Energy Balance (ignoring kinetic and potential energy):

$$\mathrm{\Delta }U=Q+W_{EC}+W_S$$

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:  $W<0$