Graphical Representations of Gas Behaviour

Pressure and volume are inversely related at constant temperature and moles, so a plot of P versus V curves downward — a hyperbola, following PV = constant. Plot P against 1/V instead, and that same relationship becomes a straight line through the origin, because P = constant x (1/V) matches the form y = mx. This is the whole trick behind reading gas graphs: pick the variable pairing that matches the mathematical form of the law, and a curve straightens out. Gay-Lussac's Law (P directly proportional to T at constant V and n) and Charles's Law (V directly proportional to T at constant P and n) both already give straight lines when graphed against Kelvin temperature, because they are direct proportions.

For a P versus T graph at constant volume, the line passes through the origin only if T is in Kelvin — extend it backward and it hits zero pressure at zero Kelvin, the theoretical point where an ideal gas would exert no pressure at all. The slope itself depends on nR/V: more moles or smaller volume makes a steeper line. For a V versus T graph, doubling the moles of gas doubles the slope, since slope = nR/P. A straight line on any of these graphs only confirms proportionality over the range you actually tested — real gases bend away from ideal lines at high pressure or low temperature, where molecules take up real space and attract each other.

This topic is the visual partner to the combined and ideal gas laws from earlier in the unit: same equations, now read off axes instead of plugged into formulas, and it sets up later comparisons between ideal and real gas behavior.