ITK-233 Termodinamika Teknik Kimia I

DICKY DERMAWANwww.dickydermawan.net78 .net

d ickydermawan@gmai l .com

ITK-233Termodinamika Teknik

Kimia I

3 SKS

5 – Relations among Thermodynamic Properties & Properties Diagrams

State Principle

The only measurable property is P, T & VHow we can find U, H, S, … from this?

We already have:

.....)orT&SorV&PorV&TorP&T(f)propertyAny( ncompositiophase

PT

V

V

1

TP

V

V

1

VV T

UC

P

P T

HC

Fundamental Relations

TSHG

TSUA

PVUH

U

dPVdTSdG

dVPdTSdA

dPVdSTdH

dVPdSTdU

)P,T(GG

)V,T(AA

)P,S(HH

)V,S(UU

Mathematical Formulation (1)

yx

2

yxxy

x

y

x

N

y

M

yx

z

y

z

xx

z

y

y

zN

x

zM

dyNdxMdz

)y,x(zz

Mathematical Formulation (2)

dzz

ydx

x

ydy)z,x(yy

dzz

xdy

y

xdx)z,y(xx

)y,x(zz)z,x(yy)z,y(xx)z,y,x(ff

xz

yz

Elimination of the differential dy gives:

0dzz

x

z

y

y

xdx1

x

y

y

x

yxzzz

Since dx and dz are independent, the coefficient of dx and dz must be zero, thus:

z

z

xy1

y

x

x

z

y

yz

yx

z

x

and:

Fundamental Relations

dPVdTSdG

dVPdTSdA

dPVdSTdH

dVPdSTdU

...

...

...

PV

U&T

S

U

SV

Fundamental Properties & Maxwell Relations

dPVdTSdG

dVPdTSdA

dPVdSTdH

dVPdSTdU

...

...

....

S

P

V

T

VS

Example H=H(T,P)

a. How does enthalpy affected by temperature and pressure?

b. Prove that c. Use the result of (a) to prove that enthalpy of ideal

gas is affected only by temperature.

d. State H=H(T,P) for virial gas:

e. State H=H(T,P) for real gas:

dPV)T1(dTCdH P

...P'DP'CP'B1(RTPV 32

RT

PVZ

Example: S=S(T,P)

a. How does entropy affected by temperature and pressure?

b. Prove that

c. Show that for ideal gas 1

2

T

T

P

P

PlnRdT

T

CS

2

1

dPVdTT

CdS P

Example: U=U(T,V)

a. How does internal energy affected by temperature and volume?

b. Express the results of (a) in term of β and κ

c. Use the result of (a) to prove that internal energy of ideal gas is not affected by pressure

Example: S=S(T,V)

a. How does entropy affected by temperature and volume?

b. Express the results of (a) in term of β and κ

c. Show that for ideal gas with constant Cv:

1

2

1

2v V

VlnR

T

TlnCS

Gibbs Energy as Generating Function

a. Prove that

b. c.

d.

TP

)RT/G(

RT

V

PT

)RT/G(T

RT

H

RT

G

RT

H

R

S

RT

PV

RT

H

RT

U

Cp, Cv & Pressure Effect

The Joule-Thomson coefficient: is important in refrigeration engineering. Show that it can be calculated using:

Prove that:

Prove that:

P

2

2

T

P

T

VT

P

C

PVVP T

V

T

PTCC

HP

T

PPH T

VTV

C

1

P

T

Example: U = U(T,P)

a. Prove that

b. Prove that the internal energy of ideal gas is not affected by pressure

c. Prove that

V)TP(P

U

T

V)PT(CT

UV

P

Thermodynamic Property Diagrams

Represents properties: P, V, T, H & S of a substance on a single plot.

The most common:T/S DiagramP/H DiagramH/S (Mollier diagram)

T – S Diagram of Air

T – S Diagram of CO

T – S Diagram of CO2

P-H Diagram of Ammonia

P-H Diagram of

Chlorine

H/S (Mollier Diagram) for NO

H/S (Mollier Diagram) for Water

Example 6.6

a. Superheated steam originally at 150 psia & 500 oF expands through a nozzle to an exhaust pressure of 50 psia. Assuming the process is reversible & adiabatic, determine the downstream state of the steam and ΔH.

b. Repeat problem (a) if the process is irreversible with thermodynamic efficiency of 88%.