Lecture 6: Intro to Entropy

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Lecture 6: Intro to Entropy"

Transcription

1 Lecture 6: Intro to Entropy Reading: Zumdahl 0., 0., 0.3 Outline: Why enthalpy isn t enough. Statistical interpretation of entropy Boltzmann s Formula Heat engine leads to Entropy as a state function Problems:Z0.-4, Z0.7, Z0.6-7, Z0.9-, Z0.5-6.

2 Enthalpy and Spontaneous Rxns Early on in the development of thermodynamics, it was believed that if a reaction was exothermic, it was spontaneous. But there are plenty of reactions that go that do not give off heat. Consider the following reaction: H O(s) H O(l) ΔH rxn = +6.0 kj Endothermic..yet spontaneous! Above 0C, but not spontaneous below 0C. Why? Consider the hot packs and cold packs again as well.

3 Enthalpy and Spontaneous Reactions: Joule s original experiment Consider the following Experiment: Mixing of a gas inside a bulb adiabatically (q = 0). q = 0, The bulbs are insulated w = 0, External Pressure is zero. ΔΤ=0, Experimental Result. ΔE = 0, and ΔH = 0.but it still happens, the gas expands (spontaneously) to fill the two bulbs. Why? 3

4 Entropy and Statistical Probability The connection between weight (Ω) and entropy (S) is given by Boltzmann s Formula: S = k ln Ω B Boltzmann s constant: = R =.38 0 N 3 For a given state (where E is fixed) Ω is the number of ways of arranging the molecules (or microstates). The difference in entropy between two states then is: k Δ S = kbln Ω kbln Ω = kbln Ω B A Ω J K 4

5 Molecules Move by Chance Between Bulbs What is the chance that a molecule will be on the left: ½ What is the chance that two molecules will be on the left: ¼ And N molecules on the left: For Large N, very small chance: The molecules move in a statistically independent way. How does the entropy change for the gas if we double the volume? How many ways to put a molecule in either side vs? Twice as many. Ω is the number of ways of arranging a molecule in one bulb, then Ω is the number of ways of arranging it in both bulbs. All particles are statistically independent so get a product of arrangements. Apply Boltzmann s definition of entropy: N N Ω Ω N Bln Bln ( B A) ln ln Ω Ω N A Δ S = k = k = k N = nr 5

6 Expansion by any amount: For each independent particle Original Weight = Ω Final Weight = Ω In the previous example the statistical weight was directly proportional to volume. Now generalizing to any two different volumes: N Ω f Ω f V f Δ S = kb ln = nrln = nrln I I V Ω Ω I 6

7 The absolute entropy for a gas in a box Avagadro s principle: mole occupies.4 liters at STP. From this we will compute the absolute entropy for a gas in a box. Imagine the the box of volume V (.4L) is divided up (conceptually anyway) into a number of sub-boxes each of which is capable of holding one molecule at a time. Assume a sub-box is about 0.05 nanometer in length (which is the Bohr radius of an atom). This give us a number of sites (sub-boxes) to put molecules in, one at a time. 3 3 V.4 0 m 9 Λ= = = V sub ( 50 m) Now count the way to put Avagadro s number of molecules in there: Ω= Λ N A N A Compute the entropy: This is the number of sites each molecule can occupy, and they are all statistically independent. So the total Weight is the product of individual weights. 9 Λ N A S = kbln Ω= kbnaln = Rln = R = 05 J This is close to the experimental values for simple gasses (like He or H), and 7 shows that the entropy is proportional to the log of the Volume. K

8 Example: Crystal of CO One can flip Each arrangement of CO is possible. Consider the depiction of crystalline CO. There are two possible arrangements for each CO molecule. For a mole of CO: Ω = N A Same result as for the Joule Experiment where the volume doubled. S = k ln Ω= k ln = k N ln = Rln = 0.7 R= 5.6 J ( N A ) ( ) ( ) B B B A 8 K

9 What is Entropy Good For? All other thing being equal, the most probable way to distribute the energy is the most likely way the system will arrange itself. Entropy is a measure of what is probable. The larger the entropy, the more probable the event. An increase in entropy is a more probably event. An increase in volume results in an increase in entropy For a chemical reaction, if entropy increases it ought be more probably (i.e. spontaneous). (See problems -4) In general then a reaction that creates a gas is going to increase its entropy, and that can make a reaction happen. Temperature can help if the entropy (change) is positive If can t get a gas, going to a liquid from solid is next best. In a reaction A+B goes to AB, what is entropy change? 9

10 Heat Engines (and Entropy) We will study the gas in a box, and determine what the entropy change is from a thermodynamic point of view, and will find that we arrive at the same answer as Boltzmann, and that entropy is a state function and a measurable quantity as well. We have examined isochoric and isobaric changes in a gas in a box. Both of these are done by raising or lowering the temperature (which can be done slowly). Now we consider isothermal processes, many of which cannot be done slowly. We need isothermal, reversible expansion/contraction process because this tells us what entropy is from thermodynamics. 0

11 Example: Isothermal Expansion Consider a mass connected to a ideal gas contained in a piston. Piston is submerged in a constant T bath such that ΔT = 0 during expansion.

