At standard temperature and pressure (STP),th | vedclass

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(C) The speed of sound in a gas is given by the formula $v = \sqrt{\frac{\gamma P}{\rho}}$,where $\gamma$ is the adiabatic index,$P$ is the pressure,a

Vedclass · Accepted Answer

$5$

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(C) The speed of sound in a gas is given by the formula $v = \sqrt{\frac{\gamma P}{ho}}$,where $\gamma$ is the adiabatic index,$P$ is the pressure,and $ho$ is the density.Rearranging for $\gamma$,we get $\gamma = \frac{v^2 ho}{P}$.At $STP$,$P = 1.013 	imes 10^5 \ Pa$.Substituting the given values: $\gamma = \frac{(330)^2 	imes 1.3}{1.013 	imes 10^5} = \frac{108900 	imes 1.3}{101300} \approx 1.4$.For an ideal gas,$\gamma = 1 + \frac{2}{f}$,where $f$ is the degree of freedom.Thus,$1.4 = 1 + \frac{2}{f} \Rightarrow 0.4 = \frac{2}{f} \Rightarrow f = \frac{2}{0.4} = 5$.

At standard temperature and pressure $(STP)$,the density of a gas is $1.3 \ kg/m^3$ and the speed of sound in the gas is $330 \ m/s$. The degree of freedom of the gas is:

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