Practice question

**Heat capacity** at constant pressure C_p and volume C_v, C_p = C_v + R per mole, for solids Dulong-Petit C_v≈3R≈25 J/mol·K. Specific heat and latent heat govern temperature changes and phase transitions, Q = m c ΔT for heating, Q = m L for melting/boiling at constant T. For adiabatic: P₁ V₁^γ = P₂ V₂^γ . 4 × 18^γ = 12 × 6^γ . (18^γ)/(6^γ) = (12)/(4) ⇒ ((18)/(6))^γ = 3 ⇒ 3^γ = 3¹ . γ = 1 , but check context—PDF uses γ > 1 , approximate γ = 1.33 from typical values.Correction: 3^γ = 3 , but recheck: 18¹.33 / 6¹.33 ≈