Chapter 1 and 2 _ Heat and Work

7/28/2019 Chapter 1 and 2 _ Heat and Work

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CHEMICAL ENGINEERINGTHERMODYNAMICS

Course no: CHE C311 / F213

Dr. Srinivas Krishnaswamy

1st Semester 2012 – 2013

DEPT. OF CHEMICAL ENGG.

BITS – PILANI, K. K. BIRLA GOA CAMPUS



Contents Reversibility and Irreversibility

What is quasi-equilibrium?

Understanding energy The concept of thermodynamic work

Evaluation of work for commonreversible processes

Work done in an irreversible process

Two inherently irreversible processes

Heat and its comparison with work



Reversibility and

Irreversibility

A process is reversible if it can be completely reversed, i.e. when carried out in the opposite

direction the system follows the same

succession of states as it followed in theforward direction (very crude definition)

A process is reversible if after the processoccurs, the system can be restored to its

original state without any effect on itssurroundings

This effect occurs only when the driving forceis infinitesimally small



Reversibility and

Irreversibility Note The 2nd definition involves the

surroundings

Important to understand that when a process

is reversible, interaction between system andsurroundings are equal and opposite indirection,i.e. both system and surroundingsare restored to initial conditions

A reversible process leaves no history of theprocess after it is reversed

No friction involved

The processes represent idealization and are

never realized in real life



Reversibility and

Irreversibility A process which is not reversible is

irreversible

Irreversible processes have friction and arecarried out with finite driving forces

If a system in this case is restored to itsoriginal state, surroundings must be altered

Caused by friction, unrestrained expansion,mixing of substances, combustion, flow of electricity through a resistor, heat transfer over a finite temperature difference etc.



Quasi-equilibrium

process

A process in which deviation fromequilibrium is infinitesimal

All states through which a system passes

during such a process can be considered asa succession of equilibrium states

Takes place very slowly with an infinitesimalchange in properties at each step

Path can be described for such a process

A quasi-equilibrium process without frictionis reversible



Understanding Energy

Difficult to define in general, but isdefined as capacity of a body to dowork (causes an effect)

Exists in various forms and can be

converted from one form to another (partial or complete), but can never bedestroyed

Can be classified as energy intransition and energy in storage

SI units: Joules



Understanding Energy

Energy transferred as a result of potentialdifference is energy is transition. Loss of identity as soon as soon as energy entersand leaves a system. E.g.: gradient of force,

temperature and potential result in transfer of mechanical work, heat and electricalenergy respectively

Stored energy possessed by a system as a

result of its position in a force field, itsmotion, its atomic or molecular structure etc.Examples are kinetic, rotational or vibrational energy, chemical or nuclear energy etc.



The concept of

thermodynamic work By definition it is Force times

displacement, the latter measured in

the direction of the force from the pointof application

But then thermodynamics talk of

system and surroundings. Hence workneeds to be defined in thermodynamic

language



The concept of

thermodynamic workWork is said to be done by a system if the soleeffect on the surroundings is reduced to

lifting of weight

Note The definition does not call for actualraising of a weight, but rather the possibility

of a weight being raised

Thermodynamic work is energy in transition

and is manifest at the system boundary onlyduring system-surrounding interaction.

Before the interaction work is present andafter the interaction no work exists



The concept of

thermodynamic work

WORK

Work crosses

system boundary

in both cases

(green and red

boundaries)

Flow of electricity

across a system is

equivalent towork crossing the

system boundary

WORK

MOTOR

WORK

MOTOR



The concept of

thermodynamic work Conventions important when solving

problems

In thermodynamics work done by a systemis positive and work done on a system isnegative

System and surroundings do equal, butopposite work

W system + W surroundings = 0

Net work done by a system is expressed as

W net = W out - W in



Work done in a frictionless

quasi-equilibrium processInitial conditions

Gas at P , T and volumeV inside frictionless

piston and cylinder arrangement in thermalequilibrium

P exerts a force F . Under equilibrium, this is

balanced by a forcecaused by atmospheric

pressure and pistonweights (-F ) which

results in P ext

F




quasi-equilibrium processRemove an infinitesimally

small weight. This willresult in reduction of pressure and slightexpansion will take

place.

