Question

Suppose you pour 0.310 kg of 20.0°C water into a 0.600 kg aluminum pan off the stove with a temperature of 167°C. Assume that the pan is placed on an insulated pad. What would be the final temperature (in °C) of the pan and water if 0.0300 kg of the water evaporated immediately, leaving the remainder to come to a common temperature with the pan?
Cw= 4186, Cal=900, Lvapor=2256000
Find final temperature

Answer 1

final temp = T

heat into water :
first .03 kg is brought to 100 and boiled off
heat into that water = .03 (2256000) + .03(4186)(100 - 20) = 77726
the rest of the water is .31 - .03 = .27 kg
so heat into it is
.27 (4186)(T-20) = 1130 (T-20)
so
total heat into water = 77726 +1130(T-20)

heat into pan = .6 (900)(167-T)
so
77726 +1130(T-20) = .6 (900)(167-T)