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For a certain ideal gas γ = 1.25. Find Cv and Cp.

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For a certain ideal gas $\gamma = 1.25$ . Find $C_v$ and $C_p$ . How much heat does $1.5\ \text{mol}$ of it need to warm by $12\ \text{K}$ at a steady pressure? ( $R = 8.31\ \text{J mol}^{-1}\text{K}^{-1}$ )

Need a reminder? The key ideaShow

Molar heat capacities: $C_v = \tfrac{f}{2}R$ and $C_p = C_v + R$ (Mayer), with $\gamma = \dfrac{C_p}{C_v}$ . Monatomic: $12.5\ \text{J mol}^{-1}\text{K}^{-1}$ , $20.8\ \text{J mol}^{-1}\text{K}^{-1}$ , $\gamma = 1.67$ . Diatomic: $20.8\ \text{J mol}^{-1}\text{K}^{-1}$ , $29.1\ \text{J mol}^{-1}\text{K}^{-1}$ , $\gamma = 1.40$ . $Q = nC\,\Delta T$ , and $\Delta U = nC_v\,\Delta T$ in every process.

The worked solution

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← A gas heated at a steady pressure takes in 1540 J.0.40 mol of a diatomic ideal gas is at 290 K and 1.5 × 10⁵ Pa. →

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