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Internal Energy and Enthalpy

The First Law

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


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:

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


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.