# PV-P diagram and the Boyle temperature

If we define y = pv and use the equation of the real gases, we obtain:

${y}^{3}-\left(bp+RT\right){y}^{2}+apy-ab{p}^{2}=0$

which will allow us to obtain the pv-p curves for a given temperature. The equation:

$b{y}^{2}-ay+2ap=0$

corresponds to the curve that connects the minimum values of the pv-p curve.

The files for this calculation are in folder pvdiagrams/3_boyle/.

Minima of the pvp-p curves.
pmin [atm] pvmin [atmL/mol]
-10.1642.236
21.3395.121
52.25412.541
60.76215.798
71.20818.514
144.72357.889
128.80396.602
64.949129.898
70.572141.145
75.548151.097

The calculated Boyle temperature is 1714.135 K.