- #1
Wellesley
- 274
- 3
Homework Statement
If you pour 0.50 kg of molten lead at 328°C into 2.5 liters of water at 20°C, what will be the final temperatures of the water and the lead? The specific heat of (solid) lead has an average value of 3.4 X 10-2 kcal/kg • °C over the relevant temperature range.
Homework Equations
Q=mass*c* [tex]\Delta[/tex] T
Qfus=m*cfus
masspb=0.50 Kg @328oC
cpb=34 cal/KgoC
Tfinal=?
cfusion=6800 cal
The Attempt at a Solution
Qfusion=6800 cal/Kg * 0.50 Kg= 3400 cal
Qpb = 3400 cal + .50Kg * 34 cal/KgoC* (328-x)
Qpb=3400+5576-17x
For Water:
QH2O=2.5 Kg * 1000 cal/KgoC * (x-20oC)
QH2O=2500x-50000
Setting these equal to each other I get:
2500x-50000=3400-17x+5576
2517x=58976 cal
x=23.4311oC
The back of the book has the answer of 22oC.
I can get 22oC as an answer only if I subtract the latent heat of fusion:
2500x-50000=17x+5576
2517x=55576
x=22.0803oC
The math seems pretty straight forward, so it makes me wonder whether the book made an error, or I did.
Any help would be appreciated! Thanks.