### Reversible and Irreversible Processes

##### Definition:

A **reversible process** is one which can be
"undone" without a affecting the surroundings. Alternatively, it is
a process that can reverse direction at any point due to an
infinitesimal change in external conditions (driving force).

##### Note:

A reversible process is an ideal one that yields the maximum
possible work attainable.

##### Example:

Consider the following isothermal expansions/compressions of an
ideal gas. Calculate the work for each step when the total mass of
the blocks is 1020kg, the area of the piston surface is 0.1 $m^2$,
the initial height of the piston is 0.4$m$ and the amount of gas
present is 1 mol.

$\Delta U + \Delta E_k + \Delta E_p = Q +
W$

$W = -Q$

$W = - Q = -\int P_E dV = -P_E \Delta
V$

##### Note:

$P_E$ is larger for the compression than for the expansion! The
work obtained from the expansion is less than that required for the
compression.

$W = - Q = -\int P_E dV = -(P_{E}\Delta
V)_{1 \to i} - (P_{E}\Delta V)_{i \to 2}$

##### Note:

The difference between $(P_{E}\Delta V)_{i \to 1(2)}$ and
$(P_{E}\Delta V)_{1(2) \to i}$ (the forward vs the reverse) is
smaller than for the 1 step process. The difference in the work
obtained/required is also smaller.

$W = - Q = -\int P_E dV = -(P_{E}\Delta
V)_{1 \to i_1} -(P_{E}\Delta V)_{i_1 \to i_2} - (P_{E}\Delta
V)_{i_2 \to i_3} - (P_{E}\Delta V)_{i_3 \to 2}$

##### Note:

Again, the difference decreases further for the multi-step
process. If the step gets even smaller, the external pressure at
each step eventually becomes essentially equal to the internal
pressure at each step ($P_E \to P$).

$W = - Q = -\int P_E dV = -\int P dV =
-\int nRT \frac{dV}{V} = -nRT\ln\left (\frac{V_2}{V_1}\right
)$

##### Outcome:

Explain the difference between a reversible and irreversible
process.

##### Note:

Because a reversible process is the ideal/limiting case, we will
use it as the reference point for efficiency calculations.