Heat and Thermodynamics

Lecturer 20

Sahraei

Physics Department, Razi University

http://www.razi.ac.ir/sahraei Change of entropy

Let us represent the process as a series of infinitesimal reversible steps. During a step, an infinitesimal quantity of heat dQ is added to the system at absolute temperature T.

Then the change of entropy for the entire process is:

2 dQ entropy change in a S  1 T reversible process

The change in entropy does not depend on the path leading from the initial to the final state but is the same for all possible processes. Carnot Cycle

QC SQC eCarnot  1  1 QH SQH T QQC SQ C η  1  C C  1 eCarnotCarnot  1  1 TH QQHH SQH T  1 C TH Carnot Cycle ENTROPY AND REVERSIBILITY

dS0

and the entropy change of the universe, which is the sum of these two changes,is zero.

If dQR is rejected by the system, then, obviously, Irreversible Processes

There is no simple definition for the entropy of an irreversible process between a system and its environment

We do know that the entropy of the universe is always increasing due to irreversible transformations

ΔSuniverseΔSsystemΔSenvironment

ΔS uni ver se 0 Reversible (equilibrium) process

ΔS uni ver se 0 Irreversible (natural) process

dQ dS r ev T ENTROPY AND IRREVERSIBILITY

Processes exhibiting external mechanical irreversibility

(a) Examples are those processes involving the isothermal dissipation of work through a system (which remains unchanged) into internal energy of a reservoir:

(b) Further examples are those processes involving the adiabatic dissipation of work into internal energy of a system open to the atmosphere, such as: For an isobaric process,

Finally, if Cp is assumed not to be a function of temperature, then the entropy change of the system is Processes exhibiting internal mechanical irreversibility

Ideal gas rushing into a vacuum (free expansion, i.e., Joule expansion).

For an isothermal process of the ideal gas,

which yields, for the entropy change of the system, Processes exhibiting external thermal irreversibility

Conduction or radiation of heat from a system to its cooler surroundings.

The entropy change of the universe is positive, because T2 is less than T1. Processes exhibiting chemical irreversibility

Diffusion of two dissimilar inert ideal gases.

A chemical reaction

which is a positive number

In general, the change of entropy is positive for any irreversible process Dissolving a gas in a liquid decreases the entropy

gas

dissolves

overall more disordered solution of gas arrangement: higher entropy in liquid, lower S Often, dissolving a solid or liquid will increase the entropy

liquid solution

dissolves

lower entropy more disordered arrangement = higher entropy solid Larger Molecules generally have a larger entropy

S small < Smedium < Slarge

Larger molecules have more internal motion All the results of this section are summarized in Table

Entropy change of the universe due to natural processes ENTROPY AND NONEQUILIBRIUM STATES

TT T  0 L f 2

TT0  L dmAdx cPP dmcAdx  TTx i 0 L T f dT T S S( volume element ) c Adx  c Adxln f f i P  T P Ti Ti T  cAdx ln f Sfi S( volumeelement ) P Ti

Tf TT0  L  cAdxP  ln TTxi 0 TT0  L L Tx0  L

TTT00 L  cAdxxP ln() TLTff

Upon integrating over the whole bar, the total entropy change of the system is Since the bar is enclosed by an adiabatic enclosure, there is no entropy change of the surroundings.

Hence, the entropy change of the universe is also given by this Eq.

In order to show that the entropy change is positive, let us take a convenient numerical case, such as

To= 400 K, TL =200 K; hence ,Tf =300 K. Then, Principle of the Increase of Entropy

 Increase of Entropy Principle:  The entropy of an isolated system during a process always increases or, in the limiting case of a reversible process, remains constant.  dS ≥ (δQ/T) where T is the thermodynamic temperature at the boundary where δQ is transferred to the surroundings

Entropy is a non-conserving property

Sgen > 0 irreversible processes

= 0 reversible processes

< 0 impossible processes Principle of the Increase of Entropy

TXX,, SSS fi 

كدام يك گزينههاي زير بازده چرخه شكل مقابل را بيان ميكند؟ T

T2 QH

T2  T1 T1 )الف( QC S T2  T1

S S2 1 T1  T2 )ب( T2  T1 QC  T1(S2  S1) T2 T1 )ج( T2 T1)( S2  S1) 2T) Q  1 H 2 T1 T2

)د( 2T2

Q 2T T T  1 C 1 1  2 1 تعريف بازده موتور گرمايي QH T2 T1 T2 T1 10 گرم آب 20 درجه سانتيگراد در فشار اتمسفر به يخ 10- درجه سانتيگراد تبديل ميشود. با فرض اينكه ظرفيت گرمايي بر گرم آب )در حالت مايع( عمال در J/gK 4/2 ثابت بماند، ظرفيت گرمايي بر گرم يخ نصف اين مقدار و همچنين گرماي ذوب يخ در دماي صفر مطلق برابر با J/g 335 باشد، تغيير آنتروپي كل سيستم را محاسبه كنيد.

273 dT  S  mc dQ  mcLi qui ddT 1  Li qui d T 293 تبديل آب 20 به آب صفر dQ  mlf mlf  S2   تبديل آب صفر به يخ صفر dQ  mcI cedT 273 dT 263 تبديل يخ صفر به يخ -10  S  mc 3  I ce 273 T  S1  2.97 J / K    S2  12.27 J / K  S  16.02 J / K   S3  0.78 J / K  What is the entropy change in a free expansion process, when the volume is doubled.

The work done by n moles of ideal gas in an isothermal expansion from V1 to V2 is:

W  nRTn(V2 /V1) 2V Q  W  nRTn  nRTn2. V Therefore the entropy change for n=1 is: Q S   nRn2  (1mol )[8.314J /(mol  K)]( n2)  5.76 J / K. T Engineering Applications of the Entropy Princiiple

Entropy and Unavailabe Energy