Molecules are hard disks of mass m = 1 (units with k_B = 1). Collisions with each other and with the walls are perfectly elastic. Pressure in 2D is force per unit wall length, measured from the momentum handed to the walls: P = sum(2 m |v_n|) / (t * perimeter).

• Ideal gas in 2D: P A = N k T, with mean kinetic energy k T per molecule (two degrees of freedom).
• Speed distribution (2D Maxwell-Boltzmann): f(v) = (m v / kT) exp(-m v^2 / 2kT), the dashed curve.
• Adiabatic compression of a monatomic 2D gas: T A^(gamma-1) = const, gamma = 2; halving the area doubles T (heat bath off).
• Finite size: second virial coefficient of hard disks b = 2 pi r^2, so P (A - N b) ~ N k T.

Simplifications: no attraction between molecules, no rotation, the piston moves slowly compared with molecular speeds. Pressure readings are noisy for a few hundred molecules (scatter about 1/sqrt of the number of wall hits).