# Internal Energy and Enthalpy¶

## The First Law¶

- Energy is always conserved, it cannot be created or destroyed (\(\Delta U=q+w\))

Definitions

Energy can only be transferred through two mechanisms:

- Work (\(w\)) - the transfer of energy as a result of unbalanced forces
- Heat (\(q\)) - transfer of energy resulting from a temperature difference

**Adiabatic processes** are those in which no heat, or mass is transferred between the system and its surroundings. Energy is only transferred through work

## State Functions¶

Are properties that depend only upon the state of the system, and not the path used to get there.

While *energy* is a state function, *work* and *heat* are not, these are called path functions

- State functions can be integrated in the form \(\int_1^2dU=U_2-U_1=\Delta U\)
- Path functions are integrated in the form \(\int_1^2\delta w=w\) (not \(\Delta w\) or \(w_2-w_1\))

The sum of heat and work (inexact differentials) is an exact differential (\(\Delta U\))

## At Constant Pressure¶

The equation can be rearranged to give \(q_P=\Delta U+P_{ext}\int_{V_1}^{V_2}dV\)

This means that \(q_P\) becomes a state function, called the enthalpy:

Info

At this point, the content came into the realm of stuff I’m already familiar with from Chemistry 2, so I copied the notes into this section, but won’t bother to add anything redundant.