12 Isothermal Expansion: Start Δh Δ V = AΔh Δh PV = PV = PV = nrt Initially, V = V Finally V = V P = P P = P Pressure of gas is equal to that created by mass: P = force/area = M g/a where A = piston area g = gravitational acceleration (9.8 m/s )

13 Isothermal Expansion: One Step (Not Reversible; it is Irreversible) One-Step Expansion. We change the weight to M =M /4, then P ext = P =(M /4)g/A = P /4 Internal pressure is larger than the external pressure so the gas will expand. The work done is defined by the external pressure. The mass will be lifted until the internal pressure equals the external pressure. In this case V = 4V Because nrt = PV = PV = PV q=-w = P ext ΔV= P /4 (4V -V ) = 3/4 P V 3

14 PV Diagram: One Step vs Reversible Work at Constant Temperature Expansion (green line) raises mass M = M in one step. 4 Compression (red line) lowers mass M in a single step and returns the system to state. w= 3PV = 3nRT 3 3 w= PV = nrt 4 4 4

15 One Step Compression State of the system after the Step Expansion: Vacuum 4 M V = 4 V P = P initial 4 initial 3 4 M What do we have to do to get the system back to its original state before -step expansion? [Pick up Weight] System did work: Raised M/4; to restore it we have to raise 3M/4 the same distance. We must do more work to restore the system than we got from it in the first place. 5

16 Reversible Isothermal Expansion: (Infinite number of steps; can go back and forth) Add up areas (integrate) from V to V V w total = PdV = nrt V dv V V V V = nrt(ln(v )) V = nrt ln V V rev V = rev = ln V q w nrt 6

17 A Thermodynamic Engine: Defining Entropy Imagine doing all steps reversibly, then compression is simpler to understand. The system variables (P,T) are always only incrementally different from the external values. Use two different heat reservoirs at two different temperatures. 4 Let s consider the four-step cycle illustrated: : Isothermal expansion : Isochoric cooling 3: Isothermal compression 3 4: Isochoric heating V V Volume 7

18 First Step of Four Cycle 4 Step : Isothermal Expansion at T = T high from V to V Now ΔT = 0; therefore, ΔE = 0 and q = -w 3 V V Volume Do expansion reversibly. Then: q = w = nrt high ln V V 8

19 4 Step 3 V V Volume Step : Isochoric Cooling to T = T low. Now ΔV = 0; therefore, w = 0 q = q V =ΔE = nc v ΔT = nc v (T low -T high ) 9

20 Step 3 4 Step 3: Isothermal Compression at T = T low from V to V. Now ΔT = 0; therefore, ΔE = 0 and q = -w 3 V V Volume Do compression reversibly, then q 3 = w 3 = nrt low ln V V 0

21 4 Step 4 3 V V Volume Step 4: Isochoric Heating to T = T high. Now ΔV = 0; therefore, w = 0 q 4 =q V = ΔE = nc v ΔT= nc v (T high -T low ) = -q

22 4 Add together: All 4 steps of the engine Δ E =Δ H = 0 Total Total (State Function) q total = q + q + q 3 + q 4 3 V V Volume q total = q + q 3 V V qtotal = nrthigh ln + nrtlow ln V V V V q = nrt ln nrt ln V qtotal = nrδ Tln = w 0 V total high low V V total

23 Joule s Experiment (Z0.6) One mole of and ideal gas at liter, and 5 Atm. expands isothermally into an evaluated bulb to reach a total volume of liters. Calculate q, w and q rev for this change of state. How do we approach this? Write down first law(s) and the formula for work. Δ E = nc Δ T = q + w but Δ T = 0 V w= PextΔ V and Pext = 0 Now that q=w=0, how do we determine the reversible heat? It is still isothermal, and we must find a reversible path. Δ E = nc Δ T = 0 = q + w q = w V rev rev rev rev V wrev = nrtln = ( PV ) ln = 5 0 ln = J = 350J V qrev qrev =+ 350J Δ S = = nrln = = 5 J T K 3

Chapter 15: Thermodynamics

Chapter 15: Thermodynamics Chapter 15: Thermodynamics The First Law of Thermodynamics Thermodynamic Processes (isobaric, isochoric, isothermal, adiabatic) Reversible and Irreversible Processes Heat Engines Refrigerators and Heat

More information

Lecture 3: State Functions

Lecture 3: State Functions Lecture 3: State Functions Reading: Zumdahl 9.3, 9.4 Outline Example of Thermo. Pathways State Functions (9.4 for laboratory) Problems: (Z9.72,Z9.84),(Z9.29,Z9.30),(Z9.32,Z9.38) Z9.13 (Find the mistake)

More information

ENTROPY AND THE SECOND LAW OF THERMODYNAMICS

ENTROPY AND THE SECOND LAW OF THERMODYNAMICS Chapter 20: ENTROPY AND THE SECOND LAW OF THERMODYNAMICS 1. In a reversible process the system: A. is always close to equilibrium states B. is close to equilibrium states only at the beginning and end

More information

Thermodynamics Answers to Tutorial # 1

Thermodynamics Answers to Tutorial # 1 Thermodynamics Answers to Tutorial # 1 1. (I) Work done in free expansion is Zero as P ex = 0 (II) Irreversible expansion against constant external pressure w = P ex (V 2 V 1 ) V 2 = nrt P 2 V 1 = nrt

More information

Definition of Enthalpy

Definition of Enthalpy Lecture 2: Enthalpy Reading: Zumdahl 9.2, 9. Outline Definition of Enthalpy (ΔH) Definition of Molar Heat Capacity (C v and C p ) Calculating using C v and C p Changes in ΔE and ΔH as well as q and w for

More information

Expansion and Compression of a Gas

Expansion and Compression of a Gas Physics 6B - Winter 2011 Homework 4 Solutions Expansion and Compression of a Gas In an adiabatic process, there is no heat transferred to or from the system i.e. dq = 0. The first law of thermodynamics

