An ideal gas having density `1.7 xx 10^(-3) g cm ^(-3)` at a pressure `1.5 xx 10^(5)Pa` is filled in Kundt tube. When the gas is resonated at a frequency of `3.0 KHz`, nodes are formed at a separation of `6.0 cm` . Calculate the molar heat capacites `(C_p and C_v)` of the gas.

Explanation

Given ` rho=1.7 xx 10^(-3) g//cm^3`
`=1.7 k//gm^3`
`P=1.5 xx 10 ^5 Pa`
`R=8.3 J//mol-K`,
`f= 3.0 KHz.`
Node separation in a Kundt's tube
`=l/2=6cm`
` l=12cm=12 xx 10^(-2) m`
So, `V = fl = 3 xx 10 ^3 xx 12 xx 10 ^-2`
`=360 m//s`
We know , speed of sound `=sqrt((gammap)/(rho))`
or `V^2 = (gammap)/(rho)`
:. `gamma=(v^2rho)/(rho) = ((360)^2 1.7)/(1.5 xx 10^5)`
`=1.4688`
` But `C_v = (R)/(gamma-1) = (8.3)/(0.4688)`
`=17.71 J//mol-K`.