Reduced gas pressure willbe balanced by reduced

weights which will beraised and work will bedone

W = F dz = (PA )dz = P dV

dz




quasi-equilibrium processLet finite weights be removed

ensuring quasi-equilibrium

process 1- 2 in which volume

changes from V

1

to V

2During this change system and

surroundings are in

equilibrium

The net work done during the

expansion 1-2 is

1W 2 = W = P dV

Final state

after weights

are removed




quasi-equilibrium process The integral represents the area under

the P – V diagram

Work done can be found by integrationprovided a relationship between P andV is known

This is displacement work and is valid

only for frictionless process This expression applies to any

compressible system of any arbitrary

shape




quasi-equilibrium processSpecific work = Work per unit mass of the system

W = mw = P dV = m P d

The integral can be evaluated by graphical or numerical methods (if path known from

experimental data) or by curve fitting

experimental data to obtain a relationship

between P and V and then using directintegration



Evaluating work for some

common processesCONSTANT PRESSURE PROCESS

P = CONSTANT

1W 2 = W = P dV = P dV

WORK DONE = P (V 2 – V 1)

V

P

1W 2

1 2




common processesCONSTANT VOLUME PROCESS

V = CONSTANT, dV = 0

WORK DONE = 0

1

V

P

2




common processesHYPERBOLIC PROCESS

PV = CONSTANT = P 1V 1 = P 2V 2

1W 2 = W = P 1V 1 (dV / V)

WORK DONE = P 1V 1 ln(V 2 / V 1) =

P 2V 2 ln(V 2 / V 1)

2

V

P

1W 2

1NOTE HYPERBOLIC

PROCESS BECOMES

ISOTHERMAL IF T IS

CONSTANT, PV = RT = C




common processesPOLYTROPIC PROCESS

PV n = P 1V 1n = P 2V 2

n = C

The index n is the polytropic index. It can beevaluated if P and V at initial and final states

are known, thus

n = ln (P 1 / P 2) / ln (V 2 / V 1)

The polytropic relation represents the mostconvenient curve fitting of actualexperimental data between P and V with thevalue of the index n evaluated with the help

of any two points on the curve




common processesFor integration purposes

P = C / V n = P 1V 1n / V n = P 2V 2

n / V n

1W 2 = W = C (dV / V n)

1W 2 = C (V 21 – n - V 1

1 – n ) / 1 – n

Substituting C = P 1V 1n = P 2V 2

n

1W 2 = (P 2V 2 - P 1V 1) / 1 –n

1W 2 = (P 1V 1 / 1 – n) [ (P 2 / P 1){(n – 1) / n}

– 1]

from V 2/V 1 =(P 1/P 2)1/n




common processes n, the polytropic index can have many

values. note that when n = 0, the

process is constant pressure (isobaric)and when n = , it is a process at

constant volume

Integration valid when n 1 For hyperbolic process n = 1




common processesIf the gas is ideal, then

P 1V 1 / T 1 = P 2V 2/T 2

A relationship between T –

P and V –

T canbe obtained thus

T 2 / T 1 = (P 2 / P 1)(n – 1 / n) = (V 1 / V 2)

(n – 1)

Putting P 2V

2= mRT

2and P

1V

1= mRT

1

1W 2 = m R (T2 - T1) / 1 – n

(Polytropic work for an ideal gas)




common processes A gas is contained in a cylinder fitted with a

piston loaded with a small number of

weights. The initial pressure of the gas is1.3 bar and the initial volume is 0.03 m3.

The gas is now heated until the volume

increases to 0.1 m3. Calculate the work

done by the gas for the a constant pressure,constant temperature process and PV 1.3 = C

process




common processesCONSTANT PRESSURE PROCESS

(CAUSED BY MOVING PISTON AS GAS ISHEATED)

WORK DONE = P (V 2 – V 1) = 9.1 kJ

CONSTANT TEMPERATURE PROCESS(REMOVE WEIGHTS AT A RATE THAT

THE TEMPERATURE REMAINSCONSTANT WHILE HEAT IS ADDED TOTHE GAS)

WORK DONE = P 1V 1 ln(V 2 / V 1) = 4.695 kJ




common processesPOLYTROPIC PROCESS (ACHIEVED

BY REMOVING WEIGHTS AT A

RATE SUCH THAT P 1V 11.3

= P 2V 21.3

DESCRIBES P – V RELATIONSHIP

WORK DONE = (P 2V 2 - P 1V 1) / 1 – n = 3.933 kJ

STATE 1 –

2 CAN BE ACHIEVED THROUGHDIFFERENT ROUTES. WORK DONE IS

DIFFERENT FOR EACH PATH. WORK IS THUS

A PATH FUNCTION (REMEMBER QUASI-

EQUILIBRIUM)




common processes Work done in a process is not only a

function of the two end states, but italso depends on the path followed ingoing from one state to another

