if 27 grams of ice at 0 degrees celsius is added to 123 grams of water at 100 degrees celsius in an insulated container, calculate the final temperature. assume specific heat of water is 4.184 J/K g
To calculate the final temperature after the ice and water are mixed, we need to determine the amount of heat transferred between the substances. This can be done by using the principle of heat transfer, which states that the heat gained by one substance must be equal to the heat lost by the other substance. Here's how we can calculate the final temperature:
1. Calculate the heat gained by the ice:
Heat gained = mass of ice × specific heat of ice × change in temperature
Since the ice is initially at 0 degrees Celsius and the final temperature is unknown, we can denote the change in temperature as ΔT.
Heat gained by the ice = 27 g × specific heat of ice × ΔT
2. Calculate the heat lost by the water:
Heat lost = mass of water × specific heat of water × change in temperature
Since the water is initially at 100 degrees Celsius, the change in temperature is 100 - final temperature.
Heat lost by the water = 123 g × 4.184 J/K g × (100 - final temperature)
3. Equate the heat gained by the ice with the heat lost by the water:
27 g × specific heat of ice × ΔT = 123 g × 4.184 J/K g × (100 - final temperature)
4. Solve the equation for ΔT by isolating ΔT:
Divide both sides of the equation by (27 g × specific heat of ice):
ΔT = (123 g × 4.184 J/K g × (100 - final temperature)) / (27 g × specific heat of ice)
5. Substitute the values and solve for ΔT:
ΔT = (123 g × 4.184 J/K g × (100 - final temperature)) / (27 g × 2.09 J/K g)
ΔT = (514.332 J × (100 - final temperature)) / 56.43 J
ΔT = (57783 - 514.332 final temperature) / 56.43
6. Multiply both sides of the equation by 56.43 to eliminate the denominator:
56.43 ΔT = 57783 - 514.332 final temperature
7. Rearrange the equation to isolate final temperature:
514.332 final temperature = 57783 - 56.43 ΔT
8. Substitute ΔT back into the equation and solve for final temperature:
final temperature = (57783 - 56.43 ΔT) / 514.332
Now, you can substitute the known values of mass, specific heat, and initial temperatures to find the final temperature.
To calculate the final temperature, we need to use the principle of energy conservation.
1. First, we need to determine the heat gained or lost by each substance.
Heat lost by the water:
Q_water = mass_water * specific heat_water * (final temperature - initial temperature)
Q_water = 123 g * 4.184 J/g°C * (final temperature - 100°C)
Heat gained by the ice:
Q_ice = mass_ice * specific heat_ice * (final temperature - initial temperature)
Q_ice = 27 g * 2.09 J/g°C * (final temperature - 0°C)
2. According to the principle of energy conservation, the heat lost by the water must be equal to the heat gained by the ice.
Q_water = Q_ice
123 g * 4.184 J/g°C * (final temperature - 100°C) = 27 g * 2.09 J/g°C * (final temperature - 0°C)
3. Solve for the final temperature.
123 * 4.184 * (final temperature - 100) = 27 * 2.09 * final temperature
514.332 * final temperature - 51433.2 = 56.43 * final temperature
(514.332 - 56.43) * final temperature = 51433.2
457.902 * final temperature = 51433.2
final temperature = 51433.2 / 457.902
final temperature ≈ 112.34°C
So, the final temperature of the mixture is approximately 112.34°C.
1. ice melts at zero C. q = mass ice x heat fusion
2. melted water at zero changes temperature to Tfinal.
q = [mass melted ice x specific heat H2O x (Tfinal-Tinitial)]
3. Warm water at 100 C cools to Tfinal
q = [mass warm water x specific heat H2O x (Tfinal-Tinitial)]
Add 1 + 2 + 3 together (I have put them in boldface type) and they equal = 0. Solve for Tfinal