Question

How does enthalpy change differ from heat flow?

Answer 1

Well, Enthalpy is defined as follows:

`H = U+PV`

`DeltaH = DeltaU + Delta(PV)`

`= DeltaU + (P_1 + DeltaP)(V_1 + DeltaV) - P_1V_1`

`= DeltaU + P_1DeltaV + V_1DeltaP + DeltaPDeltaV`

`= q + w + P_1DeltaV + V_1DeltaP + DeltaPDeltaV`

`= q cancel(- P_1DeltaV + P_1DeltaV) + V_1DeltaP + DeltaPDeltaV`
(with `w = -PDeltaV` for volume expansions/contractions)

As a result,

`DeltaH = q + V_1DeltaP + DeltaPDeltaV`

where:

• `H =` enthalpy
• `U =` internal energy
• `q =` heat flow
• `w =` work
• `P =` pressure
• `V =` volume

So you can see that enthalpy is heat flow along with a constant-volume pressure change, and enthalpy and heat flow are only the same if the pressure is constant (`q_p = DeltaH`) (like in a coffee-cup calorimeter).

We can then say that enthalpy is equivalent to heat flow in a constant-pressure system open to the air, whereas internal energy is equivalent to heat flow in a constant-volume system closed to the air.