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پيشرفته ترموديناميک

كالسيك ترموديناميك: بخش اول

مکانیک مهندسیدانشکده

مقیمی مهدي

References: Bejan A., Advanced engineering thermodynamics-Wiley (2016) Bejan A., Thermal design and optimization (1996) Wark K., Advanced Thermodynamics for Engineers (1994) Dincer, I. Exergy, Energy, Environment and Sustainable

Development (2004) Callen, Thermodynamics and an introduction to thermostatics

(1985)

Extended References: Van Wylen - Fundamentals of Thermodynamics (8th Edition) Van Wylen, John Wiley & Sons, Fundamentals of Statistical

Thermodynamics, R.E. Sonntag, G.J. J.S.Hsieh, Principles of Thermodynamics,, McGraw Hill j. Hatsopoulos and H.J. keenan, Principles of General

Thermodynamics

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هپیشرفت ترمودینامیک با مرتبط موضوعات حوزه در کالسی پروژه عنوان و موضوع -بهمن 25 تا ها پروژه تعیین مهلت -ها ضمیمه + صفحه 15 اکثر حد -96 سال اردیبهشت 30 :کالسی پروژه تحویل -

نحوه ارزیابی فعالیت

درصد 30 )فرودینهفته چهارم ( ترممیان

درصد 35 کالسیپروژه

درصد 35 پایان ترم

الزامی است تحویل تمرینها و حضور فعال

Table of Contents:

The First Law

The Second Law

Entropy Generation, Or Exergy Destruction

Single-phase Systems

Exergy Analysis

Multiphase Systems

Power Generation

Refrigeration

Entropy Generation Minimization

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Thermo-dynamics

Heat )حرارت( Moving )حرکت(

A kind of energy

ترمودینامیک

ا و نسبت آن ب گرمادر علوم و مهندسی، ترمودینامیک به بحث راجع به •.می پردازدانرژي و کار

همانند دما، انرژي داخلی،( توسط متغیرهاي ماکروسکوپیک حالت مواد •کم بر جهت توصیف و چگونگی ارتباط آن ها و قوانین حا) آنتروپی و فشار

. آن ها تعریف می شود

یمی، فیزیک، شیمی، مهندسی شبراي زمینه هاي ترمودینامیکیمحاسبات •ت ، مهندسی مکانیک، مهندسی سیستمهاي انرژي، زیسهوافضامهندسی

.الزم است یاخته، مهندسی پزشکی، دانش مواد و حتی اقتصاد شناسی

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:دیدگاهدو

) Macroscopic(دیدگاه ماکروسکوپیک . 1

به .باشد می سیستم ماکروسکوپی توصیف مبناي سیستم، حالت خواص یا کلی، مشخصات

.است سیستم آن گیري اندازه قابل و اساسی ویژگی چند کردن مشخص عبارتی

) Microscopic(دیدگاه میکروسکوپیک . 2

از کدام هر که است )مولکول N ( ملکول زیادي تعداد از متشکل سیستم یک آماري، نظرم از

است، … و 2E و 1E مساوي آنها انرژي که حالتهایی از مجموعه اي در می تواند مولکولها این

ی توانم موارد بعضی در یا و گرفت نظر در منزوي بصورت می توان را سیستم این .گیرد قرار

. اندگرفته بر در آنرا سیستمها، از جمعی یا مشابه، سیستمهاي از مجموعه اي که کرد فرض

قوانین ترمودینامیکصفرم، ن قانو: عمده مباحث تجربی ترمودینامیک در چهار قانون بنیادي آن بیان گردیده اند•

.ترمودینامیکاول، دوم و سوم .درا بیان می کندما وجود کمیتی از سیستم ترمودینامیکی به نام : قانون صفرم•:ی کندرا بیان مانرژي داخلی وجود خاصیتی از سیستم ترمودینامیکی به نام : قانون اول•

