Plot a Maxwell Boltzmann distribution graph using Sage

MaxwellBoltzmann.py

""" Maxwell–Boltzmann distribution
    See https://en.m.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution
    Written by PM 2Ring 2021.06.20
"""
# Gas constant g⋅m^2⋅s^−2⋅K^−1⋅mol^−1
R = 8314.46261815324

@interact
def _(T=('temp (°C)', 20), mass=('mass (g/mol)', 29),
  auto_update=False):
    T += 273.15
    vp2 = 2 * T * R / mass
    vp = sqrt(vp2)
    a = 4*pi / (pi * vp2)^1.5
    vm = 2 * vp / sqrt(pi)
    vr = vp * sqrt(3/2)
    print(f"Mode speed {n(vp)} m/s")
    print(f"Mean speed {n(vm)} m/s")
    print(f"RMS speed {n(vr)} m/s")

    def f(v):
        v2 = v^2
        return a * v2 * exp(-v2 / vp2)

    P = points([(v, f(v)) for v in (vp, vm, vr)], color="red")
    P += plot(f, (0, pi * vm), gridlines="major", frame=True,
       title=f"Maxwell–Boltzmann distribution, {T=:.2f} K, {mass=:.2f} g/mol",
       axes_labels=["Speed (m/s", "Probability"], axes_labels_size=1.15)
    P.show( )

Live demo on SageMathCell