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???

We know that the Ideal gas equation is
#PV = nRT#
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.
#=>PV="Constant"#

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

We can test this by plotting #PV# vs #P# of experimental values as shown below.

The computer gives the equation for the best fit line as

#PV= -0.149P + 6192.8#

This implies that the line starts at #PV = 6183.86# at the left hand end and finishes at #6163.0# at the right hand end.

Using only two significant figures for the #PV# product, it starts and ends at #6200#.

Therefore, within the limits of experimental error,

#PV = "constant"# → Boyle's Law