Three perfect gases at absolute temperatures T₁,T₂ and T₃ are mixed. The masses of molecules are m₁,m₂ and m₃ and the number of molecules are n₁,n₂ and n₃ respectively. Assuming no loss of energy, the final temperature of the mixture is

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(2) (n₁T₁ + n₂T₂ + n₃T₃)/(n₁ + n₂ + n₃). Mixing with no loss of energy means the total internal energy is conserved. For each gas the energy is nᵢf/2k_BTᵢ with the same f throughout, so the mode factor cancels. n₁T₁+n₂T₂+n₃T₃=(n₁+n₂+n₃)T. T=(n₁T₁+n₂T₂+n₃T₃)/(n₁+n₂+n₃). The molecular masses do not enter: energy per molecule depends on temperature alone.

Three perfect gases at absolute temperatures T₁,T₂ and T₃ are mixed. The masses of molecules are m₁,m₂ and m₃ and the number of molecules are n₁,n₂ and n₃ respectively. Assuming no loss of energy, the final temperature of the mixture is

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