# Graham's law

One of the gas laws, Graham's law states that the average kinetic energy of the molecules of two samples of different gases at the same temperature is identical. It is named for Thomas Graham, who formulated it.

The formula for the kinetic energy of a particle is:

[itex]KE={1 \over 2}mv^2[itex]

where KE is the kinetic energy, m is the mass of the particle, and v is the average velocity of the particles.

In order to relate the velocities of two particles, a and b, at the same temperature, this formula is written as:

[itex]{v_a \over v_b}=\sqrt{m_b \over m_a}[itex]

where [itex]m_a[itex] and [itex]v_a[itex] are the mass and velocity of particle a and [itex]m_b[itex] and [itex]v_b[itex] are the mass and velocity of particle b, respectively. Thus, the particles of hydrogen gas are four times as fast as those of oxygen, because the latter have a mass which is 16 times as large.

The law is also named Amontons' law after Guillaume Amontons, who discovered it in 1702.

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