Pressure versus temperature graph of an ideal gas is shown. Density of gas at point A is $ρ_{0}$ . Find the density of gas B?

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Solution

Given : $T_{A} = T_{o}$ $P_{A} = P$ $P_{B} = 3 P$ $T_{B} = 2 T_{o}$
Density of gas at A $d_{A} = ρ_{o}$
Ideal gas equation : $P V = n R T$
OR $P V = \frac{m}{M} R T$ where $M$ is the molar mass of the gas
Using $d = \frac{m}{V}$ we get $P M = d R T$

$⟹$ $d = \frac{P M}{R T}$ ..........(1)

$∴$ $d_{A} = \frac{P_{A} M}{R T_{A}} = \frac{P M}{R T_{o}} = ρ_{o}$ ........(a)

Also $d_{B} = \frac{P_{B} M}{R T_{B}} = \frac{(3 P) M}{R (2 T_{o})} = \frac{3}{2} \frac{P M}{R T_{o}}$
$⟹$ $d_{B} = \frac{3}{2} ρ_{o}$

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A

ρ_{0}

B

Corresponding density $(ρ)$ versus volume (V) graph will be:

T_{1}

T_{2}

T_{1}

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