The Ideal Gas Law

For a fixed amount of ideal gas, $PV = nRT = Nk_BT$, and between any two states $P_1V_1/T_1 = P_2V_2/T_2$. Every familiar two-variable rule is that relation after the apparatus has pinned one quantity: a rigid container cancels $V$, a freely sliding piston cancels $P$, a bath at one temperature cancels $T$. The temperature is always absolute, because the law drives $P$ and $V$ to zero at $T = 0$ and that point defines the kelvin scale's origin. The model behind it assumes negligible particle volume and no appreciable force between collisions, while relying on those collisions being frequent and elastic.

Three errors dominate. Feeding degrees Celsius into the law or into a before-and-after ratio, which turns a $7\%$ pressure rise into a doubling and puts the extrapolated zero-pressure intercept at $0^\circ$C. Reaching for a two-variable shortcut on a process that changed a third quantity, so a gas that was compressed and heated gets solved as though only the volume moved. And reading the model's no-force assumption as no-collision, which removes the origin of pressure and the mechanism that brings a gas to thermal equilibrium.