Chapter 1 Introduction to Thermodynamics

Chemical, Biochemical, and Engineering Thermodynamics

4th EditionStanley I. Sandler, Univ. of Delaware

ISBN: 0-471-66174-0

Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved.

State Variables

By definition, state variable refers to intensive variables of an equilibrium system, such as: temperature (T), pressure (P), specific volume( ), specific internal energy (Û), refractive index (R), and other variables (Ĥ, Ĝ, Ŝ, Â) introduced in the systems (heat engines, distillations, reactions, etcetera).

Clearly, state variable depends only on equilibrium state of the system, not on the path by which the equilibrium state was reached.

V̂

A pure fluid with single phase at equilibrium state (e.g. steam sealed in a stainless steel cylinder) indicates that if this fluid having specified T and V, it always have a certain pressure P. What is P? We must either determine P by experiment or know relationship between T, V, and P. Scientific or engineering interest is to make a lot measurements of P, V, and T to develop a mathematical volumetric equation of state.

Similarly, measurements of U, V, and T are made to develop a thermal equation of state.

ˆ ˆ( , ); ( , ) P P T V U U T V= =

f1_3_1

Two observations for characteristics of natural processes: (I) System free from forced flows will evolve to an equilibrium state.(II) Once in equilibrium, system will never spontaneously evolve to a non-equilibrium state unless a perturbation input.

Blocks in states (a) and (b) are stable to mechanical disturbances. The delicately balanced block in state (c) is not.

Stable and Unstable Processes

Frictionless piston

f1_4_1

Pressure of Gas A equals to that of Gas B in the system

Gas A’s = Gas B’s + force of gravity on the piston divided by its surface area

Pressures in Mechanics and Thermodynamics

f1_4_2

Dead Weight Pressure Tester

Total pressure in textbook refers to absolute pressure. Note that gauge pressures may be negative (in partially or completely evacuated systems), zero, or positive. So that a gauge calibrated in France may be error for pressure measurements in Taiwan.

Total pressure P = gauge pressure Ps + atmospheric pressure Pa

Ps

Constant-volume Ideal Gas Thermometer

f1_4_3

Pi = 1 bar + ρghiRTi = Pi (V)

R = constant per molei = # of runs

Ti

V

1 bar

Pi

ρ: density of Mercuryg: gravity

pg_24

Temperatures Indicated by Different Fluids

t1_2_1

t1_2_2

t1_2_3

t1_2_4

t1_4_1

t1_5_1

Water prepared at temperature T1 in an insulated container. By several experiments, energies were spent in producing a final equilibrium temperature T2. It resembles

experimental steam engine boat observation of James Prescott Joule between 1837 and 1847

What is steam engine boat?

Ships Driven By Engines

1910 later steam turbine with 30% efficiency 1912 later diesel engine 45% efficiency

1907 steam engines in a steamship15% efficiency1827 wooden paddle-wheel boat using steam Engines

2010 showboat Branson in Table Rock Lake, Branson, Missouri

2002 a steam paddle boat sailed in Rhine river, GE

Viewing the past to be able to see the futuree.g. The Propulsion of Sea-ships (Past, Present, Future)

Roman warship with sail and oars ~200 B.C. Diesel engine powers electric generator that drive a motor to move a propeller~2008

Hydrogen propulsion using a motor powered by hydrogen cell for submarines shown as left ~2020?

Sadi Nicolas L´eonard Carnot (1796-1832)

A Milestone of Thermo-Dynamics

Don’t worry, it won’t start to get complicated or scientific now!

We’ll remain on Thermo-dynamics for beginners

Even 50 years before the invention of the Otto motor, in 1824 the Frenchman, Carnot (the 1st law inventor), described a thermo-dynamic cyclic heat engine with theoretically the highest possible efficiency.

Carnot Statement:All irreversible heat engines between two heat reservoirs are less

efficient than a Carnot Engine operating between the same reservoirs.

