Question

The speed of sound in hydrogen at $0^{0}C$ is 1280 $m{s}^{-1}$. The desiny of hydrogen at STP is 0.089 kg $m^{-3}$. Calculate the molar heat capacities $C_p$ and $C_v$ of hydrogen.

Answer 1

$V=1280m/s,T=0^0={273}^{0}K$

Desiny of $H_2=0.089kg/m^3$

R = 8.3 J/mol-K

At STP, P = ${10}^{5}Pa,$

We know $V_{sound}$ = $\sqrt{\frac{\gamma p}{P}}$

1280 = $\sqrt{\frac{\gamma \times {10}^5}{0.089}}$

or $\gamma =\frac{1280\times 1280\times 0.089}{{10}^5}$

= 1.48

$\frac{C_p}{C_v}=\gamma or{C}_p-C_v=R$

$C_v=\frac{R}{\gamma -1}=\frac{8.31}{1.48-1}$

= 18.0 J\mol-K

$C_p=\gamma C_v=1.48\times 18.0$

= 26.3/mol-K