Question

A certain mass of water at 84 °C is poured into an equal mass of water at 24 °C. What will be the resulting temperature of the mixture ?

Answer 1

Data: mx = m2 = m (say), 

T₁ = 84 °C, T₂ = 24 °C, T = ? 

Heat lost by the hot water = heat gained by the cold water

∴ mc (T₁ - T) = mc (T - T₂)

∴ T₁ - T = T - T₂

∴ 2T = T₁ + T₂

∴ T = \(\cfrac{T_1+T_2}2\) = \(\cfrac{84^\circ C+24^\circ C}2\)

= \(\cfrac{108^\circ C}2\) = 54 \(^\circ\)C

Resulting temperature of the mixture = 54 °C.