Final temperature when 100g copper at 100°C is mixed with water at 25°C

[Esoremada]

Homework Statement

A 100-g sample of Cu(s), initially at 100oC, is added to 140 g of water, initially at 25oC. What is the final temperature of the mixture?

Specific heat
(in J g-1 oC-1)
Cu(s) 0.385
H2O(l ) 4.184

Homework Equations

Q = m * ΔT * c

heat lost = heat gained
= m₂ * ΔT₂ * c₂

The Attempt at a Solution

100 * (T₂ - 100) * 0.385 = 140 * (T₂ - 25) * 4.185
38.5* (T₂ - 100) = 585.9 * (T₂ - 25)
38.5T₂ - 3850 = 585.9T₂ - 14647.5
T₂ = 19.725°CBut the temperature can't be lower than both their starting temperatures, what did I do wrong? The answer is supposed to be 29.6

 

[SteamKing]

From the way you have written your equation, you are assuming that the final temperature T2 of the copper is greater than 100 C.