A 5.00 g sample of Al pellets (specific heat = .89 J/g degrees c) and a 10.00 g sample of Fe pellets (specific heat = .45 J/g degrees c) are heated to 100.0 degrees C. The mixture of hot Fe and Al is then dropped into 97.3 g of water at 22.0 degrees C. Calculate the final temp of the metal and water mixture, assuming no heat is lost to surroundings.
how do i do this problem? i'm completely lost.
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To solve this problem, we can use the principle of conservation of energy, which states that the energy gained by the metals equals the energy lost by the water. Here are the steps to calculate the final temperature of the metal and water mixture:
Step 1: Calculate the heat gained by the Al and Fe pellets:
The heat gained by a substance can be calculated using the formula:
Q = m * c * ΔT, where Q is the heat gained, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
For Al:
QAl = (mass of Al) * (specific heat of Al) * (final temperature - initial temperature)
Given:
mass of Al (mAl) = 5.00 g
specific heat of Al (cAl) = 0.89 J/g degrees C
initial temperature of Al (Tinitial, Al) = 100.0 degrees C (heated to this temperature)
For Fe:
QFe = (mass of Fe) * (specific heat of Fe) * (final temperature - initial temperature)
Given:
mass of Fe (mFe) = 10.00 g
specific heat of Fe (cFe) = 0.45 J/g degrees C
initial temperature of Fe (Tinitial, Fe) = 100.0 degrees C (heated to this temperature)
Step 2: Calculate the heat lost by the water:
The heat lost by water (Qwater) can also be calculated using the same formula as above.
Qwater = (mass of water) * (specific heat of water) * (final temperature - initial temperature)
Given:
mass of water (mwater) = 97.3 g
specific heat of water (cwater) = 4.18 J/g degrees C
initial temperature of water (Tinitial, water) = 22.0 degrees C
Step 3: Equating the heat gained and lost:
Since no heat is lost to the surroundings, we can equate the heat gained and lost:
QAl + QFe = Qwater
Step 4: Solve for the final temperature (Tfinal) using the equation from Step 3:
QAl + QFe = Qwater
(mAl * cAl * (Tfinal - Tinitial, Al)) + (mFe * cFe * (Tfinal - Tinitial, Fe)) = mwater * cwater * (Tfinal - Tinitial, water)
Now you can substitute the given values and solve for Tfinal.