If you combine 360.0 mL of water at 25.00 °C and 120.0 mL of water at 95.00 °C, what is the final temperature of the mixture? Use 1.00 g/mL as the density of water.
heat gained by cool water + heat lost by warm water = 0
[mass warm water x specific heat H2O x (Tfinal-Tinitial)] + [mass cool water x specific heat H2O x (Tfinal0Tinitial)] = 0
Substitute and solve for Tf.
To find the final temperature of the mixture, you can use the principle of energy conservation. The total amount of energy in the system before and after mixing should be equal.
To solve this problem, you can use the equation:
(mass 1 × specific heat capacity × change in temperature 1) + (mass 2 × specific heat capacity × change in temperature 2) = 0
Where:
- mass 1 is the mass of the first sample of water (360.0 mL).
- mass 2 is the mass of the second sample of water (120.0 mL).
- specific heat capacity is the amount of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius (4.18 J/g°C for water).
- change in temperature 1 is the difference between the initial temperature and the final temperature of the first sample of water (Tfinal - 25.00 °C).
- change in temperature 2 is the difference between the initial temperature and the final temperature of the second sample of water (Tfinal - 95.00 °C).
We know that the density of water is 1.00 g/mL. So we can calculate the masses of the two samples of water using their volumes (mass = volume × density).
mass 1 = 360.0 mL × 1.00 g/mL = 360.0 g
mass 2 = 120.0 mL × 1.00 g/mL = 120.0 g
Now we can substitute these values into the equation and solve for the final temperature (Tfinal).
(360.0 g × 4.18 J/g°C × (Tfinal - 25.00 °C)) + (120.0 g × 4.18 J/g°C × (Tfinal - 95.00 °C)) = 0
(1503.60 J/°C × (Tfinal - 25.00 °C)) + (502.80 J/°C × (Tfinal - 95.00 °C)) = 0
Now we can simplify the equation and solve for Tfinal:
1503.60(Tfinal) - 37590 + 502.80(Tfinal) - 47640 = 0
2006.40(Tfinal) - 85230 = 0
2006.40(Tfinal) = 85230
Tfinal = 85230 / 2006.40 = 42.5 °C
Therefore, the final temperature of the mixture is 42.5 °C.