# Thermal Energy problem

1. Oct 26, 2013

### MAC5494

1. The problem statement, all variables and given/known data

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?

2. Relevant 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.

3. The attempt at a solution

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

2. Oct 26, 2013

### Mentz114

This looks right, m1C1(Tf - 373.15) + m2C2(Tf - 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)

3. Oct 26, 2013

### MAC5494

It took a while, but it actually equals:

Tf=373.15m1c1+299.15m2c2/m2 + c2