InterviewSolution
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InterviewSolution
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If c is r.m.s. speed of molecules in a gas and v is the speed of sound waves in the gas, show that c/v is constant and independent of temperature for al diatomic gases. |
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Answer» R.m.s speed of molecules of a gas c = \(\sqrt{\frac{3P}{ρ}}\) c = \(\sqrt{\frac{3RT}{M}}\) (I) [M = Molar mass] ∵ PV = nRT n = 1 Or P = \(\frac{RT}{V}\) ∴ \(\frac{p}{ρ}=\frac{RT}{M}\) [∴\(\frac{P}{δ}=\frac{\frac{RT}{v}}{\frac{M}{v}}=\frac{RT}{M}\) ] Speed of sound wave in gas, v = \(\sqrt{\frac{rP}{ρ}}\) v = \(\sqrt{\frac{rRT}{M}}\) (II) Dividing eqn (II) by eq.n (I), \(\frac{c}{v}=\frac{\sqrt{\frac{3RT}{M}}}{\sqrt{\frac{rRT}{M}}}\) \(\frac{c}{v}=\sqrt{\frac{3}{r}}\) [r = adiabatic constant for diatomic gas] r = \(\frac{7}{5}\) Thus, \(\frac{c}{v}\) = constant |
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