Gas Physics

A Review of Basic Principles of Gas Physics.

To the Tune of The Entertainer

Energy and pressure are a function of molecular velocity.

 A molecule A molecule bouncing around inside a cube has kinetic energy, E = mv2 and pressure, P = 1/3 mv2/V.

Consider a cube of side L containing a molecule of a gas with momentum mvx. Each time it hits and recoils from a wall, it imparts an impulse, i = 2 * mvx. It reapeats this with a frequency, f = vx/(2*L) so the force on the wall, F = f * i = mvx2/L. For a number [N] of molecules, the force is F = Nmvx2/L. Now since the molecule may move in any one of three directions the average velocity [v2] = 3 * vx2. Thus, the pressure on any one wall [P] = F/A = 1/3 Nmv2/V and PV = 1/3 Nmv2.

Since the kinetic energy [Ek] = 1/2 Nmv2, PV = 2/3 Ek and Ek = 3/2 PV.

And since PV = nRT = NkT, E = 3/2 NkT and T = 2/3 E / (Nk)

Note: R = 8.31 J/mol-K and k = R/6*1023 = 1.38 * 10-23 J/molecule-K

Isothermal Expansion

For isothermal (constant temperature) processes, consider PV = NkT. Since T is constant, P = NkT / V, and pressure is directly inverse to volume.