Lecture Notes in Advanced Thermodynamics

quantity variables Gibbs relation
energy E(S, V, M) dE = T dS − pdV + µdM
Helmholtz free energy F (T, V, M) dF = −SdT − pdV + µdM
enthalpy H(S, p, M) dH = T dS + V dp + µdM
Gibbs free energy G(T, p, M) dG = −SdT + V dp + µdM
Table 2: Important thermodynamic potentials - variables
2.3 Densities, specific quantities
– the extensive and intensive properties are constraints
– one of the extensive variables can be eliminated
– it can be useful to choose a reference variable
– usually the volume (densities) and the mass (specific quantities) are
used for reference
2.3.1 Densities
transformation of the basic state variables
– energy density:
ε := E V
– mass density:
ρ := M V
transformation of the state functions
– the (E, V, M) state space can be simplified to (ε, ρ)
– considering an extensive state function:
( E
ˆf(ε, ρ) := f (ε, 1, ρ) = f
V , 1, M )
= V f ( E
, 1, )
M
V V
=
V V
f(E, V, M)
V
specially:
Ê = ε;
ˆM = ρ
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