Pressure-Volume Diagrams


math, math, math

Recall from the previous section …

ΔU = Q + W
Q > 0   system absorbs heat
Q < 0   system releases heat
W > 0   work done on the system by the environment
W < 0   work done by the system on the environment

A system can be described by three thermodynamic variables. — pressure, volume, and temperature. Well, maybe it's only two variables. With everything tied together by the ideal gas law, one variable can always be described as dependent on the other two.


P =  nRT
PV = nRT  ⇒  V =  nRT
    T =  PV

Temperature is the slave of pressure and volume on a pressure-volume graph (PV graph).

Function of State

ΔU =  3  nRΔT

Function of Path: Work

W = ∫ F · ds = ∫ P dV = − area on PV graph

Function of Path: Heat

Q = ΔU + W = ncΔT
cP  specific heat at constant pressure
cV  specific heat at constant temperature


Superman illustrates adiabatic cooling brought about by the rapid expansion of a gas, thus preventing the evil General Zod from heating the truck's fuel tank to the point of explosion. Thank you Superman. You've saved us.

… and the rest