Question

Following is the $\frac{P V}{T}v/sP$ graph for $1g$ of oxygen gas at two different temperatures $T_{1}$ and $T_{2}$ .

Find the value of $\frac{P V}{T}$ at the point $A$ and also the relation between $T_{1}$ and $T_{2}$ if it is given the density of oxygen is $1.427kgm^{- 3}$ .

• A. $0.259 \, JK^{- 1}$ and $T_{1} < T_{2}$
• B. $8.314 \, g \, Jmol^{- 1} \, K^{- 1}$ and $T_{1}>T_{2}$
• C. $0.259 \, JK^{- 1}$ and $T_{1}>T_{2}$
• D. $4.28 \, g \, JK^{- 1}$ and $T_{1} < T_{2}$

Answer 1

Answer: (C)

$PV=\mu RT=\frac{m}{M}RT$ ,
where $m$ = mass of the gas
and $\frac{m}{M}=\mu =$ number of moles.
$\frac{P V}{T}=\mu R=a$ constant for all values of $P$ .
That is why, ideally it is a straight line.
$\therefore \frac{P V}{T}=\frac{1 g}{32 g m o l^{- 1}}\times 8.31Jmol^{- 1}K^{- 1}=0.259JK^{- 1}$
Also, $T_{1}>T_{2}$