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Question
4.0 g of helium occupies 22400 cm3 at STP. The specific heat capacity of helium at constant pressure is 5.0 cal K−1 mol−1. Calculate the speed of sound in helium at STP.
Solution
Given:
Specific heat capacity at constant pressure, Cp = 5.0 cal/mol-K
Cp = 5.0 × 4.2 J/mol-K
Cp = 21 J/mol-K
Volume of helium, V = 22400 cm3 = 0.0224 m3
At STP, P = 1 atm = 105 Pa
The speed of sound in gas,
`"v" = sqrt((gamma"p")/ρ) =sqrt((gamma "R" "T")/"M") = sqrt ( (gamma "P""V")/"M")`
`"C"_"p" = ("R"gamma)/(gamma -1)`
Or 21(γ − 1) = 8.3γ
⇒ 21γ − 8.3γ = 21
⇒ 12.7γ = 21
`therefore gamma = 21/12.7 = 1.653``"v" = sqrt ((1.653 xx 1.0 xx 10^5 xx 0.0224)/ (4 xx 10 ^-3))`
v = 960 m/s
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