For a given mass of a gas if pressure is reduced to half and absolute temperature is doubled the volume ( $V$ ) of the gas becomes

4

V

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2

V^{2}

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\frac{V}{4}

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8

V

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Solution

The correct option is D $4$ $V$
The ideal gas equation is $P V = n R T$
Hence, $V = \frac{n R T}{P}$ ......(1)
Pressure is reduced to half. $P^{'} = \frac{P}{2}$ ......(2)
Absolute temperature is doubled.
$T^{'} = 2 T$ ......(3)
Substitute (2) and (3) in (1).
$V^{'} = \frac{n R (2 T)}{(\frac{P}{2})} = 4 \frac{n R T}{P} = 4$ $V$

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Assertion: Volume of gas at 50 $^{0}$ C is V. Keeping the pressure constant, the temperature is doubled. Volume becomes 2V.

Reason: At constant pressure, the volume of gas is directly proportional its to absolute temperature.

\frac{v}{3}

\frac{T}{3} .

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