How would I calculate this?
30.0 mL of pure water at 280. K is mixed with 50.0 mL of pure water at 307 K. What is the final temperature of the mixture?
heat lost by warm water + heat gained by cool water = 0
[mass warm water x specific heat water x (Tfinal-Tinitial)] + [mass cool water x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute and solve for Tf.
To calculate the final temperature of the mixture, you need to use the principle of conservation of energy.
Step 1: Determine the heat gained or lost by each sample of water.
Q1 = m1 * c * (Tf - T1)
Q2 = m2 * c * (Tf - T2)
Where:
Q1 and Q2 = heat gained or lost by each sample of water
m1 and m2 = mass of water (assuming the density of water is 1 g/mL, so the mass is equal to the volume in mL)
c = specific heat capacity of water (4.184 J/g·K, assuming the water is pure)
Tf = final temperature of the mixture
T1 = initial temperature of the first sample (280 K)
T2 = initial temperature of the second sample (307 K)
Step 2: Set up the equation using the principle of conservation of energy.
Q1 + Q2 = 0
Step 3: Substitute the values into the equation.
m1 * c * (Tf - T1) + m2 * c * (Tf - T2) = 0
Step 4: Substitute the mass values.
(30.0 g) * (4.184 J/g·K) * (Tf - 280 K) + (50.0 g) * (4.184 J/g·K) * (Tf - 307 K) = 0
Step 5: Solve for Tf.
(125.52 J/K) * (Tf - 280 K) + (208.4 J/K) * (Tf - 307 K) = 0
(125.52 J/K * Tf - 35140.8 J) + (208.4 J/K * Tf - 63980.8 J) = 0
333.92 J/K * Tf = 99121.6 J
Tf = 296.49 K
Therefore, the final temperature of the mixture is approximately 296.49 K.
To calculate the final temperature of the mixture, you can use the principle of energy conservation. The total energy before the mixing should equal the total energy after the mixing.
In this case, the energy can be calculated using the formula:
Energy = mass * specific heat capacity * temperature
Since the two substances being mixed are both pure water, they have the same specific heat capacity. Therefore, we can represent the energy equation as:
(Energy1 + Energy2) = (mass1 * temperature1 + mass2 * temperature2)
Let's break down the problem into steps:
Step 1: Calculate the energy for each sample of water.
Energy1 = mass1 * temperature1
= (30.0 mL) * (1.00 g/mL) * (280. K) (using the density of water as 1.00 g/mL)
= 8400 J
Energy2 = mass2 * temperature2
= (50.0 mL) * (1.00 g/mL) * (307 K) (using the density of water as 1.00 g/mL)
= 15350 J
Step 2: Calculate the total energy before the mixing.
Total Energy before mixing = Energy1 + Energy2
= 8400 J + 15350 J
= 23750 J
Step 3: Calculate the total mass of the mixture.
Total mass = mass1 + mass2
= (30.0 mL) * (1.00 g/mL) + (50.0 mL) * (1.00 g/mL)
= 80.0 g
Step 4: Calculate the final temperature of the mixture.
Total Energy after mixing = Total mass * final temperature
Since the total mass and total energy are known, we can rearrange the formula to solve for the final temperature:
Final temperature = Total Energy after mixing / Total mass
= 23750 J / 80.0 g
= 296.88 K
Therefore, the final temperature of the mixture is approximately 296.88 K.