Final answer:
In an isolated system with equal masses and specific heat capacities, the final temperature of a mixture of two water samples at different temperatures is the average of the initial temperatures. Thus, for water samples of 80.0°C and 10.0°C, the final temperature when mixed would be 45.0°C.
Step-by-step explanation:
The subject of this question is Physics, specifically the concept of heat transfer and thermal equilibration. The question deals with two samples of water at different temperatures being mixed and coming to a thermal equilibrium.
To find the final temperature of the water mixture, we can assume that because the mass and specific heat capacity of water are equal for both samples, the final temperature will be the average of the two initial temperatures.
This is due to the fact that in an isolated system (with no heat loss), the heat lost by the hot water will equal the heat gained by the cold water.
To calculate the final temperature, we use the formula:
(mass of hot water x specific heat capacity of water x temperature change of hot water) + (mass of cold water x specific heat capacity of water x temperature change of cold water) = 0
Since both masses and specific heat capacities are the same, and there's no heat loss to the surroundings, and ignoring the sign, the formula simplifies to:
(temperature of hot water + temperature of cold water) / 2 = final temperature
Hence, the final temperature is (80.0°C + 10.0°C) / 2 = 45.0°C.