First slide

laws

Question

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

Moderate

A

$\frac{3}{4} ρ_{0}$
B

$\frac{3}{2} ρ_{0}$
C

$\frac{4}{3} ρ_{0}$
D

$2 ρ_{0}$

Solution

PV = nRT
$\begin{array}{l} PV = \frac{m}{M} RT \\ P = \frac{ρRT}{M} \\ ρ \propto \frac{P}{T} \frac{ρ_{A}}{ρ_{B}} = \frac{P_{O}}{T_{0}} \frac{2 T_{O}}{3 P_{0}} = \frac{2}{3} \\ ρ_{B} = \frac{3 ρ_{0}}{2} \end{array}$

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