Standing waves of frequency `5.0 kHz` are produced in a tube filled with oxygen at `300k`. The separation between the consecutive nodes is `3.3 cm`. Calculate the specific heat capacities `(C_p and C_v)` of the gas.

Explanation

`f= 5 xx 10 ^3 Hz`,
`T=300K`, `l/2 = 3.3 cm`
:. `l=6.6 xx 10^(-2)m`
`V= fl=5 xx 10^3 xx 6.6 xx 10^(-2)`
`=(66 xx 5) = 330 m//s`
`v=sqrt((gammaRT)/(M)` or `v^2 = (gammaRT)/(M)`
`gamma=(330 xx 330 xx 32)/(8.3 xx 300 xx 100) = 1.3995`
`C_v=(R)/(gamma-1) = (8.3)/(0.3995)`
`=20.7J mol-K`
`C_p = C_v + R`
`=20.7J + 8.3`
`=29.07J/mol-K`.