Maxwell's Equations

MAXWELL'S EQUATIONS

Maxwell's equations relate the entropy to the three directly measurable properties such as p, v and T for pure simple compressible substances.

From first law of thermodynamics,

Q = W + ΔU

Rearranging the parameters,

Q = ΔU + W

Tds = du + pdv [⸪ Q = Tds and W = pdv]

So, du equation becomes,

Substituting the value du in equation (5.49),

dh = Tds - pdv + vdp + pdv = Tds + vdp   …. (5.50)

By Helmotz's function,

a = u - Ts

⸫ da = du - d(Ts)

=  du – Tds - sdT   ….. (5.51)

Substituting the value of du (5.48) in equation (5.51),

da = Tds - pdv - Tds - sdT=-pdv – sdT  ... (5.52)

By Gibbs functions

G = h - Ts

Dg = dh - d(Ts) = dh - Tds – sdT ... (5.53)

Substituting the value of dh (5.50) in equation (5.53),

So, dg becomes

dg= Tds + vdp – Tds – sdT (⸪ dh = Tds + vdp)

dg = vdp – sdT ... (5.54)

By inverse exact differential, it can be written the equation (5.48) as

du = Tds – pdv    ... (5.55)

Similarly, the equation (5.54) can be written as

These equations (5.58), (5.59), (5.60) and (5.61) are Maxwell's equation.