A 522g piece of copper tubing is heated to 89.5C and placed in an insulated vessel containing 159g of water at 22.8C. Assuming no loss of water and a heat capacity for the vessel of 10.0J/K, what is the final temperature of the system ( c of copper = 0.387 J/g*K)?
Heat absorbed by the water + heat absorbed by the vessel + heat given up by the heated copper tubing = 0
[mass H2O x specific heat water x (Tfinal-Tinitial)] + [10 J/C*(Tfinal-Tinitial)] + mass copper x specific heat copper x (Tfinal-Tinitial) = 0
Solve for Tfinal. Post your work if you get stuck.
36.6
Oops I did 455 g Cu to get my answer.
To find the final temperature of the system, we need to calculate the heat gained by the water and the heat lost by the copper tubing, and then equate the two.
First, let's calculate the heat gained by the water:
Qwater = mwater * cwater * ΔTwater
Where,
Qwater = heat gained by water
mwater = mass of water = 159g
cwater = specific heat capacity of water = 4.18 J/g*K
ΔTwater = change in temperature of water = final temperature - initial temperature
Next, let's calculate the heat lost by the copper tubing:
Qcopper = mcopper * ccopper * ΔTcopper
Where,
Qcopper = heat lost by copper tubing
mcopper = mass of copper tubing = 522g
ccopper = specific heat capacity of copper = 0.387 J/g*K
ΔTcopper = change in temperature of copper tubing = final temperature - initial temperature
Since we have an insulated vessel, the heat gained by the water is equal to the heat lost by the copper tubing:
Qwater = Qcopper
Now, let's substitute the values and solve for the final temperature:
mwater * cwater * ΔTwater = mcopper * ccopper * ΔTcopper
(159g) * (4.18 J/g*K) * (Tf - 22.8C) = (522g) * (0.387 J/g*K) * (Tf - 89.5C)
Now, we can solve for Tf.
159 * 4.18 * Tf - 159 * 4.18 * 22.8 = 522 * 0.387 * Tf - 522 * 0.387 * 89.5
Multiply out:
665.01Tf - 1814.67 - 2000.02Tf + 15062.77 = 202.134Tf - 18013.47
Combine like terms:
865.144Tf - 33193.22 = 202.134Tf - 18013.47
Move all the terms with Tf to one side and the constants to the other side:
865.144Tf - 202.134Tf = -18013.47 + 33193.22
663.01Tf = 15179.75
Divide both sides by 663.01 to solve for Tf:
Tf = 22.91C
Therefore, the final temperature of the system is approximately 22.91°C.