More information

The First Law of Thermodynamics

The First Law of Thermodynamics Thermodynamics The First Law of Thermodynamics Thermodynamic Processes (isobaric, isochoric, isothermal, adiabatic) Reversible and Irreversible Processes Heat Engines Refrigerators and Heat Pumps The Carnot

More information

Reading. Spontaneity. Monday, January 30 CHEM 102H T. Hughbanks

Reading. Spontaneity. Monday, January 30 CHEM 102H T. Hughbanks Thermo Notes #3 Entropy and 2nd Law of Thermodynamics Monday, January 30 CHEM 102H T. Hughbanks Reading You should reading Chapter 7. Some of this material is quite challenging, be sure to read this material

More information

Phys 2101 Gabriela González

Phys 2101 Gabriela González Phys 2101 Gabriela González If volume is constant ( isochoric process), W=0, and Tp -1 is constant. pv=nrt If temperature is constant ( isothermal process), ΔE int =0, and pv is constant. If pressure is

More information

c. Applying the first law of thermodynamics from Equation 15.1, we find that c h c h.

c. Applying the first law of thermodynamics from Equation 15.1, we find that c h c h. Week 11 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

More information

= T T V V T = V. By using the relation given in the problem, we can write this as: ( P + T ( P/ T)V ) = T

= T T V V T = V. By using the relation given in the problem, we can write this as: ( P + T ( P/ T)V ) = T hermodynamics: Examples for chapter 3. 1. Show that C / = 0 for a an ideal gas, b a van der Waals gas and c a gas following P = nr. Assume that the following result nb holds: U = P P Hint: In b and c,

More information

Lesson 42c: PV Diagrams

Lesson 42c: PV Diagrams Lesson 42c: V Diagrams From the last section, you were probably wondering what happens when we do something like add heat to a sealed cylinder. This sounds like a pretty dangerous idea if you think back

More information

Heat as Energy Transfer. Heat is energy transferred from one object to another because of a difference in temperature

Heat as Energy Transfer. Heat is energy transferred from one object to another because of a difference in temperature Unit of heat: calorie (cal) Heat as Energy Transfer Heat is energy transferred from one object to another because of a difference in temperature 1 cal is the amount of heat necessary to raise the temperature

More information

a) Use the following equation from the lecture notes: = ( 8.314 J K 1 mol 1) ( ) 10 L

a) Use the following equation from the lecture notes: = ( 8.314 J K 1 mol 1) ( ) 10 L hermodynamics: Examples for chapter 4. 1. One mole of nitrogen gas is allowed to expand from 0.5 to 10 L reversible and isothermal process at 300 K. Calculate the change in molar entropy using a the ideal

More information

Final Exam Review Questions PHY Final Chapters

Final Exam Review Questions PHY Final Chapters Final Exam Review Questions PHY 2425 - Final Chapters Section: 17 1 Topic: Thermal Equilibrium and Temperature Type: Numerical 12 A temperature of 14ºF is equivalent to A) 10ºC B) 7.77ºC C) 25.5ºC D) 26.7ºC

More information

THE CLAUSIUS INEQUALITY

THE CLAUSIUS INEQUALITY Part IV Entropy In Part III, we introduced the second law of thermodynamics and applied it to cycles and cyclic devices. In this part, we apply the second law to processes. he first law of thermodynamics

More information

Physics 2101 Section 3 April 26th: Chap. 18 : Chap Ann n ce n e t nnt : Exam #4, April Exam #4,

Physics 2101 Section 3 April 26th: Chap. 18 : Chap Ann n ce n e t nnt : Exam #4, April Exam #4, Physics 2101 Section 3 April 26 th : Chap. 18-1919 Announcements: n nt Exam #4, April 28 th (Ch. 13.6-18.8) 18.8) Final Exam: May 11 th (Tuesday), 7:30 AM Make up Final: May 15 th (Saturday) 7:30 AM Class

More information

Second Law of Thermodynamics

Second Law of Thermodynamics Thermodynamics T8 Second Law of Thermodynamics Learning Goal: To understand the implications of the second law of thermodynamics. The second law of thermodynamics explains the direction in which the thermodynamic

More information

FUNDAMENTALS OF ENGINEERING THERMODYNAMICS

FUNDAMENTALS OF ENGINEERING THERMODYNAMICS FUNDAMENTALS OF ENGINEERING THERMODYNAMICS System: Quantity of matter (constant mass) or region in space (constant volume) chosen for study. Closed system: Can exchange energy but not mass; mass is constant

More information

Thermochemistry. Thermochemistry 1/25/2010. Reading: Chapter 5 (omit 5.8) As you read ask yourself

Thermochemistry. Thermochemistry 1/25/2010. Reading: Chapter 5 (omit 5.8) As you read ask yourself Thermochemistry Reading: Chapter 5 (omit 5.8) As you read ask yourself What is meant by the terms system and surroundings? How are they related to each other? How does energy get transferred between them?

More information

Page 1. Set of values that describe the current condition of a system, usually in equilibrium. What is a state?

