[schrodingersdog]

I recently did a question, it goes like this:
When 1.00 L of 2.00 M Na2SO4 solution at 30.08C is
added to 2.00 L of 0.750 M Ba(NO3)2 solution at
30.08C in a calorimeter, a white solid (BaSO4) forms.

The temperature of the mixture increases to 42.08C. As-
suming that the specific heat capacity of the solution is

6.37 J 8C21 g21 and that the density of the final solution
is 2.00 g/mL, calculate the enthalpy change per mole of
BaSO4 formed.

It saids here that the "temperature of the mixture increases to 42.08C". Based on what I learned in the lecture, the surroundings in this case would be the water and the system would be the actual molecules of the substances that are reacting. Therefore the temperature that is increasing is the temperature of the surroundings, which means that the surroundings is absorbing heat, and the system is losing heat.
However, the right answer is one with a positive sign, which means that the system is absorbing heat (since we're in the system's POV)
Is there anything wrong with my thought process? I'm sorry if this is long, but will really appreciate it if someone can help

[mjc123]

The question says "calculate the enthalpy change"; it doesn't say of what, but we must assume of the BaSO₄, i.e. the enthalpy change of the reaction
Ba²⁺(aq) + SO₄^2-(aq)  BaSO₄(s)
This enthalpy change is negative, as the precipitation of BaSO₄ releases heat, which causes the temperature of the solution to rise.
By the way, check those numbers, they seem to give a crazy answer.