Why does Q = H for a reversible, constant pressure process?

Begin with the 1st Law:

                                                            dU = dQ - dW                                    (1)

For a reversible process with only PV work, this becomes:

                                                            dU = dQ_rev - PdV                               (2)

The definition of enthalpy is:

                                                            H = U + PV                                       (3)

Taking the derivative of equation (3):

                                                            dH = dU + d(PV)                               (4)

At constant pressure, this becomes:

                                                                                                (5)

Substituting eqn (2) into eqn (5), we get:

                                                            dH = (dQ - PdV) + PdV                     (6)

Or:

                                                            dH = dQ                                           (7)

Which, upon integrating, becomes:

                                                                            H = Q

For examples, see S&VN pg 30, pg 48-51, pg 69 (covered in recitation), and pg 152.
For thought: What relationships apply if the system is not constant in pressure?