Compare the theoretical speeds of sound in hydrogen (MH = 2.0 g/mol. γH = 1.4) with helium (MHe = 4.0 g/mol. γHe = 1.66 and R = 8334 j K-1 mol) at 0°C.

Solution

Here, by comparison we mean the ratio of speeds of sound in hydrogen and helium under the given conditions. In simple words it means that in the given condition of temperature (0°C), if sound travels with a speed of 1 m/s in hydrogen, what will be its speed in helium under this condition of temperature. Mathematically, it means to divide the speed of sound in helium by its speed in hydrogen.

Given

Mass of hydrogen = M_{H} = 2.0 g/mol

Adiabatic gas constant for hydrogen, γ_{H} = 1.4

Mass of helium = M_{He} = 4.0 g/mol

Adiabatic constant for helium, γ_{He} = 1.66

Gas constant = R = 8334 j/K mol

Temperature = T = 0°C = 273 K

Required

Ratio of speeds of sound in hydrogen and helium.

Formula

So, we calculate speed of sound in hydrogen and helium and then divide. Therefore, for hydrogen

Speed of sound in helium,

To find the ratio of speeds, divide equation (2) by equation (1),

Now put the values in this equation,

(And this means if sound travels with a speed of 1 m/s in hydrogen, it will travel with 0.77 m/s in helium under same conditions).

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