All reversible heat engines between two heat reservoirs are equally efficient with a Carnot engine operating between the same reservoirs.

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1.1 The Central Problems of ThermodynamicsIt is to resolve engineering EQUILIBRIUM problems including calculations of energy and phase equilibrium. 1.2 Equilibrium Definition(1) T is constant throughout the system- Thermal Equilibrium(2) P is constant throughout the system-Mechanical Equilibrium(3) x is constant throughout the system or parts of the system(4) No gradients in macroscopic state variables 1.3 The State Variables of The SystemTypical state variables:(1) Temperature (T)(2) Pressure (P)(3) Composition (x)(4) Phase of gas, liquid, solid (π)(5) Others, such as density, refractive index, Ĥ, Ĝ, Ŝ, Â, etcetera

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1.4 Three Laws of Thermodynamics1st law: Total energy of the system plus the surrounding is conserved. Most text books use the following internal energy change (dU) assuming surrounding stays the same. It is no kinetic energy, no potential energy and no friction loss, which is reliable for the reversible process only.

2nd law: All processes occur at such that total entropy change of the system plus the surrounding is positive.

0 for irrevesible process (or isolated cyclic)0 for reversible process (or isolated cyclic)

total system surr

totalrev

S S SS

Δ = Δ + Δ >

Δ =

dU dQ dWdU TdS PdV

= += −

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Review-3Second Law in Kelvin-Planck Form: statement

It is impossible to construct a heat engine that, operating in a cycle, produces no other effect than the absorption of energy from a reservoir

and the performance of an equal amount of work.It is explainable that any heat engine efficiency is less than that

of the Carnot heat engine (the highest).

Lack of an condenser here !

William Thomson (Lord Kelvin) (1824-1907)

Max Karl Ernst Ludwig Planck (1858-1947)

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Second Law in Clausius Form: statementNo process is possible whose sole result is the transfer of heat from a body of

lower temperature to a body of higher temperature

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It is impossible to construct a cyclical machine whose sole effect is to transfer energy continuously by heat from one object to another object at a higher temperature without the input of energy by work.

Energy does not transfer spontaneously by heat from a cold object to a hot object.

It is explainable for a refrigerator required a work (compressor) to transfer heat from cold to hot reservoirs.

Rudolf Clausius1822-1888

Entropy Inventor (Clausius)

• Entropy, S, is a state variable related to the second law of thermodynamics

• The importance of entropy grew with the development of statistical mechanics (or statistical thermodynamics)

• A main result is isolated systems tend toward disorder and entropy is a natural measure of this disorder.

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His conclusion:The entropy of the universe tends to a maximum

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Entropy and Heat• Original formulation of entropy dealt with transfer

of energy by heat in a cyclic process.• Let dQr be the amount of energy transferred by

heat when a system follows a reversible path. The change in entropy, ΔS:

proved the following from Carnot's cycle:

0 in an arbitrary cycle

Irreversible and isolated process:0 S is a state function

ClaisiusdQT

S

≤

Δ ≥

∫

rdQST

Δ =

Another version of 2nd law: statementThe entropy of the universe increases in all natural processes

• An equivalent statement of 2nd law is in any cyclic process of an isolated system, the entropy will either increase or remain the same with time.

• Thus entropy gives information about the evolution of an isolated system with time, it is said to give us the direction of “Time Arrow”.

• The amount of disorder of an isolated system increases with time. It is impossible to go from a disordered system to an ordered system without external interference.

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CH30035/28/2012 24Highly ordered (Low entropy)

Disordered (High entropy)

“Time Arrow”

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3rd law: Entropy of a perfect crystal is zero at a temperature of zero degrees Kevin.

What is entropy ? It is not disorder and it is a measure of disorder.

On the Boltzmann theorem: If the substance is a perfect crystal at T = 0 K, then all particles of the crystal is settled at the lowest Quantum Mechanic state. This condition is the same for all particles.

