Pressure versus temperature graph of an ideal gas is as shown in figure. Density of the gas at point A is ρ0. Density at point B will be

Question

Pressure versus temperature graph of an ideal gas is as shown in figure. Density of the gas at point A is ρ0. Density at point B will be (A) (3/4)ρ0 (B) (3/2)ρ0 (C) (4/3)ρ0 (D) 2ρ0

Tardigrade Admin · Accepted Answer

ρ=(P M/R T) or ρ propto (P/T) ((P/T))A=(P0/T0) and ((P/T)) B =(3/2)((P0/T0)) ((P/T))B=(3/2)((P/T))A ∴ ρB=(3/2) ρA=(3/2) ρ0

Q. 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 point $B$ will be

$\frac{3}{4} ρ_{0}$

$\frac{3}{2} ρ_{0}$

$\frac{4}{3} ρ_{0}$

$2 ρ_{0}$

$ρ = \frac{PM}{RT}$ or $ρ \propto \frac{P}{T}$
$(\frac{P}{T})_{A} = \frac{P _{0}}{T _{0}}$ and $(\frac{P}{T})_{B} = \frac{3}{2} (\frac{P _{0}}{T _{0}})$
$(\frac{P}{T})_{B} = \frac{3}{2} (\frac{P}{T})_{A}$
$∴ ρ_{B} = \frac{3}{2} ρ_{A} = \frac{3}{2} ρ_{0}$

Q. Pressure versus temperature graph of an ideal gas is as shown in figure. Density of the gas at point A is ρ0​. Density at point B will be

43​ρ0​

23​ρ0​

34​ρ0​

2ρ0​