Answer :
The final temperature of the baby formula mixture prepared from 210 ml of milk at 62°C and the same amount at 4°C will be 33°C. This is determined using the principle of conservation of energy. The heat lost by the hot milk equals the heat gained by the cold milk.
To determine the final temperature when two quantities of milk at different temperatures are mixed, we can use the principle of conservation of energy. Assuming no heat is lost to the surroundings, the heat lost by the hot milk will equal the heat gained by the cold milk.
Let T be the final temperature of the mixture. The heat lost by the hot milk is:
Qlost = mhot * c * (Tinitial, hot - T)
The heat gained by the cold milk is:
Qgained = mcold * c * (T - Tinitial, cold)
Given:
- mass of both quantities of milk (mhot and mcold) = 210 g
- specific heat capacity of water (c) = 4.18 J/g°C
- Tinitial, hot = 62°C
- Tinitial, cold = 4°C
Setting the heat lost equal to the heat gained:
210 g * 4.18 J/g°C * (62°C - T) = 210 g * 4.18 J/g°C * (T - 4°C)
Simplifying, we get:
(62°C - T) = (T - 4°C)
62 - T = T - 4
62 + 4 = 2T
66 = 2T
T = 33°C
Therefore, the final temperature of the baby formula mixture is 33°C.
