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The First Law and Other Basic Concepts (part 2)

THERMODYNAMICS 1

Department of Chemical Engineering, Semarang State University

Dhoni Hartanto S.T., M.T., M.Sc.

Equilibrium

Have you ever cooked?

Equilibrium (cont.)

Equilibrium is a word denoting a static condition, the absence of change

In thermodynamics, it means not only the absence of change but also theabsence of any tendency toward on macroscopic scale

Other definition, equilibrium is static condition in which no changes occurin the macroscopic properties of a system with time.

But, in microscopic properties, the condition is not static

Equilibrium condition all forces in exact balance

kondensor

heat

Equilibrium (cont.)

t = 0 minute

(in a certain “A” composition mixtures,

P, and T)

t = C minutes

(in a certain “B” composition mixtures,

P, and T)

Liquid

phase

Vapor

phase

Liquid

phase

Condition :

Macroscopic no changes, static

Microscopic changes, not static

A B

Phase Rule

When two intensive thermodynamic properties are set at definite values,the state of a pure homogeneous fluid is fixed.

In contrast, when two phases are in equilibrium, the state of the system isfixed when only a single property is specified

A mixture of steam + liquid water in equilibrium

373.15 K

101.325 kPa

Changing temperature

will also change the

pressure if vapor-liquid

are in equilibrium

Phase Rule (cont.)

Let’s check it out in HYSYS

Choose H2O as selected component

Go to fluid packages

Choose Peng-Robinson as property package

Go to simulation environment Choose material stream

Phase Rule (cont.)


Set temperature to 100 oC

Take basis molar flow 1 kgmole/h

Go to composition, then fill H2O mole fraction with 1, then OK

Set pressure to 101.325 kPa

Phase Rule (cont.)


With set the temperature and pressure, HYSYS automatically change the vapor phase to be 1, it means the water in vapor phase

Phase Rule (cont.)

Cook water until boiling point in mountain

What happen when you boil water in high area such as mountain which the pressure is less than 1 atm (101.32 kPa)

When the water boil

Pressure less than 1

atm (101.32 kPa)

Temperature also

less than 100 oC

Phase Rule (cont.)

Cook water until boiling point in deep blue sea

What happen when you boil water in high pressure area with pressure more than 1 atm (101.32 kPa)

When the water boil

Pressure more than

1 atm (101.32 kPa)

Temperature also

increase to more

than 100 oC

Tugas HYSYS :

Cek campuran

etanol (1)+ air (2)

konsentrasi mol

fraction 0-1 dengan

incremen 0.1 (0,0.1,

0,2 dst.)

Vapor fraction = 1

Pada P = 1 atm

Bagaimana

perubahan

temperatur,

Buat grafiknya

(mole fraction

etanol vs

temperature)

x1

T (K)

Phase Rule (cont.)

N : number of chemical speciesF : degree of freedomphi : phase

Example :Various phase can coexist , it must be in equilibrium Three-phase system at equilibrium is a saturated aqueous solution at its boiling point with excess salt crystals present.

= 3 (three phase) are crystalline salt, the saturated aqueous solution= 2 (two chemical species) are water and salt

So, degree of freedom

NF 2

Degree of freedom of the system

For any system at equilibrium, the number of independent variables that must be arbitrarily to establish its intensive state is given by the phase-ruleThe phase-rule is intensive property

N

1232 F

Phase Rule (cont.)


The intensive state of a system at equilibrium is established when its temperature, pressure, and the composition of all phase are fixed

The phase rule gives the number of variables from this set which must be arbitrarily specified to fix all remaining phase-rule variables

The minimum degree of freeedom for any system is zeroWhen F = 0The system is invariantEquation becomes

Value of phi is the maximum number of phase which can coexist at equilibrium for a system containing N chemical species

N 2

Phase Rule (cont.)


For example :The triple point of water where liquid, vapor, and the common from ice exist together in equilibrium at 273.16 K (0.01oC) and 0.0061 bar

Any change from these condition causes at least one phase to dissapear

Water at

0.01oC

0.0061 bar

liquid

vaporice

3

12

2

N

phase

Phase Rule (cont.)

How many degrees of freedom has each of the following system :a) Liquid water in equilibrium with its vaporb) Liquid water in equilibrium with a mixture of water vapor and nitrogenc) A liquid solution of alcohol in water in equilibrium with its vapor

Answer :a)

In fact, temperature or pressure but not both may be specified for a system of water in equilibrium with its vapor

b)The addition of an inert gas to a system of water in equilibrium with its vapor changes the characteristic of the system. Temperature and pressure maybe independtly varied

c)The phase-rule variables are temperature, pressure, and the phase compositionFixing the mole fraction of water in liquid phase automatically fixes the mole fraction of the alcohol

11222 NF

22222 NF

22222 NF

The Reversible Process

A process is reversible when its direction can be reversed at any point by an infinitesimal change in external conditions.

The Reversible Process (cont.)