Q.M. state (i)

i+2i+1

. i .

i-1 lowest

1

1

1

(log ); : ' constant: probability distribution of one state or multisicity

!!.......... !

... ... : . . ( ) : total molecules

i

n

i n

n

Entropy S k k Boltzman s

nn n

n n n molecules in each Q M state iN n n

= = ΩΩ

Ω =

= +…+ ( )in the system crystal

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On a statistical probability state: Entropy is total # of states that to be possibly happened in a system. What is the probability of an exception (state) happened in the system?

CaseNumber (#)

of states

(ω)

Total # of states

(Ω)

Probability of the specific state to be happened

(Ω−1)

Tossing 10 coins 2 210 (210)-1

Tossing 10 dices 6 610 (610)-1

Moving 1-mole molecules in box 10 101024 (101024)-1

24-23 10 (log ) 1.381(10) log(10 ) = 1 ~ 10 /S k J K= Ω =

Q: A system contains N molecules and supposed # of states of one molecule is moving in box, ω =10, what is entropy (S) of the system ?N: Avogadro's number=6.23(10)23; Boltzmann’s constant=1.381(10)-23

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(1) Entropy is measures of disorder and statistically always increase.

(2) Entropy increases with the number of states.(3) On the first law (energy conservation), Niagara falls

could flow upwards. But thanks for the entropy law (arrow of time), it is impossible because of the lowest probability.

Thermodynamic properties is AVERAGE BEHAVIOR of molecules

1.5 Other Postulates for Thermodynamics(a) Internal energy of the system can be in terms of x:

(b) It is impossible to have an entropy meter, but you could obtain S from CP and CV values, indirectly.

(c) It is impossible to have an internal energy meter as well, but you could obtain U from CV .

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),,( xPTfU =

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

=

nx

xx

xM2

1

The Zero law of ThermodynamicsReview-11

29CH30035/28/2012

(d) It is not a mathematical function, but called Thermo Contacted Bodiesto measure coldness and hotness of two bodies, then determine whether the systems are in thermal equilibrium or not. (e) Thermodynamic properties have been used to measure temperature:

Pressure of a gas at constant density (constant volume gas thermometry)Density (volume) of a liquid or solid (liquid in glass thermometer)Electrical resistivity (resistant thermometers, e.g. RTD thermometer)Electrical potential appearing across the junction of two dissimilar

metals (e.g. thermocouple)Vapor pressure of a pure liquidIntensity of thermal radiation (e.g. optical pyrometer)Vibration voltage of an electronic diodeMagnetic change of the magnetPhase transition (e.g. liquid crystal thermometer)

(f) What is work? It is a line integral and path dependence.

(g) What is heat? It is also path dependence.

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Both Q and W are time transit energies

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2

1

1 2

( ) ( )state

state

path path

Work W force d coordinate

dW dW

= =

≠

∫

2

1( )

state

stateHeat Q d thermal energy= = ∫

(h) There is no variations in measured properties (T, P) with time and space.All macroscopic forces (e.g. thermal, mechanical, chemical, electrical, interfacial, etc.) are in balance within the system.Coordinates of molecules, e.g. rN (position of N molecules), ΩN

(orientation) and PN (momentum) are continuously changing but average contributions do not. All these coordinates contribute to phase space.Average macroscopic properties (T, P, V, x) have no fluctuations for systems (Number of molecules > 109 for gas, N > 103 for condensed).

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Macroscopic thermodynamics equilibrium stateReview-13

z

x

y

r1

r2

P1

P2

1

2

1Ω

2Ω 1

2

=N

n

rr

r

r

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

M

1

2

=N

n

Ω⎛ ⎞⎜ ⎟Ω⎜ ⎟Ω⎜ ⎟⎜ ⎟Ω⎝ ⎠

M

1

2

=N

n

PP

P

P

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

M

Equilibrium State (ES) is useful for solving problems of the fixed state and the steady systems.