.، مربوط استآنتروپیو دمابه دو خاصیت سیستم، : قانون دوم•

ل هنگامی که انرژي یک سیستم به حداقل مقدار خود می: قانون سوم ترمودینامیک•گامی کههن: یا بطور نمادین. می کند، انتروپی سیستم به مقدار قابل چشم پوشی می رسد

0U, U 0S :از رابطه بین انرژي درونی و دما، رابطه باال را می توان به صورت زیر نوشت

⇒ T 0 ،S 00th Lawهنگامی که ، Defines Temperature (T) 1st Law ⇒ Defines Energy (U) 2nd Law ⇒ Defines Entropy (S) 3rd Law ⇒ Gives Numerical Value to Entropy

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System

Boundary

Surroundings

Equilibrium in state 1

System

ProcessEquilibrium in

state 2

EmpiricalThermodynamics

System: The part of the Universe that we choose to study

Surroundings: The rest of the Universe

Boundary: The surface dividing the System from the Surroundings

Process: When the state of the system changes

Importance of the definition of the system

Solid body mechanics

the system is indeed obvious

In fluid mechanics and heat transfer

the system is understood once the boundary conditions necessary for solving the Navier–Stokes equations are specified.

Defining the system also means sharply identifying the system’s environment or surroundings.

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What differentiates between the system and its environment is the surface called the boundary

The boundary is a surface, not another system (note that the thickness of a surface is zero; therefore, the boundary can neither contain matter nor fill a volume in space)

Boundary

The boundary and the interactions that are present at the boundary play roles in the analysis devoted to solving a

problem.

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Systems can be:

Open: Mass and Energy can transfer between the System and the Surroundings

Closed: Energy can transfer between the System and the Surroundings, but NOT mass

Isolated: Neither Mass nor Energy can transfer between the System and the Surroundings

Thermodynamic properties

The condition, or the being, of a thermodynamic system at a particular point in time is described by an ensemble of quantities called thermodynamic properties.

Thermodynamic properties are only those quantities whose numerical values do not depend on the history of the system, as the system evolves between two different states.

Measurable calculable

P, T, V U, S, H, …

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WORK TRANSFER

quasi-static

The concept of reversible work transfer

The termsYi and Xi are the generalized forces and the generalized displacements (or deformation coordinates), respectively.

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Thermodynamic systems and state variables

Extensive variables, such as volume V , particle number N, total internal energy E, magnetization M, etc., scale linearly with the system size, i.e. as the first power of the system volume. If we take two identical thermodynamic systems, place them next to each other, and remove any barriers between them, then all the extensive variables will double in size.

Intensive variables, such as the pressure p, the temperature T , the chemical potential μ, the electric field E, etc., are independent of system size, scaling as the zeroth power of the volume. They are the same throughout the system, if that system is in an appropriate state of equilibrium. The ratio of any two extensive variables is an intensive variable. For example, we write n = N/V for the number density

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Equilibrium means a condition of balance. In thermodynamicsthe concept includes not only a balance of forces but also a balance of other influences. Each kind of influence refers to a particular aspect of thermodynamic, or complete equilibrium.

Thermal equilibrium refers to an equality of temperature,Mechanical equilibrium to an equality of pressure, and Phase equilibrium to an equality of chemical potentials. Chemical equilibrium is also established in terms of chemical potentials.

For complete equilibrium the several types of equilibrium must exist individually.

Equilibrium

Defined by the collection of all macroscopic properties that are described by State variables (p, n, T, V,…)[INDEPENDENT of the HISTORY of the SYSTEM] For a one-component System, all that is required is:“n” and 2 variables. All other properties then follow.

