Lecture Notes in Advanced Thermodynamics

– the bracket equals to ∂ v p| T because of (11), therefore:
− ∂ eT | v
T 3 ∂ v p| T > 0
– ∂ e T | v is positive due to (27) and T 3 is positive due to (26), thus
∂ v p| T < 0 (28)
– (27) and (28) are a particular example of the le Chatelier-Brown principle.
2.4.3 Examples
ideal gas
– the thermic equation of state:
– the caloric equation of state:
pv = RT
e = cT
– from that the standard state functions:
– the condition of (25):
T (e, v) = e c
p(e, v) = Re
cv
( )
∂
1
∂v ∣ = 0
e
T (e, v)
( )
∂
p(e, v)
∂e∣ = 0
v
T (e, v)
they are equal, hence the ideal gas model is entropic
– the condition (26): because the energy (e) is positive by definition, the
condition for the positive temperature is:
18
c > 0