If a 100.0 g sample of water at 60.0 c is added to a 100.0 g sample of water at 10.0 c determine the final temperature of water. Assume no heat is lost to the surroundings

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,

Q ₁ = 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.