Question

An ideal gas having density $1.7\times {10}^{-3}g$ at a pressure $1.5\times {10}^5$ Pa is filled in a 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 capacities $C_{p}and{C}_v$ of the gas,

Answer 1

Given data,

$\rho =1.7\times {10}^{-3}g/c{m}^3=17kg{m}^3$

$P=1.5\times {10}^{5}Pa$

$R=8.3J/mol-K$

Resonance frequancy of the gas $=3.0kHz$

Node separation in the kundt's tube $\frac{1}{2}=6cm$

So,$l=2\times 6=12cm=12\times {10}^{-2}m$

$=V=fl=3\times {10}^3\times 12\times {10}^{-2}=360m/s$

We know

$V_{sound}=\sqrt{\frac{\gamma P}{\rho }}$

$\therefore \frac{V^2\rho }{P}=\frac{(360{)}^2\times 1.7\times {10}^{-3}}{1.5\times {10}^5}=1.4688$

$C_P-C_V=R$ and $\frac{C_P}{C_V}=\gamma$

$C_v=\frac{R}{\gamma -1}=\frac{8.3}{0.4688}=17.7J/mol-K$

$C_p=R+C_v=8.3+17.7=26J/molK$