A 1.00kg piece of aluminum at 90.0c in placed in 4.00 liters (4.00kg) of water at 25.0c. What is the final temperature(Tf)
I got 28.3
28.3
To find the final temperature (Tf) after the aluminum piece is placed in water, we can use the principle of conservation of energy. The heat lost by the aluminum will be equal to the heat gained by the water.
The formula to calculate the heat lost or gained is given by:
Q = mcΔT
Where:
Q = heat gained or lost
m = mass
c = specific heat capacity
ΔT = change in temperature
For the aluminum:
m₁ = 1.00 kg
c₁ = 0.897 J/g°C (specific heat capacity of aluminum)
T₁ = 90.0°C (initial temperature of aluminum)
For the water:
m₂ = 4.00 kg
c₂ = 4.18 J/g°C (specific heat capacity of water)
T₂ = 25.0°C (initial temperature of water)
We can solve for Tf by equating the heat lost by the aluminum to the heat gained by the water:
m₁c₁(Tf - T₁) = m₂c₂(Tf - T₂)
Now we can substitute the given values and solve for Tf:
(1.00 kg)(0.897 J/g°C)(Tf - 90.0°C) = (4.00 kg)(4.18 J/g°C)(Tf - 25.0°C)
Converting the units to SI, we have:
(1000 g)(0.897 J/g°C)(Tf - 90.0°C) = (4000 g)(4.18 J/g°C)(Tf - 25.0°C)
Simplifying the equation:
897(Tf - 90.0) = 16655(Tf - 25.0)
897Tf - 80730 = 16655Tf - 416375
-15758Tf = -335645
Solving for Tf:
Tf = (-335645) / (-15758)
Tf ≈ 21.32°C
Therefore, the final temperature (Tf) after the aluminum is placed in water is approximately 21.32°C.
To find the final temperature (Tf) of the system, we can use the principle of energy conservation. The heat gained by the water will be equal to the heat lost by the aluminum.
The heat gained by the water can be given by the equation Qw = mw * cw * (Tf - Tw), where Qw is the heat gained by water, mw is the mass of water, cw is the specific heat capacity of water, Tw is the initial temperature of water, and Tf is the final temperature of the system.
The heat lost by the aluminum can be given by the equation Qa = ma * ca * (Tf - Ta), where Qa is the heat lost by aluminum, ma is the mass of aluminum, ca is the specific heat capacity of aluminum, and Ta is the initial temperature of aluminum.
Since the aluminum is initially at 90.0°C and the water is initially at 25.0°C, Ta = 90.0°C and Tw = 25.0°C. Also, the specific heat capacity of aluminum, ca, is 0.897 J/g°C, and the specific heat capacity of water, cw, is 4.18 J/g°C.
Let's calculate the values for Qw and Qa:
Qw = mw * cw * (Tf - Tw)
Qw = 4000 g * 4.18 J/g°C * (Tf - 25.0°C) (Note: 1 liter of water = 1000 grams)
Qw = 4000 * 4.18 * (Tf - 25.0) (Note: g/g cancels out)
Qa = ma * ca * (Tf - Ta)
Qa = 1000 g * 0.897 J/g°C * (Tf - 90.0°C)
Qa = 1000 * 0.897 * (Tf - 90.0) (Note: g/g cancels out)
Since the heat gained by the water (Qw) should be equal to the heat lost by the aluminum (Qa), we can set these equations equal to each other and solve for Tf:
4000 * 4.18 * (Tf - 25.0) = 1000 * 0.897 * (Tf - 90.0)
Now, let's solve for Tf:
16640 * Tf - 415960 = 897 * Tf - 80730 (Multiplying out the equation)
15743 * Tf = 335230 (Combining like terms)
Tf = 21.30°C (Dividing both sides by 15743)
Therefore, the final temperature (Tf) of the system will be approximately 21.30°C.