Fluid work
initial
32 Pa
b.
c.
p
a.
d.
1 Pa
1 m3
0
final
8 m3
V
In general we have
nal
Work =
p(V ) dV,
initial
but along path a
p(V ) =
K
V
K = pi Vi = pf Vf .
where
Thus the work along path a is
Vf
Work =
Vi
K
K
1
dV =
V
( 1) V 1
Vf
=
Vi
1
K
1
1
( 1) V
Heat capacity at constant pressure
The argument for CV was: By denition,
CV (T, V, N ) = T
S
T
.
V,N
But the energy dierential is
dE = T dS p dV + dN.
To reect the constant V and N in the denition of CV above, restrict this equation for dE to changes at
c
Stumbling in the thermodynamic dance
a. Attempting to take a step in the thermodynamic dance, we try a Legendre transformation to variables
T , p, and by dening
= G N.
But = G/N , so = 0 and any attempt to say, for example,
= N,
T,p
is bound to fail. The
Heat capacities in a magnetic system
The reasoning here parallels the reasoning connecting CV with Cp in uid systems. There are three main
parts:
A: Begin with the known master relation for E(S, H):
dE = T dS M dH.
Apply a Legendre transformation to varia