Question

4.0 g of helium occupies 22400 $c{m}^3$ at STP. The specific heat capacity of helium at constant pressure is 5.0 cal $K^{-1}$. Calculate the speed of sound in helium at STP.

Answer 1

Given that

$C_p$ = 5.0 cal/mol-K

= $5.0\times$ 4.2 J/mol-K

= 21 J/mol-K

v = $\sqrt{\frac{\gamma p}{p}}=\sqrt{\frac{\gamma RT}{M}}=\sqrt{\frac{\gamma PV}{M}}$

$C_p=\frac{R\gamma }{\gamma -1}$

or $21(\gamma -1)=8.3\gamma$

or $21\gamma -8.3\gamma =21$

or $12.7\gamma =21$

$\therefore \gamma =\frac{21}{12.7}=1.653$

v = $\sqrt{\frac{1.653\times 1.0\times {10}^5\times 0.0221}{4\times {10}^{-3}}}$

= 960 m/s