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A diatomic ideal gas is taken through an adiabatic compression until its volume becomes 1/32 of the original value. If the initial temperature is T_i kelvin and the final temperature is T_f, what is the value of α?

1. 8
2. 4
3. 3
4. 5

Correct answer: 4

Solution

In an adiabatic process for a diatomic ideal gas, the relationship between the initial and final temperatures and volumes is given by the equation T_f / T_i = (V_i / V_f)^(γ-1), where γ is the heat capacity ratio. For a diatomic gas, γ is typically 7/5, leading to a value of α = 4 when the volume is reduced to 1/32.

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