[noblemin]

Hello all, first post on this forum but not the last.
The question itself goes like this :One piece of copper jewelry at 1058C has twice the mass of
another piece at 458C. Both are placed in a calorimeter of negligible
heat capacity. What is the final temperature inside the calorimeter
(c of copper 5 0.387 J/g?K)?

Now I know the equation to solve is (c)(m)(ΔT)=(c)(m)(ΔT)
or heat lost=heat gained.

My question is concerning the delta T. On the left side of the equation ΔT= Tfinal-Tinitial, where as on the right side it is ΔT=Tinitial-Tfinal. Why are they switched? Is it because one is calculated to be a negative value(loss) and the other positive(gain)?

Thanks in advance!

[Borek]

Why are they switched? Is it because one is calculated to be a negative value(loss) and the other positive(gain)?

Yes.

You can treat the problem a bit differently. Don't care about tracing what lost and what gained heat (sometimes you can't predict it without calculations), but write the heat balance as

[tex]\sum_i m_ic_i(T_{final} - T_{initial,~i}) = 0[/tex]

then everything gets equal treatment and you don't need to worry about signs.

[Enthalpy]

If the assignment tells one constant heat capacity at all temperatures, just use it.
But please keep in mind that the heat capacity of the solid increases with temperature, much more so as 1058°C is close to the melting point (1083°C).

https://srd.nist.gov/JPCRD/jpcrd263.pdf

J/mol/K      K
----------------
  24.45    300
  26.99    700
  32.16   1300
----------------