ and M₂ are the molecular weights of neon and water vapour respectively. If γ is the ratio of the two specific heats, then
$\frac{{\upsilon }_1}{{\upsilon }_2}=\sqrt{\frac{\text{RT }{\gamma }_{\text{neon}}}{{\text{M}}_1}}\times \sqrt{\frac{{\text{M}}_2}{\text{RT }{\gamma }_{\text{water vapour}}}}=\sqrt{\frac{{\text{M}}_2}{{\text{M}}_1}}\times \sqrt{\frac{{\gamma }_{\text{neon}}}{{\gamma }_{\text{water vapour}}}}$
Here, $M_1=2.02\times 10^{-2}kgmol{e}^{-1}$ ;
$M_2=1.8\times 10^{-2}kgmol{e}^{-1}$
$\therefore \frac{{\upsilon }_1}{{\upsilon }_2}=\sqrt{\frac{1\cdot 8\times 10^{-2}\times 5/3}{2\cdot 02\times 10^{-2}\times 4/3}}=1\text{.}1$