Question

$O_2$ is filled in a cylinder. When pressure is increased $2$ times, temperature becomes four times, then how much times their density will become

• A. $2$
• B. $4$
• C. $\frac{1}{4}$
• D. $\frac{1}{2}$

Answer 1

The correct option is D $\frac{1}{2}$

Apply ideal gas equation

$PV=n\overline{R}T$

$P=\frac{m}{M_{o}V}\overline{R}T$

$P=\frac{m}{V}\frac{\overline{R}T}{M_o}=\frac{\rho \overline{R}T}{M_o}$

$\rho =\frac{P{M}_o}{\overline{R}T}.......\left(1\right)$

In second event

${\rho }_2=\frac{P_2{M}_o}{\overline{R}{T}_2}=\frac{2P{M}_o}{\overline{R}\times 4T}=\frac{1}{2}\frac{P{M}_o}{\overline{R}T}=\frac{1}{2}\rho$

Hence, density become half