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

1 Answer
May 18, 2017

#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.