Page 1. Set of values that describe the current condition of a system, usually in equilibrium. What is a state? What is a state? Set of values that describe the current condition of a system, usually in equilibrium Is this physics different than what we have learned? Why do we learn it? How do we make the connection

More information

THE KINETIC THEORY OF GASES

THE KINETIC THEORY OF GASES Chapter 19: THE KINETIC THEORY OF GASES 1. Evidence that a gas consists mostly of empty space is the fact that: A. the density of a gas becomes much greater when it is liquefied B. gases exert pressure

More information

Chemistry 433. The Third Law of Thermodynamics. Residual Entropy. CO: an Imperfect Crystal. Question. Question. Lecture 12 The Third Law

Chemistry 433. The Third Law of Thermodynamics. Residual Entropy. CO: an Imperfect Crystal. Question. Question. Lecture 12 The Third Law Chemistry 433 Lecture 12 he hird Law he hird Law of hermodynamics he third law of thermodynamics states that every substance has a positive entropy, but at zero Kelvin the entropy is zero for a perfectly

More information

Laws of Thermodynamics

Laws of Thermodynamics Laws of Thermodynamics Thermodynamics Thermodynamics is the study of the effects of work, heat, and energy on a system Thermodynamics is only concerned with macroscopic (large-scale) changes and observations

More information

Thermodynamics AP Physics B. Multiple Choice Questions

Thermodynamics AP Physics B. Multiple Choice Questions Thermodynamics AP Physics B Name Multiple Choice Questions 1. What is the name of the following statement: When two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium

More information

The first law: transformation of energy into heat and work. Chemical reactions can be used to provide heat and for doing work.

The first law: transformation of energy into heat and work. Chemical reactions can be used to provide heat and for doing work. The first law: transformation of energy into heat and work Chemical reactions can be used to provide heat and for doing work. Compare fuel value of different compounds. What drives these reactions to proceed

More information

The Equipartition Theorem

The Equipartition Theorem The Equipartition Theorem Degrees of freedom are associated with the kinetic energy of translations, rotation, vibration and the potential energy of vibrations. A result from classical statistical mechanics

More information

Gibbs Free Energy and Chemical Potential. NC State University

Gibbs Free Energy and Chemical Potential. NC State University Chemistry 433 Lecture 14 Gibbs Free Energy and Chemical Potential NC State University The internal energy expressed in terms of its natural variables We can use the combination of the first and second

More information

2. A process that releases heat into the surroundings is called. A process that can be reversed by an infinitesimal change in a parameter

2. A process that releases heat into the surroundings is called. A process that can be reversed by an infinitesimal change in a parameter Sample quiz and test questions Chapter 2. I. Terms and short answers 1. A system that can exchange neither matter nor energy with its surroundings is called isolated 2. A process that releases heat into

More information

Course 2 Mathematical Tools and Unit Conversion Used in Thermodynamic Problem Solving

Course 2 Mathematical Tools and Unit Conversion Used in Thermodynamic Problem Solving Course Mathematical Tools and Unit Conversion Used in Thermodynamic Problem Solving 1 Basic Algebra Computations 1st degree equations - =0 Collect numerical values on one side and unknown to the otherside

More information

2.5(a) Enthalpy. Chapter 2. The First Law. P.27

2.5(a) Enthalpy. Chapter 2. The First Law. P.27 2.5(a) Enthalpy Chapter 2. The First Law. P.27 Justification 2.1 The relation H = q p For a general infinitesimal change in the state of the system, U changes to U + du, p changes to p + dp, and V changes

More information

Problem Set 3 Solutions

Problem Set 3 Solutions Chemistry 360 Dr Jean M Standard Problem Set 3 Solutions 1 (a) One mole of an ideal gas at 98 K is expanded reversibly and isothermally from 10 L to 10 L Determine the amount of work in Joules We start

More information

THE SECOND LAW OF THERMODYNAMICS

THE SECOND LAW OF THERMODYNAMICS 1 THE SECOND LAW OF THERMODYNAMICS The FIRST LAW is a statement of the fact that ENERGY (a useful concept) is conserved. It says nothing about the WAY, or even WHETHER one form of energy can be converted

More information

Heat and Work. First Law of Thermodynamics 9.1. Heat is a form of energy. Calorimetry. Work. First Law of Thermodynamics.

Heat and Work. First Law of Thermodynamics 9.1. Heat is a form of energy. Calorimetry. Work. First Law of Thermodynamics. Heat and First Law of Thermodynamics 9. Heat Heat and Thermodynamic rocesses Thermodynamics is the science of heat and work Heat is a form of energy Calorimetry Mechanical equivalent of heat Mechanical

More information

Thermodynamics: First Law, Calorimetry, Enthalpy. Calorimetry. Calorimetry: constant volume. Monday, January 23 CHEM 102H T.

Thermodynamics: First Law, Calorimetry, Enthalpy. Calorimetry. Calorimetry: constant volume. Monday, January 23 CHEM 102H T. Thermodynamics: First Law, Calorimetry, Enthalpy Monday, January 23 CHEM 102H T. Hughbanks Calorimetry Reactions are usually done at either constant V (in a closed container) or constant P (open to the

More information

Physics 5D - Nov 18, 2013

Physics 5D - Nov 18, 2013 Physics 5D - Nov 18, 2013 30 Midterm Scores B } Number of Scores 25 20 15 10 5 F D C } A- A A + 0 0-59.9 60-64.9 65-69.9 70-74.9 75-79.9 80-84.9 Percent Range (%) The two problems with the fewest correct

More information

PSS 17.1: The Bermuda Triangle

PSS 17.1: The Bermuda Triangle Assignment 6 Consider 6.0 g of helium at 40_C in the form of a cube 40 cm. on each side. Suppose 2000 J of energy are transferred to this gas. (i) Determine the final pressure if the process is at constant

More information

Absorption of Heat. Internal energy is the appropriate energy variable to use at constant volume

Absorption of Heat. Internal energy is the appropriate energy variable to use at constant volume 6 Absorption of Heat According to the First Law, E = q + w = q - P V, assuming P-V work is the only kind that can occur. Therefore, E = q V. The subscript means that the process occurs at constant volume.

