Pressure versus temperature graph of an ideal gas is as shown in … - Vidyadip

MCQ

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
$\frac{3}{4}\,{\rho _0}$
✓
$\frac{3}{2}\,{\rho _0}$
C
$\frac{4}{3}\,{\rho _0}$
D
$2\,{\rho _0}$

✓

Answer

Correct option: B.

$\frac{3}{2}\,{\rho _0}$

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 $\left(\frac{P}{T}\right)_{B}$

$=\frac{3}{2}\left(\frac{P_{0}}{T_{0}}\right)\left(\frac{P}{T}\right)_{B}=\frac{3}{2}\left(\frac{P}{T}\right)_{A}$

$\therefore \quad \rho_{B}=\frac{3}{2} \rho_{A}=\frac{3}{2} \rho_{0}$

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