The ratio of the speed of sound in helium gas to that in nitrogen gas at same temperature is (γHe = \(\frac {5}{3}\), γN2 = 4 , M N2 =28)
The ratio of the speed of sound in helium gas to that in nitrogen gas at same temperature is (γHe = \(\frac {5}{3}\), γN2 = 4 , M N2 =28)
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v = √(rRT / M)
For Helium (He) and Nitrogen (N2), we have:
vHe / vN2 = √(5/3RT / 4)
vHe / vN2 = √(7/5RT / 14)
vHe / vN2 = √(5 x 28 / 7R)
vHe / vN2 = √(5RT / 3 x 4)
vHe / vN2 = 5 / √3
\(\frac {5}{\sqrt {3}}\)
\(\sqrt{\frac {7}{5}}\)
\(\sqrt{\frac {2}{7}}\)
\(\sqrt{\frac {5}{3}}\)
The Correct Option is A
Solution and Explanation
We know that
v = \(\sqrt {\frac {rRT}{M}}\)
\(\frac {v_{He}}{v_{N_2}}\) = \(\frac {\sqrt {\frac {5/3 RT}{4}}}{\sqrt {\frac {7/5 RT}{14}}}\)
\(\frac {v_{He}}{v_{N_2}}\) = \(\sqrt {\frac {5\times 28}{7R}} \sqrt {\frac {5RT}{3\times 4}}\)
\(\frac {v_{He}}{v_{N_2}}\) = \(\frac {5}{\sqrt {3}}\)
Therefore the correct option is (A) \(\frac {5}{\sqrt {3}}\)
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