The speed of sound in hydrogen at `0^@C` is `1280 m s^(-1)`. The density of hydrogen at STP is `0.089 kg m^(-3)`. Calculate the molar heat capacities `(C_p and C_v)` of hydrogen.

Explanation

`V=1280 m//s`, `T=0^@C=273^@K`
Density of `H_2 = 0.089 kg//m^3`,
`R=8.3 J//mol-K`
At STP, `P=10^5 Pa`,
we know `V_(sound)= sqrt((gammap)/(rho))`
`1280= sqrt((gamma xx 10 ^5)/(0.089))`
or ` gamma= (1280 xx 1280 xx 0.089)/10^5`
`=1.48`
`C_p/C_v = gamma` or `C_p - C_v =R`
`C_v = (R)/(gamma-1) = (8.31)/(1.48-1)`
`=18.0 J//mol-k`
`C_p = gammaC_v=1.48 xx 18.0`
`=26.3//mol-K`.