Question

Calculate the ratio of the speed of sound in neon to that in water vapours at any temperature. (molecular weight of neon$=2.02\times {10}^{-2}kgmol{e}^{-1}$ and for water vapours$=1.8\times {10}^{-2}kgmol{e}^{-1}$ )

• A. 0.055
• B. 1.055
• C. 2.055
• D. 3.055

Answer 1

The correct option is B 1.055

In terms of temperature and molecular weight,
$\frac{v_{Ne}}{v_w}=\sqrt{\frac{{\gamma }_{Ne}}{M_{Ne}}\times \frac{M_W}{{\gamma }_W}}$ $[as{T}_n=T_W]$
Now as neon is monatomic $(\gamma =\frac{5}{3})$
while water vapours poly atomic
$(\gamma =\frac{4}{3})$ ; so
$\frac{v_{Ne}}{v_W}=\sqrt{\frac{\left(\frac{5}{3}\right)\times 1.8\times {10}^{-2}}{\left(\frac{4}{3}\right)\times 2.02\times {10}^{-2}}}$
$=\sqrt{\frac{5}{4}\times \frac{1.8}{2.02}}=1.055$