# SL: Entropy of a Rev/irreversible Adiabatic Expansion/Compression

### Entropy of a Rev/irreversible Adiabatic Expansion/Compression

##### Example:

What is the entropy change of the system and surroundings in the (ir)reversible adiabatic expansion from $P_1, T_1$ to a final pressure $P_2$?

$\Delta S = \int_{initial}^{final} \frac{\delta Q_{sys}}{T}$

##### Recall:

By definition adiabatic means $Q=0$!

$\Delta S_{sys_{rev}} = \Delta S_{surr_{rev}} = \Delta S_{univ_{rev}} = 0$

For irreversible:
$\Delta S_{surr} = 0$
$\Delta S_{sys} = \Delta S_{univ} \neq 0$. Why?

##### Outcome:

Identify, formulate, and solve simple engineering problems (such as expansion/compression and power cycles)

##### Example:

Let's try it with numbers now.

Compare the entropy change of the system, the surroundings, and the universe when you alternatively expand an ideal gas (assume $c_p=\frac{7}{2}$R) adiabatically by:

• a reversible expansion from $P_1=$2 bar and $T_1=$962K to $P_2=$1 bar
• an irreversible expansion from $P_1=$2 bar and $T_1=$962K to $P_2=$1 bar and $T_2=$820K