V =f(n,p,T) or p = g(n,V,T) • Notation: 3 H2 (g, 1 bar, 100 °C)

3 moles gas(n=3) p=1 bar T=100 °C

The State of a System at Equilibrium:

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- Reversible (always in Equilibrium) - Irreversible (defines direction of time) - Adiabatic (no heat transfer between system

and surroundings) - Isobaric (constant pressure) - Isothermal (constant temperature) - Constant Volume - …

Process: Describes the Path

Notation:3 H2 (g, 5 bar, 100 °C) = 3 H2 (g, 1 bar, 50 °C) Path: Sequence of initial state, intermediate states, final state

P

V

1

2i

ii

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HEAT TRANSFER

the Tenth General Conference on Weights and Measures (1954)

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One principle is the equivalence of work transfer and heat transfer as possible forms of energy interactions. This principle is encapsulated in the first law of thermodynamics, which, in Max Planck’s words,“is nothing more than the principle of the conservation of energy applied to phenomena involving the production or absorption of heat”

Two principles of classical thermodynamics

The second principle is the inherent irreversibility of all processes that occur in nature. Everything flows in one direction, from high to low.

The internal energy U of a system is increased by

the transfer of either heat or work into the system.

حرارتکار

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Path dependence of the energy interactions Q1–2 and W1–2

If the process executed by the closed system is a cycle, the first law reduces to

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A falling mass turns a paddle in an insulated

beaker of water in this schematic

representation of Joule’s apparatus for measuring

the temperature increase produced by

doing mechanical work on a system.

Steam issuing from the kettle makes the pinwheel turn in this simple steam turbine. Work could be done to lift a small weight with such an engine.

Heat released by burning gasoline in the cylinder of

an automobile engine causes the piston to

move, converting some of the heat

to work.

آزمایش ژول

کامل گازهاي براي مقدار محاسبه

ایده ال گاز یک درونی انرژي مطالعه با ارتباط در مهمی آزمایش 1843 سال در کی به منجر کم حساسیت با و ابتدائی آزمایش این گرفت انجام ژول توسط

اررفت کردن مشخص براي معیار یک عنوان به امروزه که گردید نتیجه گیري از کیی که بالن دو شامل است دستگاهی آزمایش این .می آید شمار به گاز ایده آل

ود این که گردیده تخلیه دیگري و شده پر اتمسفر 20 تقریباً فشار و هوا با آنها به یک به مجهز که آب حمام یک در آنگاه شده اند جدا هم از شیر یک توسط بالن

داده قرار شده عایق بندي اطراف محیط به نسبت و است ترمومتر و مزنه یک از حمام در موجود آب و بالن ها بین کار و گرما آزمایش این در .می شوند

یاجزای که گاز و آب براي لذا .نمی شود مبادله دیگر طرف از اطراف محیط و طرف.نوشت می توان هستند مطالعه مورد سیستم از

T

E

V

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Eآب+ Eسیستم= مقدار ثابت

dEآب+ dEسیستم= 0

رابطه با حمام آب و گاز به مربوط درونی انرژي تغییرات :می شود داده نشان زیر دیفرانسیلی

می گردد منبسط گاز و می شود باز بالن دو بینما شیر وقتی می باشد dT = 0 لذا نمی شود ایجاد حمام آب در يتغییر هیچگونه

dV می توان که نمی دهد حجم تغییر حمام آب دیگر طرف از و.گرفت نظر در صفر نیز را آب به مربوط

T V T V

E E E EdV dT dV dT 0

V T V T

J A ´ TvÃw

T

EdV 0

V

´ TvÃw

dV چون گازهاي براي این و می باشد لذا است 0.است صادق کامل

یک درونی انرژي ثابت دماي در که است این بیانگر حاصل نتیجه ارمعی یک عنوان به امروزه و می باشد آن حجم از مستقل کامل گاز

ظرن در گاز یک ایده ال رفتار سنجش براي دیگر معیارهاي بر عالوه

.می شود گرفته

T

E0

V

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Internal Energy

• Joule’s Law

ValveClosed

AirVacuum

Thermally Insulated

Internal Energy

• Joule’s Law

Thermally Insulated

ValveOpen

AirAir

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Internal Energy

ValveOpen

AirAir

• Joule’s Law

– Air expands to fill container

• Change in volume

– No heat added (dq=0)

• Thermally isolated container

Internal Energy

• Joule’s Law

– The experiment showed NO CHANGE IN TEMPERATURE!!!!!!!!

