# Internal Energy and Enthalpy¶

## The First Law¶

1. 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:

\begin{align} q_P&=\Delta U+P\Delta V\\ &=\Delta H \end{align}

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.