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An ideal gas undergoes adiabatic expansion from an initial condition (Tₐ, V₀) to a final condition (T₆, 5V₀). Another mole of the same gas expands isothermally from a different starting point (T₆, V₀) to the same final point (T₆, 5V₀). If the ratio of specific heats at constant pressure and volume for this gas is γ, what is the value of Tₐ/T₆?

1. 5 raised to the power of (γ-1)
2. 5 raised to the power of (1-γ)
3. 5 raised to the power of γ
4. 5 raised to the power of (1+γ)

Correct answer: 5 raised to the power of (γ-1)

Solution

For the adiabatic step, Ta*V0^(gamma-1) = T6*(5V0)^(gamma-1), so Ta/T6 = (5V0/V0)^(gamma-1) = 5^(gamma-1). That is option index 0, not the stored index 1 (5^(1-gamma)).

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