sqrt8RTM

sqrt8RTM is an algebraic expression consisting of the square root of eight times the universal gas constant R, the temperature T, and the molar mass M. Because no parentheses are specified, its meaning depends on how it is written in a given context. The two common interpretations are sqrt(8RTM) and sqrt(8RT/M).

If written as sqrt(8RTM), this yields a quantity whose units depend on the units assigned to R, T, and M. With R ≈ 8.314 J/(mol·K), T in kelvin, and M in kg/mol, sqrt(8RTM) has unconventional units and is not a standard physical constant in thermodynamics or kinetic theory. It may appear in specialized or derived expressions but is not widely used as a standalone quantity.

If written as sqrt(8RT/M), the result has units of velocity, since RT/M has units of J/kg = m^2/s^2, and taking the square root gives m/s. In kinetic theory, sqrt(8RT/M) is closely related to a characteristic speed scale. Specifically, sqrt(8RT/M) = sqrt(π) times the most probable speed v_mp = sqrt(8RT/(πM)). Thus, it serves as a velocity scale that is larger than the root-mean-square or most probable speeds by a factor of about 1.77 to 2.83, depending on comparison.

Example: for dry air at 300 K, M ≈ 0.029 kg/mol, RT/M ≈ 8.6×10^4 m^2/s^2, giving sqrt(8RT/M) ≈ 8.3×10^2 m/s.

In summary, sqrt8RTM lacks a single universal meaning and is context-dependent; when interpreted as sqrt(8RT/M), it provides a velocity scale related to standard speed measures in kinetic theory. See also Maxwell-Boltzmann distribution, kinetic theory, root-mean-square speed.