Enthalpy

In the half hour before today's heartwarming quiz, we explored two conditions that change the First Law into simple statements about heat transfer. First, under constant volume conditions, in which no work other than PV-work is possible, the infinitesimal change in the internal energy dU was shown to equal dq_V.

If we define a new thermodynamic function, called the enthalpy, as H=U+PV, we quickly find, under constant pressure and reversible conditions, that its infinitesimal change is equal to dq_P. These relations allow us to further connect the heat capacities C_P and C_V to H and U respectively. This is only the first of many instances in which we will see the pressure|enthalpy and volume|internal energy links this quarter.

A comment on where we are so far. I am attempting to demonstrate how thermodynamics can be systematically used to calculate work and heat transfer, for any process, before moving onto their directionality. Since work and heat transfer are not directly measurable, we need some way to infer what's going on using directly measurable properties, like pressure, volume and temperature. We'll find out that these variables are not sufficiently rich to fully describe thermodynamic behavior, so we'll soon add other functions, like entropy and gibbs energy, to add to our growing toolbox.