When heated, CaCO3 decompossed forms CaO and CO2

When weight is increased, CO2 pressure is increased and CO2 combines with CaO to form CaCO3 allowing the weight to fall slowly


Summary :

A reversible process has the following condition :1. Is frictionless2. Is never more than differentially removed from equilibrium 3. Traverses a succession of equilibrium states 4. Is driven by forces whose imbalance is differential in magnitude 5. Can be reversed at any point by a differential change in external conditions 6. When reversed, retraces its forward path, and restores the initial state of

system and surroundings


Mechanically reversible

t

t

V

V

tdVPW2

1

Example : A horizontal piston/cylinder arrangement is placed in a constant-temperaturebath. The piston slides in the cylinder with negligible friction, and an externalforce holds it in place against an initial gas pressure of 14 bar. The initial gasvolume is 0.003 m3 . The external force on the piston is reduced gradually andthe gas expands isothermally as its volume doubles. If the volume of the gas isrelated to its pressure so that the product PVt is constant, what is the workdone by the gas in moving the external force?

How much work would be done if the external force were suddenly reduced tohalf its initial value instead of being gradually reduced?


Solution :The process is mechanically reversibleIf PVt = k , then P=k/Vt

JW

JVPPVk

mVmV

V

Vk

V

dVkdVPW

tt

tt

V

V t

t

t

tV

V

tt

t

t

t

291122ln42000

42000)03.0)(10.14(

06.0;03.0

ln

5

11

3

2

3

1

1

22

1

2

1

Final pressure :

barPaV

kP

t7700000

06.0

42000

2

2


Solution :In the second case, a half of the initial force has been removedThe gas under goes a sudden expansion against a constant force equivalent topressure of 7 bar. Thus is the same as before and the net workaccomplished equals the equivalent external pressure times the volume change.

JW 21000)03.006.0)(10.7( 5

tV

This second case is irreversible, and compared with reversible one theefficiency is

%1.72721.029112

21000orefficiency

Constant V and Constant P Process

Energy balance for a homogeneous closed system of n moles :

dWdQnUd )(

Work in mechanically reversible :

)(nVPddW

Combine this two equation, yield :

)()( nVPddQnUd

General first-law equation for mechanically reversible and closed system

Constant V (volume) Process

In constant total volume process, the work is 0, thus the equation will be :

Thus for a mechanically reversible, constant-volume, closed-system process, the heat transferred is equal to the internal-energy change of the system.

UnQ

nUddQ

)(

Constant P (Pressure) Process

Arrange the equation below to solve dQ :

yield,

)()( nVPddQnUd

)()( nVPdnUddQ

For constant pressure

)]([)()( PVUndnVPdnUddQ

Where U + PV is the definition of enthalpy

PVUH

The equation become

HnQ

nHddQ

)(

Thus for a mechanically reversible, constant-pressure, closed-system process, the heat transferred is equal to the enthalpy change of the system.

Enthalpy

Unit of enthalpy (H) : energy per mole or unit mass

Enthalpy is state function due to U, V, and P are state function

Enthalpi is intensive property

)(

)(

PVUH

PVddUdH

These equation apply to a unit mass or a mole of substance

Heat Capacity

Heat has relation with its effect on the objectThis is the origin of the idea that a body has capacity

The smaller the temperature change in a body caused by the transfer of a given quantity of heat, the greater its capacity

dT

dQC

In fact, there are 2 kind of heat capacities are in common use for homogeneous fluids. Both are state function

There are :1. Heat capacity at constant volume (Cv)2. Heat capacity at constant pressure (Cp)

Heat Capacity at constant volume (Cv)

2

1

T

TV

V

V

V

dTCU

dTCdU

T

QC

For mechanically reversible at constant volume process

2

1

T

TV dTCnUnQ

Heat Capacity at constant pressure (Cp)

2

1

T

TP

P

P

P

dTCH

dTCdH

T

HC

For mechanically reversible at constant pressure process :

2

1

T

TP dTCnHnQ

Open System Energy Balance

zguU 2

2

1

system

Q

m

W

E(system) + E(surrounding) = 0

First Law:

Per unit mass containing energy:

Total energy carried out:

zguUm 2

2

1


dt

mUd

Energy in the system can change due to accumulation or loss :

Thus:

WQgzuUmgzuUm

dt

mUd

i

iiii

j

jjjj

22

2

1

2

1

(input) (output)


Work: caused by fluid pushing in and out or piston (Wf)

and shaft work (Ws)

sf WWW

i

iii

j

jjjf mVPmVPW

input output

s

i

iii

j

jjj

i

iiii

j

jjjj WmVPmVPQgzuUmgzuUmdt

mUd

22

2

1

2

1

Remember: PVUH


s

j

jjjj

i

iiii WQgzuHmgzuHmdt

mUd

22

2

1

2

1

input output

In general:

•Steady state:

•one inlet and outlet stream:

0

dt

mUd

mmm ji

sWQzguHm

2

2

1

sWQzguH 2

2

1

Rate of energy

Rate of energy per unit mass or mole

Thank you

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