What will the final temperature of the coffee be?

[Richie Smash]

Homework Statement

150g of milk at 10°C is added to 150g of hot coffee at 80°C. Assume they have the same specific heat capacity.

The temperature of the coffee decreases:
A: to 35 °C B: to 70°C
C: by 70°C D:by 35°C

Homework Equations

Eh= mass x (c) x ΔT

Where (c) is specific heat capacity
and (Eh) is heat energy.

The Attempt at a Solution

I know that the heat gained by the milk is the same lost by the coffee

SO using the method of mixtures I can say

Eh of milk = Eh of coffee

I have the mass of both so its 0.15Kg
But from this point I am stuck as I don't have the change in temperature and now I'm just unsure.

I know that if I could figure the heat energy for one of them, I can find the change in temperature but... at this point I am stuck.

But I've thought of something,

0.15kg *c * θ-10°C= 0.15 *c * 80°C - θ

Divide by (c)
0.15kg* θ-10°C = 0.15kg *80°C - θ

Divide by 0.15kg

So

80°C - θ=θ-10°C
so 2*θ= 90°C
θ= 45°C

So the answer would be D: by 35°C

 

[kuruman]

Your answer is correct.