More information

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 7 Ideal Gas Laws, Different Processes Let us continue

More information

Entropy and the Second Law of Thermodynamics. The Adiabatic Expansion of Gases

Entropy and the Second Law of Thermodynamics. The Adiabatic Expansion of Gases Lecture 7 Entropy and the Second Law of Thermodynamics 15/08/07 The Adiabatic Expansion of Gases In an adiabatic process no heat is transferred, Q=0 = C P / C V is assumed to be constant during this process

More information

Problem Set 1 3.20 MIT Professor Gerbrand Ceder Fall 2003

Problem Set 1 3.20 MIT Professor Gerbrand Ceder Fall 2003 LEVEL 1 PROBLEMS Problem Set 1 3.0 MIT Professor Gerbrand Ceder Fall 003 Problem 1.1 The internal energy per kg for a certain gas is given by U = 0. 17 T + C where U is in kj/kg, T is in Kelvin, and C

More information

Chapter 5 Energy Relationships in Chemistry: Thermochemistry

Chapter 5 Energy Relationships in Chemistry: Thermochemistry Chapter 5 Energy Relationships in Chemistry: Thermochemistry In order to study thermochemical changes, we first have to define (a) system that specify part of the universe of interest to us. (b) surrounding

More information

ENERGY. Thermochemistry. Heat. Temperature & Heat. Thermometers & Temperature. Temperature & Heat. Energy is the capacity to do work.

ENERGY. Thermochemistry. Heat. Temperature & Heat. Thermometers & Temperature. Temperature & Heat. Energy is the capacity to do work. ENERGY Thermochemistry Energy is the capacity to do work. Chapter 6 Kinetic Energy thermal, mechanical, electrical, sound Potential Energy chemical, gravitational, electrostatic Heat Heat, or thermal energy,

More information

Esystem = 0 = Ein Eout

Esystem = 0 = Ein Eout AGENDA: I. Introduction to Thermodynamics II. First Law Efficiency III. Second Law Efficiency IV. Property Diagrams and Power Cycles V. Additional Material, Terms, and Variables VI. Practice Problems I.

More information

Chapter 19 Thermodynamics

Chapter 19 Thermodynamics 19.1 Introduction Chapter 19 Thermodynamics We can express the fundamental laws of the universe which correspond to the two fundamental laws of the mechanical theory of heat in the following simple form.

More information

Esystem = 0 = Ein Eout

Esystem = 0 = Ein Eout AGENDA: I. Introduction to Thermodynamics II. First Law Efficiency III. Second Law Efficiency IV. Property Diagrams and Power Cycles V. Additional Material, Terms, and Variables VI. Practice Problems I.

More information

Chapter 19. Chemical Thermodynamics. The reverse reaction (two eggs leaping into your hand with their shells back intact) is not spontaneous.

Chapter 19. Chemical Thermodynamics. The reverse reaction (two eggs leaping into your hand with their shells back intact) is not spontaneous. Chapter 19. Chemical Thermodynamics SOURCE: Chemistry the Central Science: Prentice hall I. Spontaneous Processes Thermodynamics is concerned with the question: will a reaction occur? First Law of Thermodynamics:

More information

Lecture 36 (Walker 18.8,18.5-6,)

Lecture 36 (Walker 18.8,18.5-6,) Lecture 36 (Walker 18.8,18.5-6,) Entropy 2 nd Law of Thermodynamics Dec. 11, 2009 Help Session: Today, 3:10-4:00, TH230 Review Session: Monday, 3:10-4:00, TH230 Solutions to practice Lecture 36 final on

More information

Thermal Properties of Matter

Thermal Properties of Matter Chapter 18 Thermal Properties of Matter PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 18 To relate the

More information

Define the notations you are using properly. Present your arguments in details. Good luck!

Define the notations you are using properly. Present your arguments in details. Good luck! Umeå Universitet, Fysik Vitaly Bychkov Prov i fysik, Thermodynamics, 0-0-4, kl 9.00-5.00 jälpmedel: Students may use any book(s) including the textbook Thermal physics. Minor notes in the books are also

More information

Answer, Key Homework 6 David McIntyre 1

Answer, Key Homework 6 David McIntyre 1 Answer, Key Homework 6 David McIntyre 1 This print-out should have 0 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making

More information

Give all answers in MKS units: energy in Joules, pressure in Pascals, volume in m 3, etc. Only work the number of problems required. Chose wisely.

Give all answers in MKS units: energy in Joules, pressure in Pascals, volume in m 3, etc. Only work the number of problems required. Chose wisely. Chemistry 45/456 0 July, 007 Midterm Examination Professor G. Drobny Universal gas constant=r=8.3j/mole-k=0.08l-atm/mole-k Joule=J= Nt-m=kg-m /s 0J= L-atm. Pa=J/m 3 =N/m. atm=.0x0 5 Pa=.0 bar L=0-3 m 3.

