139 g of water at 4.9 degrees Celsius mixed with 241 g of water at 96.0 degrees Celsius (Tf=62.7)
To find the final temperature of the mixture, you can use the principle of conservation of energy, which states that the total heat gained by the colder substance is equal to the total heat lost by the hotter substance.
The heat gained or lost by a substance can be calculated using the formula:
Q = m * c * ΔT
Where:
Q = Heat gained or lost by the substance (in joules)
m = Mass of the substance (in grams)
c = Specific heat capacity of the substance (in joules/gram-degree Celsius)
ΔT = Change in temperature of the substance (in degrees Celsius)
Let's calculate the heat gained or lost by each substance:
For the 139 g of water at 4.9 degrees Celsius:
Q1 = 139 g * c_water * (Tf - 4.9°C) ----(1)
For the 241 g of water at 96.0 degrees Celsius:
Q2 = 241 g * c_water * (Tf - 96.0°C) ----(2)
In these equations, we assume that the specific heat capacity of water (c_water) is constant and equal to 4.18 J/g°C.
Since the total heat gained by the colder substance is equal to the total heat lost by the hotter substance, we can set up the equation:
Q1 + Q2 = 0
Plugging in the values from equations (1) and (2), we have:
139 g * c_water * (Tf - 4.9°C) + 241 g * c_water * (Tf - 96.0°C) = 0
Now, let's solve this equation to find the final temperature (Tf):
139 * 4.18 * (Tf - 4.9) + 241 * 4.18 * (Tf - 96.0) = 0
Apply the distributive property:
580.22 * Tf - 564.802 + 985.78 * Tf - 24799.08 = 0
Combine like terms:
1565 * Tf - 25363.882 = 0
Add 25363.882 to both sides:
1565 * Tf = 25363.882
Divide both sides by 1565:
Tf ≈ 25363.882 / 1565
Tf ≈ 16.2°C
Therefore, the final temperature (Tf) of the water mixture is approximately 16.2 degrees Celsius.