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QPages 77-80: Q33: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Pages 77-80: Q33 Solution: 4.0 g of helium occupies at STP. The specific heat capacity of…

4.0 g of helium occupies 22400 cm322400 \text{ cm}^3 at STP. The specific heat capacity of helium at constant pressure is 5.0 cal K−1 mol−15.0 \text{ cal K}^{-1} \text{ mol}^{-1}. Calculate the speed of sound in helium at STP.

Step-by-Step Verified Solution

**Answer:** v=1020v = 1020 m/s. **Step-by-Step Explanation:** Given: He mass = 4 g, volume = 22400 cm_ at STP, Cp=5.0C_p = 5.0 cal/mol-K. Cp=5.0×4.18=20.9C_p = 5.0 \times 4.18 = 20.9 J/mol-K. Cv=Cp−R=12.6C_v = C_p - R = 12.6 J/mol-K. γ=Cp/Cv=1.66\gamma = C_p/C_v = 1.66. v=γP/ρ=1.66×1054×10−3/22.4×10−3=1020v = \sqrt{\gamma P/\rho} = \sqrt{\frac{1.66 \times 10^5}{4 \times 10^{-3}/22.4 \times 10^{-3}}} = 1020 m/s.

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