The volume of a gas is ______ when the pressure is reduced to half and the absolute temperature is doubled.

halved

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doubled

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tripled

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quadrupled

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Solution

The correct option is C quadrupled
From ideal gas equation, we know the relation, $\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$
Here, $P_{1} = P T_{1} = T V_{1} = V P_{2} = \frac{P}{2} T_{2} = 2 T V_{2} = ?$
$\frac{P V}{T} = (\frac{P}{2}) (\frac{V_{2}}{2 T}) V_{2} = 4 V$
So, volume is $q u a d r u p l e d .$

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