One mole of an ideal gas starts at temperature T₁ and volume V₀ and expands adiabatically to a common final state at temperature T₃ and volume 5V₀. Another mole of the same gas starts at temperature T₂ and volume V₀ and expands isothermally to the same final state. If γ=Cₚ/Cᵥ, find T₁/T₂.
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Question

One mole of an ideal gas starts at temperature T₁ and volume V₀ and expands adiabatically to a common final state at temperature T₃ and volume 5V₀. Another mole of the same gas starts at temperature T₂ and volume V₀ and expands isothermally to the same final state. If γ=Cₚ/Cᵥ, find T₁/T₂.

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G1 Physics · Accepted Answer

Apply energy conservation. Sensible heat is Q=mcΔT and phase-change heat is Q=mL. Heat lost by hotter parts equals heat gained by colder parts. Evaluating the given data/statements gives A: 5γ-1. Therefore the correct answer is A.