Kinetic Theory of Gases Lab - Physics Simulations

t = 0.00s

Live Telemetry & Summary

Helium (4g/mol) has high speeds; Argon (40g/mol) moves sluggishly at the same temperature.

RMS Speed (v_rms):1367.7 m/s

Mean Molecular KE:6.213e-21 J

Molar Mass (M):4 g/mol

Variable Adjuster

Temperature (T)300K

100500

Molar Mass (M)4g/mol

440

Kinetic Theory of Gases

KINE

The Kinetic Theory of Gases models gas behavior as a large number of submicroscopic particles (atoms/molecules) in constant, rapid, random motion. The average translational kinetic energy of the molecules is directly proportional to the absolute temperature. Heavier molecules travel slower at a given temperature than lighter ones.

v_{rms} = \sqrt{\frac{3RT}{M}}, \quad KE_{avg} = \frac{3}{2} k_B T

Whiteboard Solver Steps

Step 1

Root-Mean-Square Molecular Velocity

The RMS speed is the measure of the speed of particles in a gas, which depends directly on the absolute temperature and inversely on molecular mass.

v_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3 \cdot 8.314 \cdot 300}{0.004}} = 1367.7 \text{ m/s}

Step 2

Mean Kinetic Energy of Molecule

According to kinetic theory, temperature is a direct macro measurement of the average translational kinetic energy of the gas molecules.

KE_{avg} = \frac{3}{2} k_B T = 1.5 \cdot (1.38 \cdot 10^{-23}) \cdot 300 = 6.213e-21 \text{ J}