More information

Problem Set 4 Solutions

Problem Set 4 Solutions Chemistry 360 Dr Jean M Standard Problem Set 4 Solutions 1 Two moles of an ideal gas are compressed isothermally and reversibly at 98 K from 1 atm to 00 atm Calculate q, w, ΔU, and ΔH For an isothermal

More information

System. System, Boundary and surroundings: Nature of heat and work: Sign convention of heat: Unit-7 Thermodynamics

System. System, Boundary and surroundings: Nature of heat and work: Sign convention of heat: Unit-7 Thermodynamics Unit-7 Thermodynamics Introduction: The term Thermo means heat and dynamics means flow or movement.. So thermodynamics is concerned with the flow of heat. The different forms of the energy are interconvertible

More information

THERMOCHEMISTRY & DEFINITIONS

THERMOCHEMISTRY & DEFINITIONS THERMOCHEMISTRY & DEFINITIONS Thermochemistry is the study of the study of relationships between chemistry and energy. All chemical changes and many physical changes involve exchange of energy with the

More information

Entropy and The Second Law of Thermodynamics

Entropy and The Second Law of Thermodynamics The Second Law of Thermodynamics (SL) Entropy and The Second Law of Thermodynamics Explain and manipulate the second law State and illustrate by example the second law of thermodynamics Write both the

More information

Spontaneity of a Chemical Reaction

Spontaneity of a Chemical Reaction Spontaneity of a Chemical Reaction We have learned that entropy is used to quantify the extent of disorder resulting from the dispersal of matter in a system. Also; entropy, like enthalpy and internal

More information

CHAPTER 12. Gases and the Kinetic-Molecular Theory

CHAPTER 12. Gases and the Kinetic-Molecular Theory CHAPTER 12 Gases and the Kinetic-Molecular Theory 1 Gases vs. Liquids & Solids Gases Weak interactions between molecules Molecules move rapidly Fast diffusion rates Low densities Easy to compress Liquids

More information

Entropy and the Kinetic Theory: the Molecular Picture

Entropy and the Kinetic Theory: the Molecular Picture previous index next Entropy and the Kinetic Theory: the Molecular Picture Michael Fowler 7/15/08 Searching for a Molecular Description of Entropy Clausius introduced entropy as a new thermodynamic variable

More information

Exam 4 -- PHYS 101. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Exam 4 -- PHYS 101. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Name: Class: Date: Exam 4 -- PHYS 101 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A steel tape measure is marked such that it gives accurate measurements

More information

Entropy and the Second Law

Entropy and the Second Law Class Notes 9, Phyx Entropy and the Second Law I. THERMODYNAMIC DEFINITION OF ENTROPY P-V DIAGRAM for IDEAL MONATOMIC GAS Entropy is a term that crops up from time to time in everyday conversations. This

More information

Chapter 18 Temperature, Heat, and the First Law of Thermodynamics. Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57

Chapter 18 Temperature, Heat, and the First Law of Thermodynamics. Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57 Chapter 18 Temperature, Heat, and the First Law of Thermodynamics Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57 Thermodynamics study and application of thermal energy temperature quantity

More information

HEAT UNIT 1.1 KINETIC THEORY OF GASES. 1.1.1 Introduction. 1.1.2 Postulates of Kinetic Theory of Gases

HEAT UNIT 1.1 KINETIC THEORY OF GASES. 1.1.1 Introduction. 1.1.2 Postulates of Kinetic Theory of Gases UNIT HEAT. KINETIC THEORY OF GASES.. Introduction Molecules have a diameter of the order of Å and the distance between them in a gas is 0 Å while the interaction distance in solids is very small. R. Clausius

More information

1. (10) Argon, Ar, exists at T = K, P = 4.87 MPa. Find its specific volume via

1. (10) Argon, Ar, exists at T = K, P = 4.87 MPa. Find its specific volume via NAME: SOLUTION AME 03 Thermodynamics Examination Profs. A. M. Ardekani and J. M. Powers 4 February 0. (0) Argon, Ar, exists at T = 65.9 K, P = 4.87 MPa. Find its specific volume via (a) the ideal gas law,

More information

Chemical Thermodynamics

Chemical Thermodynamics Chemical Thermodynamics David A. Katz Department of Chemistry Pima Community College Tucson, AZ 85709, USA First Law of Thermodynamics The First Law of Thermodynamics was expressed in the study of thermochemistry.

More information

Statistical Mechanics, Kinetic Theory Ideal Gas. 8.01t Nov 22, 2004

Statistical Mechanics, Kinetic Theory Ideal Gas. 8.01t Nov 22, 2004 Statistical Mechanics, Kinetic Theory Ideal Gas 8.01t Nov 22, 2004 Statistical Mechanics and Thermodynamics Thermodynamics Old & Fundamental Understanding of Heat (I.e. Steam) Engines Part of Physics Einstein

More information

3. Of energy, work, enthalpy, and heat, how many are state functions? a) 0 b) 1 c) 2 d) 3 e) 4 ANS: c) 2 PAGE: 6.1, 6.2

3. Of energy, work, enthalpy, and heat, how many are state functions? a) 0 b) 1 c) 2 d) 3 e) 4 ANS: c) 2 PAGE: 6.1, 6.2 1. A gas absorbs 0.0 J of heat and then performs 15.2 J of work. The change in internal energy of the gas is a) 24.8 J b) 14.8 J c) 55.2 J d) 15.2 J ANS: d) 15.2 J PAGE: 6.1 2. Calculate the work for the

More information

Rate of Reaction and the Collision Theory. Factors that Affect the Rate of a Chemical Reaction

Rate of Reaction and the Collision Theory. Factors that Affect the Rate of a Chemical Reaction Chemical Kinetics and Thermodynamics Chemical Kinetics- concerned with: 1. Rates of Chemical Reactions- # of moles of reactant used up or product formed Unit time Or 2. Reaction Mechanisms- Rate of Reaction

More information

Chapter 17 Temperature, Thermal Expansion, and the Ideal Gas Law. Copyright 2009 Pearson Education, Inc.

