An adiabatic cylinder contains an ideal gas. It is fitted with a freely movable insulating piston. In one experiment the piston is pulled out very fast to double the volume of the gas. In another experiment starting from same initial state, the piston is pulled out very slowly to double the volume of the gas. Which of the following is true?

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The final pressure in second experiment is higher than its original value

The final pressure in experiment I is higher than its original value

In both the experiments, the final pressure is lesser than the original value

In both the experiments, the final pressure is higher than original one

answer is D.

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Detailed Solution

When the piston is pulled out very fast, it is like free expansion of the gas. The gas temperature does not change. Therefore, PV = a constant and at the end the pressure becomes half the original value.
In second experiment the gas performs work. Therefore, its internal energy falls (notice that $∆$ Q = 0). It means final temperature of the gas is less than its initial temperature.
$∴ P_{1} V_{1} > P_{2} V_{2}$
If V₂ = 2V₁, it means final pressure will be less then the original value.