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Question

Air in a cylinder is suddenly compressed by a piston, which is then maintained at the same position. With the passage of time :

A
the pressure decreases
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B
the pressure increases
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C
the pressure remains the same
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D
the pressure may increase or decrease depending upon the nature of the gas
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Solution

The correct option is A the pressure decreases
From the First Law of Thermodynamics,
dQ=dU+dW
Sudden processes are adiabatic, so dQ=0
dU=dW
In compression, dW<0
So, dU>0 which means dT>0
With passage of time (i.e. slow process), piston is maintained at the same place. Hence, Volume is constant.
So, P α T.
As temperature decreases with time, pressure decreases too.

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