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4.0 g of helium occupies 22400 cm3 at STP. The specific heat capacity of helium at constant pressure is 5.0 cal/mol-K. Calculate the speed of sound in helium at STP.

4.0 g of helium occupies 22400 cm3 at STP. The specific heat capacity of helium at constant pressure is 5.0 cal/mol-K. Calculate the speed of sound in helium at STP.

Grade:11

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
9 years ago
Sol. μ = 4g = 4 × 10^–3 kg, V = 22400 cm^3 = 22400 × 10^–6 m3 C base P = 5 cal/mol-ki = 5 × 4.2 J/mol-k = 21 J/mol-k C base P = γR/γ – 1 = γ * 8.3/γ – 1 ⇒ 21(γ – 1) = γ (8.3) ⇒ 21 γ - 21 = 8.3 γ ⇒ γ = 21/12.7 Since the condition is sTP, P = 1 atm = 10^5 pa V = √γf/f = √21/12.7 * 10^5/4 * 10^-3/22400 * 10^-6 = √21 * 10^5 * 22400 * 10^-6/12.7 * 4 * 10^-3 = 962.28 m/s

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