Chapter 17 Temperature, Thermal Expansion, and the Ideal Gas Law. Copyright 2009 Pearson Education, Inc. Chapter 17 Temperature, Thermal Expansion, and the Ideal Gas Law Units of Chapter 17 Atomic Theory of Matter Temperature and Thermometers Thermal Equilibrium and the Zeroth Law of Thermodynamics Thermal

More information

Problems of Chapter 2

Problems of Chapter 2 Section 2.1 Heat and Internal Energy Problems of Chapter 2 1- On his honeymoon James Joule traveled from England to Switzerland. He attempted to verify his idea of the interconvertibility of mechanical

More information

The First Law of Thermodynamics

The First Law of Thermodynamics The First Law of Thermodynamics (FL) The First Law of Thermodynamics Explain and manipulate the first law Write the integral and differential forms of the first law Describe the physical meaning of each

More information

AP Practice Questions

AP Practice Questions 1) AP Practice Questions The tables above contain information for determining thermodynamic properties of the reaction below. C 2 H 5 Cl(g) + Cl 2 (g) C 2 H 4 Cl 2 (g) + HCl(g) (a) Calculate ΔH for

More information

Lecture 6: Thermochemistry

Lecture 6: Thermochemistry Lecture 6: Thermochemistry Contents Preamble First law of thermodynamics Various heat effects Conclusions References Key words: thermo chemistry, Heat of formation, Heat of reaction, Kirchoff s law Preamble

More information

Boltzmann Distribution Law

Boltzmann Distribution Law Boltzmann Distribution Law The motion of molecules is extremely chaotic Any individual molecule is colliding with others at an enormous rate Typically at a rate of a billion times per second We introduce

More information

AP Chem Lab 2 Quiz #1 Calorimetry. Conceptual Understanding. Write complete sentences to show your understanding.

AP Chem Lab 2 Quiz #1 Calorimetry. Conceptual Understanding. Write complete sentences to show your understanding. AP Chem Lab 2 Quiz #1 Calorimetry Name Conceptual Understanding. Write complete sentences to show your understanding. Differentiate between kinetic energy and potential energy. Energy may be transferred

More information

Chapter 5 Thermochemistry

Chapter 5 Thermochemistry Chapter 5 Thermochemistry I. Nature of Energy Energy units SI unit is joule, J From E = 1/2 mv 2, 1J = 1kg. m 2 /s 2 Traditionally, we use the calorie as a unit of energy. 1 cal = 4.184J (exactly) The

More information

THERMODYNAMIC PROPERTIES AND CALCULATION. Academic Resource Center

THERMODYNAMIC PROPERTIES AND CALCULATION. Academic Resource Center THERMODYNAMIC PROPERTIES AND CALCULATION Academic Resource Center THERMODYNAMIC PROPERTIES A quantity which is either an attribute of an entire system or is a function of position which is continuous and

More information

AP* Chemistry THERMOCHEMISTRY

AP* Chemistry THERMOCHEMISTRY AP* Chemistry THERMOCHEMISTRY Terms for you to learn that will make this unit understandable: Energy (E) the ability to do work or produce heat ; the sum of all potential and kinetic energy in a system

More information

20 Entropy and the Second Law of Thermodynamics

20 Entropy and the Second Law of Thermodynamics 20 Entropy and the Second Law of Thermodynamics An anonymous graffito on a wall of the Pecan Street Cafe in Austin, Texas, reads: Time is God s way of keeping things from happening all at once. Time also

More information

The First Law of Thermodynamics: Closed Systems. Heat Transfer

The First Law of Thermodynamics: Closed Systems. Heat Transfer The First Law of Thermodynamics: Closed Systems The first law of thermodynamics can be simply stated as follows: during an interaction between a system and its surroundings, the amount of energy gained

More information

18 Q0 a speed of 45.0 m/s away from a moving car. If the car is 8 Q0 moving towards the ambulance with a speed of 15.0 m/s, what Q0 frequency does a

18 Q0 a speed of 45.0 m/s away from a moving car. If the car is 8 Q0 moving towards the ambulance with a speed of 15.0 m/s, what Q0 frequency does a First Major T-042 1 A transverse sinusoidal wave is traveling on a string with a 17 speed of 300 m/s. If the wave has a frequency of 100 Hz, what 9 is the phase difference between two particles on the

More information

Thermodynamics. Energy can be used * to provide heat * for mechanical work * to produce electric work * to sustain life

Thermodynamics. Energy can be used * to provide heat * for mechanical work * to produce electric work * to sustain life Thermodynamics Energy can be used * to provide heat * for mechanical work * to produce electric work * to sustain life Thermodynamics is the study of the transformation of energy into heat and for doing

More information

Stirling heat engine Internal combustion engine (Otto cycle) Diesel engine Steam engine (Rankine cycle) Kitchen Refrigerator

Stirling heat engine Internal combustion engine (Otto cycle) Diesel engine Steam engine (Rankine cycle) Kitchen Refrigerator Lecture. Real eat Engines and refrigerators (Ch. ) Stirling heat engine Internal combustion engine (Otto cycle) Diesel engine Steam engine (Rankine cycle) Kitchen Refrigerator Carnot Cycle - is not very

