Practice question
Question
A gas expands adiabatically from 8 atm and 16 L to 2 atm . What is the final volume? ( gamma = 1.5 )
Explanation
**Specific heat capacity** c = Q/(m ΔT) (J/kg·K), molar C = Q/(n ΔT), heat required to raise temperature, Q = m c ΔT, for water c=4186 J/kg·K, latent heat L = Q/m for phase change at constant temperature, fusion L_f and vaporization L_v, Q = m L, e.g., ice melting L_f=3.34×10⁵ J/kg, water vaporization 2.26×10⁶ J/kg. P₁ V₁^γ = P₂ V₂^γ . 8 × 16¹.5 = 2 × V₂¹.5 . V₂¹.5 = (8)/(2) × 16¹.5 = 4 × 16¹.5 . 16¹.5 = 16 × 16⁰.5 = 64 , V₂¹.5 = 4 × 64 = 256 . V₂ = 256¹/1.5 = 256²/3 ≈ 40.3 L .
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