[Coreyt123]

If given the mass, initial temp and specific heat of a substance as well as the mass and initial temp of water  (I know specific heat is 4.18 J/gC) how do I solve for the final temperature at thermal equilibrium?

[Enthalpy]

Hi Coreyt123, welcome!

The substance is put in the water and both together are insulated from the rest of the world, is that it? Then you could write that the total heat is the same before the contact and after equilibrium. Express the heats as a function of the temepratures, solve.

All temperatures are probably mild enough that the heat capacities are constant. If not, for instance if water begins to boil, it gets more complicated.

Just a sub-sub-detail: temperature changes are to be written in kelvin, so a heat capacity is in J/kg/K, not /°C.

[Coreyt123]

Thank you! That is the correct set-up with instructions to negate heat lost to the calorimeter. That helps a lot. Temperatures are low enough to solve that way (Pb at initial 10.3 C and water at initial 52.6 C). However, wouldn't expressing heat capacity in C or K be the same since it takes the exact same energy to raise one gram of a given substance one degree in C or K (C=K+273)? Either way thanks for the advice solving the problem!

[Enthalpy]

Same value - it's just that K is the only correct unit for a temperature change or difference. °C means only a temperature relative to water's melting point. Also mind the °, since C without it is a coulomb - but K takes no °.

[Coreyt123]

Gotcha. I appreciate the help. I'm only typing the C without a degree symbols because my iPad doesn't have one (although I now notice there's one I can use on the webpage itself). I'm sure using K over C will come into play for me in the future. Right now, I'm just doing Gen Chem 1 and the prof. said he's OK with using whichever one the temperature reading on the problem uses, for purposes of calculations, as long as we remember how to convert back and forth. Again, I've only done some pretty basic stuff to this point, but good to know for the future. Thanks again!