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Degrees of Freedom and Kinetic Theory of Gases
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How many degrees of freedom the gas molecules have if under STP the gas density $\rho = 1.3 kg/m^3$ and the velocity of sound propagation in it is $330 ms^{-1}$?
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A
$5$
💡 Explanation:
Using v = sqrt(gamma * P / rho) and P = (rho/M)RT, we find gamma. Since v = 330 m/s, rho = 1.3 kg/m^3, and P = 1.013e5 Pa, gamma = v^2 * rho / P = 1.71. However, for standard gases, gamma = 1 + 2/f. With gamma = 1.4 (diatomic), f = 5. The provided data yields gamma approx 1.4, corresponding to f = 5.