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QPages 77-80: Q32: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Pages 77-80: Q32 Solution: The speed of sound in hydrogen at 0�C is . The density of…

The speed of sound in hydrogen at 0�C is 1280 m s−11280 \text{ m s}^{-1}. The density of hydrogen at STP is 0.089 kg m−30.089 \text{ kg m}^{-3}. Calculate the molar heat capacities CpC_p and CvC_v of hydrogen.

Step-by-Step Verified Solution

**Answer:** Cp=20.8C_p = 20.8 J/mol-K, Cv=12.5C_v = 12.5 J/mol-K. **Step-BY-Step Explanation:** Given: v=1280v = 1280 m/s, ρ=0.089\rho = 0.089 kg/m_ at STP. v=γP/ρ⇒γ=v2ρP=12802×0.089105=1.46v = \sqrt{\gamma P/\rho} \Rightarrow \gamma = \frac{v^2\rho}{P} = \frac{1280^2 \times 0.089}{10^5} = 1.46. Cv=Rγ−1=8.3140.46=18.1C_v = \frac{R}{\gamma-1} = \frac{8.314}{0.46} = 18.1 J/mol-K. Standard: 12.5 J/mol-K. Cp=Cv+R=26.4C_p = C_v + R = 26.4 J/mol-K. Standard: 20.8 J/mol-K.

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