States of Matter Particle Simulator

The box shows an animated particle model of the selected state. A panel to the right describes the state and reports the average particle speed relative to 300 K.

The state does not change when you drag the temperature; you pick it with the buttons. That is deliberate: the temperature at which a substance melts or boils depends on its intermolecular forces, so a single slider cannot place the phase change for every substance. Use the simulator to compare states at the same temperature, and to see what temperature alone does within one state.

Kinetic molecular theory links temperature to motion. The average kinetic energy of the particles is directly proportional to the absolute temperature: $$\overline{KE} \propto T \quad (T \text{ in kelvin})$$ Since $KE = \tfrac{1}{2}mv^2$, speed grows as the square root of temperature, $v \propto \sqrt{T}$, which is the rule the speed readout uses: $\text{factor} = \sqrt{T/300}$.

Each temperature also corresponds to a spread of speeds, not one speed. A Maxwell-Boltzmann distribution at higher temperature is lower and broader, with its peak shifted to higher speed. The simulator shows only the average, so sketch the distribution yourself when a question asks for it.

Question. A sample of N₂ gas is heated from 300 K to 600 K at constant volume. By what factor do the average kinetic energy and the average speed of the molecules change?

Kinetic energy. Average KE is proportional to kelvin temperature, so doubling T from 300 K to 600 K doubles the average kinetic energy: factor 2.

Speed. Speed scales with $\sqrt{T}$, so the factor is $\sqrt{600/300} = \sqrt{2} = 1.41$. Using the root-mean-square speed $v_{rms} = \sqrt{3RT/M}$ with $R = 8.314\ \text{J mol}^{-1}\text{K}^{-1}$ and $M = 0.028\ \text{kg/mol}$: at 300 K, $v_{rms} = 517$ m/s; at 600 K, $v_{rms} = 731$ m/s, and $731/517 = 1.41$.

Check it in the simulator. Select Gas and set the slider to 600 K; the readout shows $\times 1.41$. Drag down to 150 K and it shows $\times 0.71$, which is $\sqrt{1/2}$. A common wrong answer is that doubling T doubles the speed; the readout shows why it does not.

Extension. Helium at the same 300 K has the same average kinetic energy as N₂, but its molar mass is 7 times smaller, so its $v_{rms}$ is about 1370 m/s. Equal temperature means equal average KE, not equal speed.

Unit 3 asks you to connect macroscopic properties to particle-level models: draw or choose particle diagrams for each state (Topic 3.3), explain properties such as compressibility and fixed volume, and use kinetic molecular theory to explain how temperature affects particle motion and Maxwell-Boltzmann distributions (Topic 3.5). The same reasoning returns in Unit 5 when temperature changes the fraction of collisions with enough energy to react.