Question

Is ΔH=mCΔT and q=mCΔT the same thing? If so, which is more scientific?

Answer 1

`q = mcDeltaT` is correct, but only at constant pressure, but it can be shown that `DeltaH = mcDeltaT` is also correct.

But `q ne DeltaH` unless we are at constant system pressure. So no, they are definitely not quite the same thing. Neither is more "scientific", whatever that means...

---

`q` is heat flow in any condition. `DeltaH` is the change in enthalpy, and is the heat flow only at constant system pressure.

By definition,

`((delH)/(delT))_P = C_P -= c`

That is, the specific heat capacity you use is really for constant pressure. So then,

`int_((1))^((2)) dH = int_(T_1)^(T_2) C_PdT`

and in a small-enough temperature range,

`DeltaH = C_PDeltaT`

And therefore, whereas `C_P` is typically used in `"J/mol"cdot"K"`, we can redefine this using `c`, which has units of `"J/g"^@ "C"`, and thus

`color(blue)(DeltaH = mcDeltaT)`

That is "more" correct. However, this only applies at constant pressure anyway, so really, `q = DeltaH` and neither is actually wrong.