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Heat and Thermodynamics 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 ΔSuniverseΔSsystemΔSenvironment 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 dm Adx cPP dm c Adx T T x i 0 L T f dT T S S( volume element) c Adx c Adxln f f i P T P Ti Ti Sfi S( volumeelement ) T c Adx ln f P TT Tx 0 L 0 L TTT00 L cP Adxln( x ) Tff LT Upon integrating over the whole bar, the total entropy change of the system is TT T T0 L x i 0 L Tf cP Adxln Ti 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( عمﻻ 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 nRTn(V2 /V1) 2V Q W nRTn nRTn2. V Therefore the entropy change for n=1 is: Q S nRn2 (1mol )[8.314J /(mol K)]( n2) 5.76 J / K. T Engineering Applications of the Entropy Princiiple Entropy and Unavailabe Energy .
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