CHAPTA SIX 😂 🫵 Flashcards
legendre transformation
alternative derivation method that may be used to transform one thermodynamic property with its natural variable into a new thermodynamic function with a different pair of independent variables.
aka expressing a natural function in terms of different state properties using additional derivatives
conjugate pairs
pairs of state variables that stay paired in all transforms {T,S}, {P,V}
convenience property
a property that is defined to be useful in problems where reversible heat flow and pressure are manipulated
helmholtz energy
A = U-TS
Gibbs Energy
G = U-TS +PV = A + PV = H-TS
what happens when T and P are constant in relation to Gibbs?
when T,P are constant -> dG = 0. the driving forces sum to zero and Gibbs energy is minimized
free energies
when increases in entropy detract from increases in energy (helmholtz and gibbs)
what would happen if entropy was always maximized
molecules would spread apart and everything would be a gas. spreading generated by entropic driving forces balances the compaction generated by energetic driving forces only at a narrow range of conditions.
internal energy fundamental relation (all info)
FUNDAMENTAL RELATION: dU = TdS-PdV
NATURAL VARIABLES: U(S,V)
LEGENDRE TRANSFORMATION: N/A
TRANSFORMED VARIABLE SETS: N/A
enthalpy fundamental relation (all info)
FUNDAMENTAL RELATION: dH = TdS+VdP
NATURAL VARIABLES: H(S,P)
LEGENDRE TRANSFORMATION: H = U+PV
TRANSFORMED VARIABLE SETS: {V,P}
helmholtz fundamental relation (all info)
FUNDAMENTAL RELATION: dA = -SdT - PdV
NATURAL VARIABLES: A(T,V)
LEGENDRE TRANSFORMATION: A=U-TS
TRANSFORMED VARIABLE SETS: {S,T}
gibbs fundamental relation (all info)
FUNDAMENTAL RELATION: dG = -SdT+VdP
NATURAL VARIABLES: G(T,P)
LEGENDRE TRANSFORMATION: G=U-TS+PV
TRANSFORMED VARIABLE SETS: {T,S} {V,P}
measurable properties
- P-V-T and partial derivatives involving only P-V-T.
- CP and CV which are known functions of temperature at low pressure (in fact, CP and CV are special names for derivatives of entropy).
- S is acceptable if it is not a derivative constraint or within a derivative term. S can be calculated once the state is specified.
State Variables
{T, S, P, V, U, H, A, G}
experimentally measurable
Cp, Cv, P, V, T (have gauges that measure them)
Equations of State
written in terms of Cp, Cv, P, V, T -> they link P,V,T
what are the two measurable derivatives
the isothermal compressibility and the isobaric coefficient of thermal expansion.
What properties does the Joule-Thomson coefficient relate?
relates to the physical situation of temperature changes as pressure drops through an isenthalpic throttle valve
are experimental measurements or theories better?
experimental measurements beat theories every time. but experiments can be expensive and time consuming
Steps of the Scientific Method
1) make a falsifiable hypothesis
2) observe (measurements independent of observer)
3) analysis
4) refine,refute,reject hypothesis -> reformulate
5) repeat 2,3
6) make conclusions
how can you express the Cp(T,P) relation in words?
Cp at a certain temperature and pressure can be determine from Cp (IG) and the correction factor
which path do you use??
THREE LEGS!!! (gets you to ideal gas)
What is a departure function?
the departure of the real fluid property and the same ideal gas property at the same {T,P} or {T,V}
how the real departs from the ideal –> REAL-IDEAL!!!
start with the ideal and go the real (final - initial)
what is an EOS?
an equation of state is a thermodynamic equation relating state variables, under certain conditions
what kind of system do we assume?
simple system!! no rigid, impermeable, adiabatic walls, no T or concentration gradient, no external/inertial forces
how do you explain how Z changes in respect to X and Y -> Z(x,y)
infinetesimal changes in Z are dependent on changes in X and Y
who is abbey’s least favorite person in the world
stephen paddison
