Maxwell-Boltzmann Speed Distribution Calculator mechanism

Model scope

The formulas and stated computation are standard after the molar-mass conversion, but the spec is ambiguous because it names molar mass M while writes formulas in terms of molecular mass m. The exact review item is the missing definition/conversion of m versus M, plus the unstated domain T>0 and plot-density units. Verdict is NEEDS_REVIEW rather than PASS until those are made explicit.

• The speed formulas are correct only when m is the mass of one molecule in kilograms. The stated input is molar mass M, so the implementation must explicitly convert m=M/N_A, or use the equivalent forms v_p=sqrt(2RT/M), v_avg=sqrt(8RT/(pi M)), and v_rms=sqrt(3RT/M).
• The distribution formula is correct for the normalized three-dimensional speed probability density f(v), with v>=0, T>0, and m>0. It must not be labeled as a probability at an exact speed; probabilities require integrating f(v) over a speed interval.
• The specification does not state the required plot normalization, although the supplied f(v) has units of s/m and integral 1 over v from 0 to infinity.
• The model is specifically classical Maxwell-Boltzmann equilibrium statistics, not a general ideal-gas distribution at arbitrary density or temperature. The honest label should also mention the nonrelativistic and dilute-gas assumptions.

Units and conventions

• T is absolute temperature in kelvin, with T>0.
• M is molar mass in kg/mol after conversion from any displayed g/mol value; R=8.314462618 J/(mol K).
• Equivalently, m is molecular mass in kg and k_B=1.380649e-23 J/K.
• v is in m/s and f(v) is in (m/s)^-1, numerically s/m.
• The distribution plot is f(v)=4*pi*(M/(2*pi*R*T))^(3/2)*v^2*exp(-M*v^2/(2*R*T)) when using molar mass.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "M": 0.004,
    "M_unit": "kg/mol",
    "T": 300,
    "R": 8.314462618,
    "sampled_speeds_m_per_s": [
      0,
      1116.767
    ]
  },
  "expected_outputs": {
    "v_p_m_per_s": 1116.767,
    "v_avg_m_per_s": 1260.138,
    "v_rms_m_per_s": 1367.755,
    "plot_samples": {
      "f_0_s_per_m": 0,
      "f_at_v_p_s_per_m": 0.0007433
    },
    "curve_features": {
      "root": "v=0",
      "maximum": "v=v_p=1116.767 m/s",
      "high_speed_asymptote": "f(v)->0 as v->infinity"
    }
  },
  "working": "First compute RT/M=(8.314462618*300)/0.004=623584.69635 m^2/s^2. Then v_p=sqrt(2*623584.69635)=sqrt(1247169.3927)=1116.767 m/s. v_avg=sqrt((8/pi)*623584.69635)=sqrt(158? approximately 1587946.8)=1260.138 m/s. v_rms=sqrt(3*623584.69635)=sqrt(1870754.08905)=1367.755 m/s. For the density, alpha=M/(2RT)=0.004/(2*8.314462618*300)=8.01815e-7 s^2/m^2. At v=0, f=constant*0^2*exp(0)=0. At v=v_p, alpha*v^2=1, so f=(4/sqrt(pi))*sqrt(alpha)*exp(-1)=(2.25675833)*(1/1116.767)*0.367879=0.0007433 s/m."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification exposes undefined or nonphysical inputs at T=0, M=0, and T<0, and a factor-of-31.6 unit-convention error is possible if molar-mass units are not enforced. The calculator should reject these cases or clearly label the limiting behavior and units.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json