How to Calculate Final Temperature in a Water and Aluminum System?

[MAC5494]

Homework Statement

160 grams of boiling water (temperature 100° C, heat capacity 4.2 J/gram/K) are poured into an aluminum pan whose mass is 950 grams and initial temperature 26° C (the heat capacity of aluminum is 0.9 J/gram/K).
(a) After a short time, what is the temperature of the water?

Homework Equations

ΔE = ΔKsys + Δ(Msysc^2) + ΔUsys + ΔEint = Wsurr + Q

Wsurr + Q = 0 because the surroundings aren't effecting the problem, and ΔEint isn't changing.

ΔEint = 0

So...

m1C1*ΔT + m2C2*ΔT = 0

m1C1(Tf - 373.15K) + m2C2(Tf - 299.15K) = 0




From there I don't know what to do. I know I have to solve for Tf, but I guess my problem is I don't know how to solve for Tf.

I know that Tf is the same for both of them, but that doesn't really help me solve for it. I'm probably just not thinking straight right now.

The Attempt at a Solution

Couldn't get an answer because I can't figure out how to solve for Tf.

 

[Mentz114]

This looks right, m₁C₁(T_f - 373.15) + m₂C₂(T_f - 299.15) = 0
so rearranging terms this gives Tf(m₁C₁-m₂C₂) = 373.15m ₁C₁-299.15 m₂C₂

Tf = (373.15 m₁C₁-299.15 m₂C₂)/(m₁C₁-m₂C₂)

 

[MAC5494]

It took a while, but it actually equals:

T_f=373.15m₁c₁+299.15m₂c₂/m₂ + c₂