If the absolute temperature of a gas is doubled and the pressure is reduced to one half, the volume of the gas will:

Question

If the absolute temperature of a gas is doubled and the pressure is reduced to one half, the volume of the gas will: (A) remain unchanged (B) be doubled (C) increase four fold (D) be halved

Tardigrade Admin · Accepted Answer

For a gas, (P1V1/T1)=(P2V2/T2) (where T2=2T1,P2=(1/2),P1,V2=? ) (P1V1/T1) = (1/2) (P1× V2/2T1) V1=(V2/4) ∴ V2=4V1

Q. If the absolute temperature of a gas is doubled and the pressure is reduced to one half, the volume of the gas will:

remain unchanged

be doubled

increase four fold

be halved

be reduced to one-fourth

For a gas,
$\frac{P _{1} V _{1}}{T _{1}} = \frac{P _{2} V _{2}}{T _{2}}$ (where $T_{2} = 2 T_{1}, P_{2} = \frac{1}{2}, P_{1}, V_{2} = ?$ )
$\frac{P _{1} V _{1}}{T _{1}}$ = $\frac{1}{2}$ $\frac{P _{1} \times V _{2}}{2 T _{1}}$
$V_{1} = \frac{V _{2}}{4}$
$∴$ $V_{2} = 4 V_{1}$