Specific heat capacity, Q = mcθ

[a129]

Homework Statement

Here is the original question (just read the English version).

Homework Equations

Q = mcθ
Specific heat capacity of water, c = 4200 J/kg °C

The Attempt at a Solution

I did Q_(absorbed) = Q_(released)
mcθ = mcθ
mθ = mθ

And I solved for the final temperature, which is 23.33°C. However the correct answer here is A. I'm pretty sure this question is assuming that there is no heat lost to the surroundings.
Thanks!

 

[Orodruin]

However the correct answer here is A.

No it isn't. It is C. (You are correct.)

 

[a129]

No it isn't. It is C. (You are correct.)

Thank you!

 

[Orodruin]

Note that this is true even if you take into account that the heat capacity of water changes slightly decreases with temperature. (It does not change enough for the final temperature to deviate significantly from 23.33 °C.)

Here is a plot of the heat added to the initially 10 °C water and the heat lost by the initially 30 °C water:

The coloured lines are numerical integrations of the tabulated temperature dependent heat capacity of water. The dotted black lines represent the approximation of the heat capacity being 4.2 kJ/kg K. (I used 500 g and 1 kg masses, but only the proportion is relevant for the intersection point in T)