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Question
The speed of sound in hydrogen at 0°C is 1280 m s−1. The density of hydrogen at STP is 0.089 kg m−3. Calculate the molar heat capacities Cp and Cv of hydrogen.
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Solution
Given:
Velocity of sound in hydrogen, V = 1280 m/s
Temperature, T = 0°C = 273 K
Density of H2 = 0.089 kg/m3
R = 8.3 J/mol-K
At STP,
P = 105 Pa
We know:
`"V"_"sound" = (sqrt (gamma"p")/ρ )`
1280 = `sqrt ((gamma xx10 ^5)/0.089)`
Or `gamma = (1280 xx 1280 xx 0.089)/10^5`
= 1.46
`"C"_"p"/ "C"_"v" = gamma or "C"_"p" -"C"_"v" = "R" `
`"C"_"v" = "R"/(gamma-1) = 8.3 /(1.46-1)`
= 18.0J /mol -K
Cp = γ Cv =1.46 × 18.0
= 26.28 ≈ 26.3 / mol -K
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