Work

Ph 1a definition:

Force $F_{x}$ through displacement $d x$ in direction of the force
Units: $J = N \cdot m = k g \cdot m^{2} \cdot s^{- 2}$
$W = \int \partial W = \int F_{x} d x$
- Path-dependent

Key points:

$W > 0$ if done by the system
$W < 0$ if done to the system

What is work?

Compression of gas

Ex: motion of a piston
System: has inside chamber
Process: from state 1 to state 2

W_{1 \to 2} = \int_{1}^{2} F_{x} d x = \int_{1}^{2} P A d x = \int_{1}^{2} P d V = P_{1} (V_{2} - V_{1})

Key observations

Process from state 1 to state 2 via states 3 to states 4
$W_{1 \to 3 \to 4 \to 2}$

Better Definition

Energy (Units: $J = N \cdot m$ ) transferred across boundaries of a system whose sole effect on surroundings is the raising of a weight.