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(D) The density $\rho$ of an ideal gas is given by the formula $\rho = \frac{M_w P}{RT}$,where $M_w$ is the molar mass,$P$ is the pressure,$R$ is the

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$0.5$

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(D) The density $\rho$ of an ideal gas is given by the formula $\rho = \frac{M_w P}{RT}$,where $M_w$ is the molar mass,$P$ is the pressure,$R$ is the gas constant,and $T$ is the absolute temperature.Given that the pressure $P' = 2P$ and the temperature $T' = 4T$.The new density $\rho'$ is given by $\rho' = \frac{M_w P'}{R T'}$.Substituting the values,we get $\rho' = \frac{M_w (2P)}{R (4T)} = \frac{1}{2} \left( \frac{M_w P}{RT} \right)$.Therefore,$\rho' = 0.5 \rho$.The density becomes $0.5$ times the original density.

$O_2$ gas is filled in a cylinder. If the pressure is doubled and the temperature is quadrupled,what will be the factor by which the density changes?

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