Question

What type of graph will you get when PV is plotted against P at constant temperature?

Answer 1

Hint: the fundamental units used in this question are pressure (P), volume(V) and temperature (T). We know that all these terms are correlated by certain laws like Boyle’s law, Charles’s law and Avogadro’s law. By using these three ideal gas equations were given.
Ideal gas equation: PV=nRT
Where, P=pressure
V=volume
n=number of moles
R=gas constant
T=temperature.

Complete answer:
Let us look at all the 3 laws in short and then come to the question.
Boyle’s law: Robert Boyle gave a law that states that pressure is inversely proportional to volume. That is $ P \propto \dfrac{1}{V} $ .
Charles’s law : Jacques Charles discovered that volume is directly proportional to temperature, that is $ V \propto T $ .
Avogadro’s law: Avogadro stated that volume is directly proportional to the number of moles of the compound. That is $ V \propto n $
Hence combined effect of these 3 laws gave the ideal gas equation:
 $ V \propto \dfrac{{nT}}{P} $
Or, $ VP = RnT $
Where R is the gas constant (universal constant).It has various values based on units,
 $ R = 8.3145Jmo{l^{ - 1}}{K^{ - 1}} $ or,
 $ R = 0.082L.atm.mo{l^{ - 1}}.{K^{ - 1}} $
Hence we see that according to ideal gas equation,
 $ PV = nRT $ , observe this equation, we see that R and n are constants. Now according to the question it has been given that temperature is constant , thus the R.H.S of the equation becomes constant.
Hence : PV=constant

Let us now plot PV against P,
And take temperature constant
Hence we will get a straight line parallel to the x axis.

Note:
Note that temperature has been kept constant the line will be parallel to x-axis(P) and not y (PV). This is because PV here is taken as y axis. It means y=constant. And a graph for y=constant is always parallel to the x axis.