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A monoatomic ideal gas is enclosed in a thermally insulating container and fitted with a movable insulating piston. The gas is compressed slowly until its volume becomes 12.5% of the original value. If the initial temperature is T0, what is the final temperature of the gas?

1. 4T0
2. 3T0
3. (2/3)T0
4. T0

Correct answer: 4T0

Solution

In an adiabatic process for a monoatomic ideal gas, the relationship between temperature and volume is given by the equation T1 * V^(γ-1) = T2, where γ (gamma) is the heat capacity ratio. For a monoatomic gas, γ = 5/3, and since the volume is reduced to 12.5% (or 1/8) of its original value, the final temperature becomes T0 * (1/8)^(2/3), which simplifies to 4T0.

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