The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 K, is
Question
The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 K, is
Solution
The speed of sound in a gas is given by the formula:
v = sqrt(γRT/M)
where:
- v is the speed of sound,
- γ is the adiabatic index (which is approximately 1.4 for both nitrogen and helium at room temperature),
- R is the universal gas constant,
- T is the temperature in Kelvin,
- M is the molar mass of the gas.
Given that the temperature and γ are the same for both gases, the ratio of the speed of sound in nitrogen to that in helium is therefore given by the square root of the inverse ratio of their molar masses.
The molar mass of nitrogen (N2) is approximately 28 g/mol, and the molar mass of helium (He) is approximately 4 g/mol.
Therefore, the ratio of the speed of sound in nitrogen to that in helium is sqrt(4/28) = sqrt(1/7) ≈ 0.378.
So, the speed of sound in nitrogen is approximately 0.378 times the speed of sound in helium at 300 K.
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