Thermodynamics
1
Basic Derivatives V(T,P) dV = ( ∂V ∂T ) ˚ P dT + ( ∂V ∂P ) ˚ T dP α = 1 V ( ∂V ∂T ) ˚ P isobaric thermal expansivity, coefficient of thermal expansion β = κ = – 1 V ( ∂V ∂P ) ˚ T isothermal compressibility dV = V α dT - V κ dP do α and κ give everything we need to know about mechanical behavior? ( ∂P ∂T ) ˚ V = ? 0 = dV = ( ∂V ∂T ) ˚ P dT + ( ∂V ∂P ) ˚ T dP ( ∂V ∂P ) ˚ T dP = –( ∂V ∂T ) ˚ P dT dP = ˚– ( ∂V ∂T ) ˚ P ˚˚dT ( ∂V ∂P ) ˚ T ˚ ( ∂P ∂T ) ˚ V = ˚– ( ∂V ∂T ) ˚ P ˚˚˚ ( ∂V ∂P ) ˚ T ˚ for small changes V doesn't change much: V 2245 V o cst.˚P dV = V α dT ∫ ˚ ˚V 1 ˚˚V 2 ˚˚ dV = ∫ ˚˚ T 1 ˚˚T 2 ˚ V˚ α˚dT ∆V = V o α ∆T cst.˚T dV = -V κ dP ∆V = -V o κ ∆P
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Basic Derivations Thermodynamics
Transcript of Thermodynamics
Basic Derivatives
V(T,P)
dV = (∂V∂T)
P dT + (∂V∂P)
T dP
α = 1V (∂V
∂T) P isobaric thermal expansivity, coefficient of thermal expansion
β = κ = – 1V (∂V
∂P) T isothermal compressibility
dV = V α dT - V κ dP
do α and κ give everything we need to know about mechanical behavior?
(∂P∂T)
V = ?
0 = dV = (∂V∂T)
P dT + (∂V∂P)
T dP
(∂V∂P)
T dP = –(∂V∂T)
P dT
dP = –(∂V
∂T) P dT
(∂V∂P)
T
(∂P∂T)
V = –(∂V
∂T) P
(∂V∂P)
T
for small changes V doesn't change much: V ≅ Vo
cst. P dV = V α dT
∫ V1
V2
dV = ∫ T1
T2
V α dT ∆V = Vo α ∆T
cst. T dV = -V κ dP ∆V = -Vo κ ∆P