Steady State (SS or called pseudo equilibrium state)means that external force is still counted, in that case, there may be a pressure (or temperature) difference within the system. SS is a set including ES.

All pressures and temperatures are constant in all places for both states (SS and ES).

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Equilibrium State (ES) and Steady State (SS)Review-14

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Comments on Development of ThermodynamicsReview-15

Classical Thermodynamics(or Thermo-Physics)

Application to practical industrial problems

Using numerical solutions with databank

StatisticalThermodynamics Theorems Molecular Thermodynamics

A

CB

D

E

A: Formal definitions and thermodynamics property relationships such as Legendre’s transformation; Chain rules; Triple product rule; Euler theroem; Maxwell equations; Conservations of mass; Energy and Entropy balances; Heat engines; Gibbs-Duhem and Gibbs-Helmholtz equations; Equlibrium rules including energy and entropy calculations (Sandler Chapters 2,3,4,5,6)

B: Using intermolecular forces relationship to explain what is Thermodynamics. It’s very accurate and sound fundamentals but application is rare. (Prausnitz textbook)

C: Corresponding state theory, van der Waal, Redlich-Kwong and Peng-Robinson fugacity coefficient equations of state; van-Larr, Margules, Wilson, NRTL, UniQuac, Unifac activity coefficient liquid models. (Sandler Chapters 7,8,9,10,11,12)

D: Assumming systems approximation to equilibrium or steady state, such as Chemical Vapor Deposition or Plasma Deposition for TFT-LCD thin films; Biotechnology processing for health supplements, pharmaceutics, Neutraceutics. (Sandler Chapters 13,14,15)

E: Tools such as ASPEN Plus (i.e. Hysys) or ChemCad or SimSci (PRO-II) or PE2000; Databanks such as DIPPR or ASOG. (Junior courses)

• 1660 Boyle PV=constant at constant T• 1687 Newton principle of work• 1714 Fahrenheit Fahrenheit temperature scale• 1742 Celsius Celsius temperature scale• 1768 Watt steam engine• 1787 Charles P ∝ T at constant V• 1798 Thompson conversion of work to heat• 1802 Gay-Lussac V ∝ T at constant P• 1803 Henry Henry’s law• 1805 Dalton total pressure = sum of partial pressures• 1811 Avogadro Avogadro’s number• 1824 Carnot thermal efficiency of heat engines, 1st law• 1834 Clapeyron dP/dT of two phase transition equilibrium

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Time-Table and Milestones of Thermo-dynamicsReview-16

• 1842 Joule Joule’s mechanical equivalent of heat, 1st law• 1848 Kelvin thermodynamic temperature scale• 1854 Joule, Thomson Joule-Thomson coefficient• 1865 Clausius defined entropy, 2nd law• 1873 van der Waals equation of state and corresponding states• 1875 Gibbs thermodynamic fundamental relations, μ• 1881 Ponyting Poynting equation• 1900 Onnes virial equation • 1901 Lewis defined fugacity• 1906 Nerst 3rd law of thermodynamics• 1906 van Laar van Laar equation • 1907 Lewis defined activity• 1924 Lennard Jones Lennard-Jones potential energy and forces

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• 1924 de Broglie particles have wave-like properties• 1926 Schrodinger wave equation• 1929 Hildebrand defined regular solution• 1936 Keenan and Keye steam tables• 1946 Wohl Wohl’s expansion of excess Gibbs energy • 1949 Redlich-Kwong R-K equation of state• 1955 Pitzer acentric factor• 1958 Reid and Prausnitz The properties of gases and liquids• 1964 Wilson “Local composition” model• 1968 Renon & Prausnitz Non-Random Two-Liquid theory• 1969 Carnahan & Starling Hard-sphere equation of state• 1975 Lee & Kesler Generalized equation of state • 1976 Peng-Robinson P-R equation of state

• Any New Recently ???

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