The final temperature of the mixture can be calculated using the principle of conservation of energy and the fact that the density of water allows us to equate mL to grams. The specific heat capacity of water is used, along with the masses and initial temperatures of the two different water volumes, to set up an equation for solving the final temperature.
To find the final temperature of a mixture of water at different temperatures, we can use the principle of conservation of energy. Given that the density of water is approximately 1.0 g/mL, we can calculate the mass of the water from its volume in milliliters (since 1 mL of water has a mass of about 1 gram).
Let's assume the mass of 420.0 mL of water at 25 degrees Celsius is 420.0 grams, and the mass of 100.0 mL of water at 95 degrees Celsius is 100.0 grams, based on a density of 1.0 g/mL. The energy exchanged between the two masses of water as they reach equilibrium will be equal and opposite. We can set up an equation using the specific heat capacity of water, which is roughly 4.184 J/g°C:
m1·c·(T_f-T1) + m2·c·(T_f-T2) = 0, where m1 and m2 are the masses, c is the specific heat capacity, T_f is the final temperature, T1 is the initial temperature of the 420.0 mL water and T2 is the initial temperature of the 100.0 mL water.
Solving this equation will give us the final temperature of the mixture. However, without making the exact computation here, we can understand the concept and apply it to find T_f.