ValveOpen

AirAir

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ENERGY CHANGE

The term energy, which in thermodynamics was proposed by William Thomson in 1852, had been coined in 1807 by Thomas Young, the discoverer of the phenomenon of optical interference

Example 1.1.

Consider a rigid and evacuated container (bottle) of volume V that is surrounded by the atmosphere (T0, P0). At some point in time, the neck valve of the bottle opens, and atmospheric air gradually flows in. The wall of the bottle is thin and conductive enough so that the trapped air and the atmosphere eventually reach thermal equilibrium. In the end, the trapped air and the atmosphere are also in mechanical equilibrium, because the neck valve remains open. Determine the net heat interaction that takes place through the wall of the bottle during the entire filling process.

we identify the total air mass that eventually rests inside the bottle:

The final state of the system is represented by the properties (T0,P0,V).

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The first Law of Thermodynamics, U = Q - W, means:

A. Heat cannot be added to a system without work being done.

B. Work cannot be done without heat being added.

C. The amount of work done always equals the amount of heat added.

D. The total internal energy of a system is conserved.

E. All of the above

F. None of the above are true.

CHOOSE THE TRUE STATEMENT.

What is a heat engine?

• Thermal heat QH is introduced into the engine.

• Some of this is converted into mechanical work, W.

• Some heat is released into the environment at a lower temperature, QC.

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What does the First Law tell us about heat engines?

U = Q - W = QH - QC -W

The internal energy U of a heat engine does not change from cycle to cycle, so U =0.

Hence, Q = W.

The net heat flowing into the engine equals the work done by the engine:

W = QH - QC

OPEN SYSTEMS

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OPEN SYSTEMS

In the fields of gas dynamics and compressible fluid mechanics, the group

is recognized as the local stagnation enthalpy of the flowing fluid.

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Example 1.2.

Consider again the problem stated in Example 1.1, this time inthe context of open systems: This phenomenon is the common “filling” process.The object is to determine the heat interaction that occurs across the bottle wall during the filling process.

The mass conservation equation and the first law require at any instant that

Or, since the open system is initially evacuated

we arrive at the same answer as in Example 1.1:

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The Second Law

First Law: showed the equivalence of work and heat ΔU= q -w, ∫dU = 0 for cyclic process ⇒ q =w Suggests engine can run in a cycle and convert heat into useful work. Work and heat are identical.

Second Law: - Puts restrictions on useful conversion of q to w - Follows from observation of a directionality to natural or spontaneous processes

Provides a set of principles for - determining the direction of spontaneous change - determining equilibrium state of system

Heat reservoir : A very large system of uniform T,

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Different statements of the Second Law

Kelvin:

Clausius:

(in a cycle)

Alternative Clausius statement: All spontaneous processes are irreversible. (e.g. heat flows from hot to cold spontaneously and irreversibly)

Mathematical statement:

Another restatement to be discussed next time:

The entropy of an isolated system can only increase or remain constant. Its entropy cannot decrease.

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The Carnot engine: is an ideal system which turns out to have the maximum possible efficiency:

If T1 is the hottest temperature in the engine, and T2 is temperature outside the engine (in Kelvin), then the efficiency is:

This shows that it is not possible too have an efficiency of 100%. You always lose some energy into heating the environment.

In rev. isotherm process: ΔU=0 q = w

In rev. adiabatic process: ,

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Wrev=εqH=qH(1-TC/TH)

According to the Second Law of Thermodynamics, heat will not flow from a colder body to a warmer body.

1. True

2. False

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According to the Second Law of Thermodynamics, heat will not flow from a colder body to a warmer body.

1. True

2. False

OPEN SYSTEMS

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Example

We are now in a position to study the application of the second lawto the unsteady filling process discussed in preceding examples. We adopt the open system approach, where the system is the space V confined by the internal surface of the bottle wall. In the beginning, the system is evacuated while in the end it is filled with air at atmospheric conditions

To answer the question of whether the filling process is reversible, we calculate the entropy generated during the entire process,

The instantaneous entropy generation rate is