• id: JTHERM-02-N15
• title: Temperature Dependence of the Maxwell-Boltzmann Distribution
• tags: distribution, temperature-effect, peak-shift

As temperature increases: (1) the peak of the Maxwell-Boltzmann distribution shifts to higher speeds ($v_p \propto \sqrt{T}$), (2) the peak height decreases, (3) the distribution broadens — more molecules have high speeds. The total area remains constant ($N$ molecules). At very low temperatures, the distribution is narrow and sharply peaked near zero. At high temperatures, it becomes broad and flat. The fraction of molecules above a given speed increases with temperature — this is why reaction rates increase with temperature (Arrhenius equation) and why lighter molecules can escape planetary atmospheres (escape velocity threshold). For two different gases at the same temperature, the lighter gas has a broader, more spread-out distribution.