Question

The correct graph among the following given, if $T_1>T_2>T_3$ is:

• A.
  
• B.
• C.
• D. All of the above

Answer 1

The correct option is D All of the above

According to Boyle's law,
Pressure is inversely proportional to the volume of a gas at constant temperature. Thus, $PV=K,\text{where K is any constant}$
$\therefore P=\frac{K}{V}$
So P Vs V is a rectangular parabola.
From Gay lussac's law and Charles law $P$ and $V$ is proportional to temperature.
Greater the $T$ greater the $P$ and $V$

Thus the plot $P$ Vs $\frac{1}{V}$ is a straight line.
Again, according to ideal gas equation,
$PV=nRT$.
So as the temperature increases, $K$ also increases and accordingly the slope of the graph also increases.

Again, $PV=K$
$\Rightarrow lnP+lnV=lnK$
$\Rightarrow lnP=lnK-lnV$
Hence $lnP$ vs $lnV$ is a straight line with a negative slope.
Again, as the temperature increases, the value of $K$ also increases and hence intercept increases with increasing temperature.
Hence all are correct.