A 30.0 g sample of water at 10.0°C is mixed with 50.0 g of water at 57.0°C in a calorimeter. Calculate the final temperature of the mixture
heat lost by warm water + heat gained by cold water = 0
[mass warm water x specific heat H2O x (Tfinal-Tintial)] + [mass cool water x speicif heat H2O x (Tfinal-Tinitial)] \ 0
Substitute and solve for Tfinal.
To calculate the final temperature of the mixture, we can use the principle of conservation of energy.
Here's how we can solve this problem step by step:
1. Determine the heat gained or lost by each sample of water.
- The heat gained or lost by a substance can be calculated using the formula:
Q = mcΔT
where Q is the heat absorbed or released, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
2. Calculate the heat gained by the colder water.
- The initial temperature of the colder water is 10.0°C.
- The specific heat capacity of water is approximately 4.184 J/g°C.
- Assuming no phase change, the heat gained or lost by the colder water is:
Q1 = m1cΔT1
where m1 is the mass of the colder water (30.0 g), c is the specific heat capacity of water, and ΔT1 is the change in temperature of the colder water.
3. Calculate the heat lost by the hotter water.
- The initial temperature of the hotter water is 57.0°C.
- Assuming no phase change, the heat gained or lost by the hotter water is:
Q2 = m2cΔT2
where m2 is the mass of the hotter water (50.0 g), c is the specific heat capacity of water, and ΔT2 is the change in temperature of the hotter water.
4. Since the heat gained by the colder water is equal to the heat lost by the hotter water, we can set up an equation:
Q1 = -Q2
m1cΔT1 = -m2cΔT2
5. Rearrange the equation to solve for the final temperature of the mixture:
ΔT1/ΔT2 = -m2/m1
(ΔT1 + 10.0°C) / (57.0°C - ΔT2) = -50.0 g / 30.0 g
6. Solve the equation for ΔT1 and ΔT2.
ΔT1 = -60.0ΔT2 / 17.0
ΔT2 = -510.0ΔT1 / 17.0
7. Substitute the calculated values of ΔT1 and ΔT2 into the equation to solve for the final temperature of the mixture.
(ΔT1 + 10.0°C) / (57.0°C - ΔT2) = -50.0 g / 30.0 g
8. Solve for the final temperature, which is given by ΔT1 + 10.0°C.
By following these steps, you should be able to calculate the final temperature of the mixture of water.