CHAPTA SIX 😂 🫵

Question 1

legendre transformation

Answer 1

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

Question 2

conjugate pairs

Answer 2

pairs of state variables that stay paired in all transforms {T,S}, {P,V}

Question 3

convenience property

Answer 3

a property that is defined to be useful in problems where reversible heat flow and pressure are manipulated

Question 4

helmholtz energy

Answer 4

A = U-TS

Question 5

Gibbs Energy

Answer 5

G = U-TS +PV = A + PV = H-TS

Question 6

what happens when T and P are constant in relation to Gibbs?

Answer 6

when T,P are constant -> dG = 0. the driving forces sum to zero and Gibbs energy is minimized

Question 7

free energies

Answer 7

when increases in entropy detract from increases in energy (helmholtz and gibbs)

Question 8

what would happen if entropy was always maximized

Answer 8

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.

Question 9

internal energy fundamental relation (all info)

Answer 9

FUNDAMENTAL RELATION: dU = TdS-PdV
NATURAL VARIABLES: U(S,V)
LEGENDRE TRANSFORMATION: N/A
TRANSFORMED VARIABLE SETS: N/A

Question 10

enthalpy fundamental relation (all info)

Answer 10

FUNDAMENTAL RELATION: dH = TdS+VdP
NATURAL VARIABLES: H(S,P)
LEGENDRE TRANSFORMATION: H = U+PV
TRANSFORMED VARIABLE SETS: {V,P}

Question 11

helmholtz fundamental relation (all info)

Answer 11

FUNDAMENTAL RELATION: dA = -SdT - PdV
NATURAL VARIABLES: A(T,V)
LEGENDRE TRANSFORMATION: A=U-TS
TRANSFORMED VARIABLE SETS: {S,T}

Question 12

gibbs fundamental relation (all info)

Answer 12

FUNDAMENTAL RELATION: dG = -SdT+VdP
NATURAL VARIABLES: G(T,P)
LEGENDRE TRANSFORMATION: G=U-TS+PV
TRANSFORMED VARIABLE SETS: {T,S} {V,P}

Question 13

measurable properties

Answer 13

1. P-V-T and partial derivatives involving only P-V-T.
2. CP and CV which are known functions of temperature at low pressure (in fact, CP and CV are special names for derivatives of entropy).
3. S is acceptable if it is not a derivative constraint or within a derivative term. S can be calculated once the state is specified.

Question 14

State Variables

Answer 14

{T, S, P, V, U, H, A, G}

Question 15

experimentally measurable

Answer 15

Cp, Cv, P, V, T (have gauges that measure them)

Question 16

Equations of State

Answer 16

written in terms of Cp, Cv, P, V, T -> they link P,V,T

Question 17

what are the two measurable derivatives

Answer 17

the isothermal compressibility and the isobaric coefficient of thermal expansion.

Question 18

What properties does the Joule-Thomson coefficient relate?

Answer 18

relates to the physical situation of temperature changes as pressure drops through an isenthalpic throttle valve

Question 19

are experimental measurements or theories better?

Answer 19

experimental measurements beat theories every time. but experiments can be expensive and time consuming

Question 20

Steps of the Scientific Method

Answer 20

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

Question 21

how can you express the Cp(T,P) relation in words?

Answer 21

Cp at a certain temperature and pressure can be determine from Cp (IG) and the correction factor

Question 22

which path do you use??

Answer 22

THREE LEGS!!! (gets you to ideal gas)

Question 23

What is a departure function?

Answer 23

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)

Question 24

what is an EOS?

Answer 24

an equation of state is a thermodynamic equation relating state variables, under certain conditions

Question 25

what kind of system do we assume?

Answer 25

simple system!! no rigid, impermeable, adiabatic walls, no T or concentration gradient, no external/inertial forces

Question 26

how do you explain how Z changes in respect to X and Y -> Z(x,y)

Answer 26

infinetesimal changes in Z are dependent on changes in X and Y

Question 27

who is abbey’s least favorite person in the world

Answer 27

stephen paddison