Energy Balance (ignoring kinetic and potential energy):

\[\Delta U = Q + W_{EC} + W_S\]

where \(Q\) is the heat added to the system
\(W_{EC}\) is the expansion/compression work (moving a piston in a cylinder)
\(W_S\) is shaft work
For most processes of importance in chemical engineering, kinetic and potential energies can be ignored.

Adiabatic/reversible compression/expansion for an ideal gas:

\[\frac{T_2}{T_1} = \left( \frac{P_2}{P_1}\right) ^\frac{R}{C_P}\]

where \(T_1\) and \(T_2\) are the absolute temperatures of the gas at the initial and final states, respectively
\(P_1\) and \(P_2\) are the initial and final pressures, respectively
\(R\) is the ideal gas constant
\(C_P\) is the heat capacity at constant pressure

Heat added to the system:  \(Q > 0\) 
Heat removed from the system:  \(Q < 0\)
Adiabatic system:  \(Q = 0\)
Work added to the system:  \(W > 0\)
Work removed from the system:  \(W < 0\)