### Work in General Ideal Gas Processes

**Important:** Positive work means work done
*by* an external force *on* a system.

For a mechanical system, the work done
*by* an external force *on* the system is:

W = ∫
F_{ext} dx

For a gas, F_{ext} = - F_{gas} = - P A. Here P is the
pressure exerted *by* the gas.

#### Basic Facts about Pressure:

- Pressure = force/area
- Units of pressure: 1 pascal ≡ 1 Pa = 1 N/m
^{2}
- Atmospheric pressure: 1 atm ≈ 10
^{5} Pa = 10^{2} kPa ≈ 14.7 lbs/sq. in.

For the work done *on* a gas, we have:

W = -
∫_{vi}^{vf} P A dx = -
∫_{vi}^{vf} P d(Ax) = -
∫_{vi}^{vf} P
dV.

Meaning of the minus sign:

*Positive * work is done
*on* the gas when the gas is compressed;

*negative * work
is done
*on* the gas when the gas expands.

*zero * work
is done
*on* the gas when the gas volume is fixed.

Geometrically, the work done *on* a gas is the negative of the area under the curve traced out by
the process in the P-V plane (see transparency).