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Practice & Assess

Kinetic Theory of Gases

Watch gas molecules in motion and understand temperature at the molecular level

Live Metrics

Mean Kinetic Energy

Sim

Target

9.79Target: 10.13

RMS Speed Estimate

Sim

Target

4.4 m/sTarget: 4.5 m/s

Pressure

0.0 kPa

Sum of molecular collisions on walls

Live Calculation

Mean Kinetic Energy

\overline{E_{k}} = \frac{3}{2} k_{B} T

= \frac{3}{2} \times 1.38 \times 1 0^{- 23} \times 300 K

\approx 6.21 \times 1 0^{- 21} J

RMS Speed Estimate

v_{rms} = \frac{3 k _{B} T}{m}

= \frac{3 \times 1.38 \times 1 0 ^{- 23} \times 300}{1 u}

\approx 4.4 m s^{- 1}

Speed DistributionAvg Speed: 4.1 m/s

—Maxwell–Boltzmann

PEAK: 10

0Speed Distribution (m/s)11

Experiment Setup

Temp (K)300 K

Gas Type1u / particle

N Molecules80

Key Concepts

DSE Definition

Temperature is a measure of the average random kinetic energy of gas molecules.

Ideal Gas

Assume: Point masses, no intermolecular forces, perfectly elastic collisions.

Maxwell–Boltzmann Distribution

At a fixed temperature, gas molecules have a spread of speeds. The Maxwell–Boltzmann distribution describes how many molecules move at each speed — not all molecules move at the same rate.

Speed DistributionAvg Speed: 4.1 m/s

—Maxwell–Boltzmann

PEAK: 10

0Speed Distribution (m/s)11