Final answer:
Using the formula Q = mcΔT, we can calculate the final temperature to be 50°C.
Step-by-step explanation:
To find the final temperature of the mixture, we can use the principle of energy conservation.
The heat lost by the hot water is equal to the heat gained by the cold water. We can calculate the heat lost or gained using the formula Q = mcΔT, where Q is the heat, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, we have 100 mL of water at 10 °C and 100 mL of water at 90 °C.
The specific heat capacity of water is 4.18 J/g °C. Let's assume the density of water is 1 g/mL for simplicity.
Using the formula Q = mcΔT, we can calculate the heat lost by the hot water:
Q(lost) = mcΔT = (100g)(4.18 J/g °C)(90 °C - T)
Similarly, we can calculate the heat gained by the cold water:
Q(gained) = mcΔT = (100g)(4.18 J/g °C)(T - 10 °C)
Since the heat lost is equal to the heat gained, we can equate the two equations:
(100g)(4.18 J/g °C)(90 °C - T)
= (100g)(4.18 J/g °C)(T - 10 °C)
Simplifying and solving for T, we find that the final temperature of the mixture is 50 °C.