Work is a path function and an inexactdifferential

Thus 1W 2 = W W 2 –

W 1. Hencenever speak of work in state 1 or state2. There is only W in and W out which iswork in transition



Work done in an

irreversible process Not all processes confirm to idealized

quasi-equilibrium conditions. Actual

process are inherently irreversible, i.e.surroundings are altered even whensystem returns to original state

A process maybe irreversible

essentially in two ways, i.e. non-equilibrium irreversible or due tofriction



Work done in an

irreversible process In a non-equilibrium process, there is a finite

change. Path of the process is not known.Only end states are known

In a process where friction is present quasi-static conditions can exist, i.e.

P ext F / A = P

Local temperature changes due to frictionnear piston cylinder contacts.Thermodynamic equilibrium is thus absent.Work is dissipated as heat and cannot berecovered



Work done in a non-

equilibrium process Actual case where finite weights are

removed. Only initial and final states

are known. The system andsurroundings are not in equilibrium at

each step

F

1

P ext =

P 1

2

P ext = P 2

V

P 1

21W 2



Work done in a non-

equilibrium process P dV does not represent work

But some work has been done becausevolume has changed and this is finitechange, i.e. V

W = P ext V (work done in a non-equilibriumprocess)

Note pressure P ext here is external pressureand during the process never equal to P , thepressure of the gas.



Work done in a process

with friction In this case P ext + F / A = P or P ext - F / A =

P is possible depending on whether expansion or compression takes place

For compression P ext > P and for expansion P ext < P (P is the gaspressure)

Thus in a process with frictionW = P extdV (P ext = P F / A)

Less work obtained during expansion andmore work required during compression



Work done in an

irreversible processLost work = P dV - P extdV

It is seen that for a reversible process, for a

given change of state, work output duringexpansion is maximum and work input

during compression is minimum. In an

irreversible process during expansion work

output is less than maximum and duringcompression more than minimum

An irreversible process is always inferior



Two inherently

irreversible process Free expansion where P dV is finite,

but work done is zero. Finite means

can be evaluated

Q = 0Fluid, state

2, P 2, V 2W = 0

Q = 0Fluid, state

1, P 1, V 1W = 0

Vacuum,

P ext = 0

P ext = 0

Not quasi-

equilibrium

P extdV = 0

No work done

during free

expansion



Two inherently

irreversible process

MOTOR Paddle wheel

work

Volume does not

change and

friction not

involved

System boundary

does not move

A situation whereP dV is zero, but

work is still done



The State Postulate

Simple system: A system which involves only

one work mode

State Postulate: The number of independent

intrinsic properties required to define thestate of a system is equal to one plus the

number of possible work modes

Thus for a simple system, the number of

independent intrinsic properties required is 2



The concept of heat

In the case of paddle wheel work,temperature rises, i.e. a change of state occurs

The same state can be brought aboutif heat entered the system instead of work

Effect of heat on a system could besame as the effect of work

Heat is energy as work is and hasunits of work



The concept of heat

Heat is thus defined as energy in

transition flowing by a virtue of a

temperature difference between twosystems or between a system and it s

surroundings

It manifests only at the system boundaryand cannot be contained



The concept of heat

Sign convention of heat is just opposite to

that of work

Heat entering a system is positive (addedto) and leaving a system is negative

A process in which no heat transfer takes

place is an adiabatic process

In a closed system an application of work or

heat can cause a change of state



The concept of heat

When heat is added to a pure substance it

is seen that either the phase changes with

temperature remaining constant (saturationstate) or temperature changes with

substance remaining in the same phase

In the former case it is called latent heat and

in the latter sensible heat Heat transfer by 3 modes: conduction,

convection or radiation



Objective Assessment

Concept of reversibility andirreversibility

Concept of work

Estimating work for various processes

Concept of heat

There are two ways of meeting difficulties:you alter the difficulties or you alter yourself

meeting them. It is better than running away

from them.

Chapter 1 and 2 _ Heat and Work

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