A 25 gram sample of H2O at 37.3C is mixed with 45 grams of H2O at 72.9C. What is the Temperature final of the mixture.
To find the final temperature of the mixture, we can use the principle of conservation of energy. The total heat gained by the cooler water is equal to the total heat lost by the hotter water. We can use the equation:
(m1 * c1 * ΔT1) + (m2 * c2 * ΔT2) = 0
where:
m1 and m2 are the masses of the substances
c1 and c2 are the specific heat capacities of the substances
ΔT1 and ΔT2 are the changes in temperature for the substances
In this case, m1 is 25 grams, c1 for water is approximately 4.18 J/g°C, and ΔT1 is the change in temperature for the cooler water, which is equal to the final temperature minus the initial temperature (Tf - 37.3).
Similarly, m2 is 45 grams, c2 is 4.18 J/g°C , and ΔT2 is the change in temperature for the hotter water, which is equal to the final temperature minus the initial temperature (Tf - 72.9).
Using this equation, we can solve for the final temperature (Tf).
(25 * 4.18 * (Tf - 37.3)) + (45 * 4.18 * (Tf - 72.9)) = 0
125.5Tf - 5264.5 + 1887.9Tf - 30548.5 = 0
2013.4Tf = 35813
Tf = 17.8°C
Therefore, the final temperature of the mixture is approximately 17.8°C.