# Sketch the graph of pV vs p when the temperature of the gas is constant. here p means pressure and V means volume - showing you the direct relationship b/w p and V (by using pV). how to sketch it???

Jun 28, 2016

We know that the Ideal gas equation is
$P V = n R T$
where
$P$ is the pressure
$V$ is the volume
$n$ is the number of moles of amount of substance of gas
$R$ is the ideal, or universal, gas constant.
$T$ is the temperature of the gas

Since temperature is kept constant the RHS of the equation is a constant.
$\implies P V = \text{Constant}$

As such the graph of $P V$ against $P$ should be a straight line parallel to the $P$ axis.

We can test this by plotting $P V$ vs $P$ of experimental values as shown below.

The computer gives the equation for the best fit line as

$P V = - 0.149 P + 6192.8$

This implies that the line starts at $P V = 6183.86$ at the left hand end and finishes at $6163.0$ at the right hand end.

Using only two significant figures for the $P V$ product, it starts and ends at $6200$.

Therefore, within the limits of experimental error,

$P V = \text{constant}$Boyle's Law