Question

A thermally insulated vessel contains two liquids with initial temperatures T₁ and T₂ and specific heats c₁ and c₂ , separated by a nonconducting partition. The partition is removed, and the difference between the initial temperature of one of the liquids and the temperature T established in the vessel turns out to be equal to half the difference between the initial temperatures of the liquids.

Determine the ratio m₁/m₂ of the masses of the liquids.

Answer 1

Let us suppose that the temperature of the mixture of the liquids having the initial temperatures T₁ and T₂ has become T. Since the vessel containing the mixture is thermally insulated (ΔQ= 0), we can write

i.e. the ratio of the masses of these liquids is inverse to the ratio of their specific heats.