Question

Pressure versus temperature graph of an ideal gas is as shown in figure. Density of the gas at point $A$ is $\rho_{0}$. Density at point $B$ will be

• A. $\frac{3}{4}\rho_{0}$
• B. $\frac{3}{2}\rho_{0}$
• C. $\frac{4}{3}\rho_{0}$
• D. $2\rho_{0}$

Answer 1

Answer: (B)

$ \rho=\frac{P M}{R T}$ or $\rho \propto \frac{P}{T}$
$\left(\frac{P}{T}\right)_{A}=\frac{P_{0}}{T_{0}} $ and $\left(\frac{P}{T}\right)_{ B }=\frac{3}{2}\left(\frac{P_{0}}{T_{0}}\right)$
$\left(\frac{P}{T}\right)_{B}=\frac{3}{2}\left(\frac{P}{T}\right)_{A}$
$\therefore \rho_{B}=\frac{3}{2} \rho_{A}=\frac{3}{2} \rho_{0}$