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 solve for tf?
That problem has been anwered by another tutor (Bob Pursley) below.
A 100 g sample of a liquid with a specific heat
of 2 J/g
·
C absorbs 4000 J of heat energy. If the sample started at 30
◦
C, what is the final temperature? No phase change took place.
To solve for the final temperature (Tf) of the metal and water mixture, you can use the principle of conservation of energy. The heat gained by the water and metal equals the heat lost by the metal:
Heat gained by water = Heat lost by Al + Heat lost by Fe
To calculate the heat gained by the water, you can use the formula:
Qwater = mwater * Cwater * ΔTwater
Where:
- Qwater is the heat gained by the water
- mwater is the mass of water
- Cwater is the specific heat capacity of water (4.18 J/g °C)
- ΔTwater is the change in temperature of the water (final temperature - initial temperature)
Next, calculate the heat lost by the aluminum (Al) and the iron (Fe) using the formula:
Qmetal = mmetal * Cmetal * ΔTmetal
Where:
- Qmetal is the heat lost by the metal (either Al or Fe)
- mmetal is the mass of the metal (either Al or Fe)
- Cmetal is the specific heat capacity of the metal (0.89 J/g °C for Al or 0.45 J/g °C for Fe)
- ΔTmetal is the change in temperature of the metal (initial temperature - final temperature)
Since the aluminum and iron are at the same initial temperature and are dropped into the water, their initial temperatures are the same.
Now, equate the heat gained by the water to the sum of heat lost by the aluminum and iron:
Qwater = QAl + QFe
Plug in the values you know, and solve for Tf:
(mwater * Cwater * ΔTwater) = (maluminum * Caluminum * ΔTmetal) + (miron * Ciron * ΔTmetal)
Rearrange the equation to solve for Tf:
Tf = (Qwater - QAl - QFe) / (mwater * Cwater) + initial temperature
Substitute the known values for mass, specific heat, and initial temperatures, and solve to find Tf.