# 19.3: Work and Heat are not State Functions, but Energy is a State Function

### Compression two (reversible)

In most cases the external pressure is not constant, it consists of the pressure of the atmosphere outside plus whatever pressure your hand is exerting on the piston. Because the gas molecules adjust the internal pressure pretty fast (with the speed of sound!) to any changes your hand imposes to the outside pressure, the two pressures are pretty much the same at all times.

Reversible:

$P_{external} \approx P_{internal}$

Reversible:

$P_{external} \approx P_{internal} + \delta P$

1. Start with cylinder 1 liter, both external and internal pressure 1 bar.
2. Gently push the piston until V= 1/2 l and P=2 bar

In that case both the pressure inside and out will follow the reciprocal function (a hyperbola) and w is the area under that curve. (I.e. you need to integrate).

## Reversible versus irreversible

You'll say, what's the big difference. In both cases we go from 1bar/1 liter to 2bar/1/2liter. The key is the word suddenly. By pegging we have created a situation where Pext=2Pint artificially and now we pull. Because it's done suddenly in path one Pexternal > Pinternal for most of the time, because the internal pressure is struggling to catch up with the external one. During the second compression we have $$P_{ext}=P_{internal}$$ at all times. It's a bit like falling off a cliff versus gently sliding down a hill. Path one is called an irreversible path, the second a reversible path

##### Reversible vs. Irreversible Processes

A reversible path is a path that follows a series of states at rest (i.e., the forces are allowed to balance at all times). In an irreversible one the forces only balance at the very end of the process.