Because heat and work are not state functions, we cannot simply equate them individually to changes in state functions. However, under particular conditions this is possible.
For example, if we operate under conditions of constant volume, then the PV work is zero. In this case, the change in internal energy is simply equal to the heat flow.
\[q_v = \Delta U\]
We denote the conditions of constant volume with the subscript v.
However, in chemistry we almost always operate under conditions of constant pressure rather than constant volume. We would like a new state function that is equal to the heat flow at constant pressure. So we invent one and call it the enthalpy, H.
The heat at constant pressure is given by
\[q_p = \Delta U - w = \Delta U +P\Delta V\]
\[q_p = (U_f - U_i) +P(V_f - V_i) = (U_f + PV_f) - (U_i + PV_i)\]
Therefore, if we define a new state function, H that is defined as\[H = U +PV \]
We end up with the nice relation that the heat flow at constant pressure is equal to \(\Delta H\)\[q_p = H_f - H_i = \Delta H\]
So the enthalpy is nothing more than an invention of a new energy that is equivalent to the heat flow as measured at constant pressure. If the change is not at constant pressure then enthalpy is something, but it is not equal to the heat flow.
There are two other important chemical terms that we associate with enthalpy change. When a process lowers the enthalpy of the system, \(\Delta H < 0\), we call this process, exothermic. For an exothermic process at constant pressure, energy flows from the system to the surroundings in the form of heat. Combustion is an exothermic process that we are all familiar with. When a process increases the enthalpy of the system, \(\Delta H > 0\), we call this process endothermic. Ice melting is an endothermic process. Energy is absorbed by the system in the form of heat flow that leads to the solid converting to a liquid.