An ideal gas with γ = 1.5 and an initial volume of 1 litre at 300 K is suddenly compressed until its volume is halved. Determine the ratio of the final pressure to the initial pressure.

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Correct answer: A. 2 2

For a sudden compression, the process is adiabatic.

The relation between pressure and volume is

P_1 V_1^\gamma = P_2 V_2^\gamma

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The ratio of the final pressure to the initial pressure is

\dfrac{P_2}{P_1} = \left(\dfrac{V_1}{V_2}\right)^\gamma

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Given that the final volume is half the initial volume,

V_1 = 2V_2

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Substituting the values gives

\dfrac{P_2}{P_1} = (2)^{1.5} = 2^{3/2} = 2\sqrt{2}

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An ideal gas with γ = 1.5 and an initial volume of 1 litre at 300 K...

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