Relationship between Kinetic Energy and Temperature

Average translational kinetic energy of particles $――――― 𝐸 k - t r a n s$ and temperature $𝑇$ enjoy a direct, one-to-one proportionality, as shown by the Ideal gas law

――――― 𝐸 k - t r a n s = 12 𝑚 ―― 𝑣 2 = 32 𝑘 𝑇

where $𝑘 = 1.381 \times 10 - 23 J K - 1$ is Boltzmann's constant.

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