Question

Match the following graphs of ideal gas with their co-ordinates :
(X) (Y)
(Z)

$\begin{array}{cccc}& \text{Graphs}& & \text{x and y co-ordinates}\\ \text{(A)}& \text{X}& \text{i)}& pV\text{vs.}V\\ \text{(B)}& \text{Y}& \text{ii)}& p\text{vs.}V\\ \text{(C)}& \text{Z}& \text{iii)}& p\text{vs.}\frac{1}{V}\end{array}$

Answer 1

From ideal gas equation $pV=nRT$
$\frac{pV}{nT}=$ constant
At constant $n$ and $T$ ,
$pV=$ constant

$\left(X\right)\to \left(ii\right)$,



If we plot a graph between $p$ and $V$, on decreasing the pressure, volume will increase. This is because according to Boyle’s law, $p$ and $V$ are inversely related.
$pV=$ constant ( For, constant $n$ and $T$) So, the plot of $p$ vs $V$ should be hyperbola.
Hence, option $\left(A\right)$ is the correct match for option $\left(ii\right)$.

$\left(Y\right)\to \left(iii\right)$,
If we plot a graph between $p$ vs. $\frac{1}{V}$ , we will get a straight line. This is because according to Boyle’s law, pressure is inversely proportional to the volume. But in this case, the value of the volume is $\frac{1}{V}$
Therefore, $p\propto \frac{1}{V}$
$V^{\prime }=\frac{1}{V}$ , puts this value in the above equation.
$p=1\times V^{\prime }$
$p\propto V^{\prime }$
Since, $p$ is directly proportional to $\frac{1}{V}$ ,
thus, on increasing the value of $p$, the value of $\frac{1}{V}$ will also increase and plot will be a straight line.


Hence, option $\left(B\right)$ is the correct match for option $\left(iii\right)$.

$\left(Z\right)\to \left(i\right)$,
If we plot a graph $pV$ vs. $V$, in this case, $pV$ is constant (at constant temperature and for constant $n$). Hence, the value of $pV$ will be constant irrespective of the value of $V$. So, the plot will be a horizontal straight line.


Hence, option $\left(C\right)$ is the correct match for option $\left(i\right)$.

The correct matches can be represented as:

$\begin{array}{cccc}& \text{Graphs}& & \text{x and y co-ordinates}\\ \text{(A)}& \text{X}& \text{i)}& p\text{vs.}V\\ \text{(B)}& \text{Y}& \text{ii)}& p\text{vs.}\frac{1}{V}\\ \text{(C)}& \text{Z}& \text{iii)}& pV\text{vs.}V\end{array}$