We can use the heat
equation,
Q = mcΔT
Where Q is the amount of energy transferred (J), m is
the mass of the substance (kg), c is the specific heat (J g⁻¹ °C⁻¹) and ΔT is the temperature
difference (°C).
Let's say
heat gained by 100.10 g of water at 10°C = Q₁
heat lost from 100.0 g of water at 60 °C = Q₂
Final temperature of the mixture = T
Since, there is no heat is lost to the surroundings,
Q₁ = Q₂ mc(T - 10) = mc(60 - T)
Since, m is same for both sides (100.0 g) and c is a constant for the water, we can cut off m and c from both sides. Then,
(T - 10) =(60 - T)
2T = 60 + 10
2T = 70
T = 35 °C
Hence, final temperature of water is T = 35 °C.
