Final answer:
The final temperature of the mixture can be calculated using the principle of energy conservation. We can use the equations Q = mcΔT and ΔT = Q/(mc) to calculate the heat transferred and the final temperature, respectively.
Step-by-step explanation:
In this question, we can calculate the final temperature of the mixture using the principle of energy conservation. First, we calculate the heat transferred from each substance using the formula Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Then, we add up the heat transferred from both substances and equate it to the heat gained by the final mixture. Finally, we solve for the final temperature using the formula ΔT = Q/(mc).
For the 50g of water at 10 degrees Celsius, the heat transferred is Q1 = (50g)(4.18 J/g°C)(T - 10). For the 120g of water at 80 degrees Celsius, the heat transferred is Q2 = (120g)(4.18 J/g°C)(T - 80). Since the system is isolated, the heat gained by the final mixture is equal to the sum of Q1 and Q2. So, Q1 + Q2 = (50g)(4.18 J/g°C)(T - 10) + (120g)(4.18 J/g°C)(T - 80). Solving this equation for T gives us the final temperature of the mixture.
Now, substituting the values in the equation and solving it, we get T = 60 degrees Celsius.