Are you getting tired of gases?dU = TdS - pdV

dW = -pdV worked well for gases!!

However, in other physical systems, dW = xdX.[x, X] conjugate variables

x: force (intensive variables)X: displacement (extensive variables)

System x X dWfluids -p V -pdV

elastic rods f (tension) L fdL

liquid films surface tension

A dA

dielectric materials E (electric field) pe Edpe

magnetic materials H (magnetic field) m= -MV Hdm

Magneto X men

Adiabatic Demagnetization

Entropy exchanged between spins and phonons !

TdS equations (TediouS equations)

(1)

(2)

(3)

pV

T

p p

p V T

p p

TTdS C dT dV

TdS C dT TV dp

C CdVTdS dp

V

The TdS equations are useful for calculating :

1.heat transferred in reversible processes2.entropy by dividing by temperature and then integrating 3.heat flow in terms of measurable properties4.relationship between coordinates for isentropic processes