When 112 g of water at a temperature of 22.5°C is mixed with 65.1 g of water at an unknown temperature, the final temperature of the resulting mixture is 46.3°C. What was the initial temperature of the second sample of water?
loss heat hot water + gain of heat by cold water = 0
[Mass1H2O x specific heat x (Tfinal-Tinitial)] + [mass2H2O x specific heat x (Tfinal-Tinitial)] = 0
To find the initial temperature of the second sample of water, we can use the principle of conservation of energy. The total heat gained by the water at 22.5°C is equal to the total heat lost by the water at the unknown temperature.
The heat gained or lost by a substance can be calculated using the formula:
Q = mcΔT
Where:
Q = heat gained or lost
m = mass of the substance
c = specific heat capacity of the substance
ΔT = change in temperature
For water, the specific heat capacity is approximately 4.18 J/g°C.
Given:
Mass of water at 22.5°C = 112 g
Final temperature of the mixture = 46.3°C
Mass of water at unknown temperature = 65.1 g
Let's calculate the heat gained by the water at 22.5°C:
Q1 = (mass of water at 22.5°C) x (specific heat capacity of water) x (change in temperature)
= 112 g x 4.18 J/g°C x (final temperature - initial temperature of water at 22.5°C)
Now, let's calculate the heat lost by the water at the unknown temperature:
Q2 = (mass of water at unknown temperature) x (specific heat capacity of water) x (final temperature - initial temperature of water at unknown temperature)
= 65.1 g x 4.18 J/g°C x (final temperature - initial temperature of water at unknown temperature)
Since the total heat gained is equal to the total heat lost, we can set up the following equation:
Q1 = Q2
112 g x 4.18 J/g°C x (46.3°C - 22.5°C) = 65.1 g x 4.18 J/g°C x (46.3°C - initial temperature)
Simplifying the equation:
4949.776 = 2735.038 - 4.18 x 65.1 x initial temperature
Rearranging and solving for the initial temperature:
initial temperature = (2735.038 - 4949.776) / (4.18 x 65.1)
After performing the calculation, we find that the initial temperature of the second sample of water is approximately 16.9°C.