More information

Basic problems for ideal gases and problems to the first law of thermodynamics and cycles

Basic problems for ideal gases and problems to the first law of thermodynamics and cycles Basic problems for ideal gases and problems to the first law of thermodynamics and cycles SHORT SUMMARY OF THE FORMS: Equation of ideal gases: Number of moles: Universal gas constant: General gas equation

More information

RATE OF REACTION AND EQUILIBRIUM

RATE OF REACTION AND EQUILIBRIUM Rate of Reaction and Equilibrium Seite 1 von 6 chemistry 3 rd Kanti study sheet for the test on the 11/15/2011 author: version: publish date: Linus Metzler 1.0b 11/12/2011 RATE OF REACTION AND EQUILIBRIUM

More information

Test Review # 9. Chemistry R: Form TR9.13A

Test Review # 9. Chemistry R: Form TR9.13A Chemistry R: Form TR9.13A TEST 9 REVIEW Name Date Period Test Review # 9 Collision theory. In order for a reaction to occur, particles of the reactant must collide. Not all collisions cause reactions.

More information

1 CHAPTER 10 THE JOULE AND JOULE-THOMSON EXPERIMENTS

1 CHAPTER 10 THE JOULE AND JOULE-THOMSON EXPERIMENTS AER 0 E JOLE AND JOLE-OMON EXERIMEN 0 Introduction Equation 84, γ constant, tells us how to calculate the drop in temperature if a gas expands adiabatically and reversibly; it is expanding against an external

More information

ME 201 Thermodynamics

ME 201 Thermodynamics ME 0 Thermodynamics Second Law Practice Problems. Ideally, which fluid can do more work: air at 600 psia and 600 F or steam at 600 psia and 600 F The maximum work a substance can do is given by its availablity.

More information

= 1.038 atm. 760 mm Hg. = 0.989 atm. d. 767 torr = 767 mm Hg. = 1.01 atm

= 1.038 atm. 760 mm Hg. = 0.989 atm. d. 767 torr = 767 mm Hg. = 1.01 atm Chapter 13 Gases 1. Solids and liquids have essentially fixed volumes and are not able to be compressed easily. Gases have volumes that depend on their conditions, and can be compressed or expanded by

More information

The Relationships Between. Internal Energy, Heat, Enthalpy, and Calorimetry

The Relationships Between. Internal Energy, Heat, Enthalpy, and Calorimetry The Relationships Between Internal Energy, Heat, Enthalpy, and Calorimetry Recap of Last Class Last class, we began our discussion about energy changes that accompany chemical reactions Chapter 5 discusses:

More information

Chapter 6: Thermochemistry (Chemical Energy) (Ch6 in Chang, Ch6 in Jespersen)

Chapter 6: Thermochemistry (Chemical Energy) (Ch6 in Chang, Ch6 in Jespersen) Chapter 6: Thermochemistry (Chemical Energy) (Ch6 in Chang, Ch6 in Jespersen) Energy is defined as the capacity to do work, or transfer heat. Work (w) - force (F) applied through a distance. Force - any

More information

Reading: Moore chapter 18, sections 18.6-18.11 Questions for Review and Thought: 62, 69, 71, 73, 78, 83, 99, 102.

Reading: Moore chapter 18, sections 18.6-18.11 Questions for Review and Thought: 62, 69, 71, 73, 78, 83, 99, 102. Thermodynamics 2: Gibbs Free Energy and Equilibrium Reading: Moore chapter 18, sections 18.6-18.11 Questions for Review and Thought: 62, 69, 71, 73, 78, 83, 99, 102. Key Concepts and skills: definitions

More information

Physics Final Exam Chapter 13 Review

Physics Final Exam Chapter 13 Review Physics 1401 - Final Exam Chapter 13 Review 11. The coefficient of linear expansion of steel is 12 10 6 /C. A railroad track is made of individual rails of steel 1.0 km in length. By what length would

More information

In a cyclic transformation, where the final state of a system is the same as the initial one, U = 0

In a cyclic transformation, where the final state of a system is the same as the initial one, U = 0 Chapter 4 Entropy and second law of thermodynamics 4.1 Carnot cycle In a cyclic transformation, where the final state of a system is the same as the initial one, U = 0 since the internal energy U is a

More information

AP Chemistry 2007 Scoring Guidelines Form B

AP Chemistry 2007 Scoring Guidelines Form B AP Chemistry 2007 Scoring Guidelines Form B The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to

More information

Section 7. Laws of Thermodynamics: Too Hot, Too Cold, Just Right. What Do You See? What Do You Think? Investigate.

Section 7. Laws of Thermodynamics: Too Hot, Too Cold, Just Right. What Do You See? What Do You Think? Investigate. Chapter 6 Electricity for Everyone Section 7 Laws of Thermodynamics: Too Hot, Too Cold, Just Right What Do You See? Learning Outcomes In this section, you will Assess experimentally the final temperature

More information

Phys222 W11 Quiz 1: Chapters 19-21 Keys. Name:

Phys222 W11 Quiz 1: Chapters 19-21 Keys. Name: Name:. In order for two objects to have the same temperature, they must a. be in thermal equilibrium.

More information

The Kinetic Theory of Gases Sections Covered in the Text: Chapter 18

The Kinetic Theory of Gases Sections Covered in the Text: Chapter 18 The Kinetic Theory of Gases Sections Covered in the Text: Chapter 18 In Note 15 we reviewed macroscopic properties of matter, in particular, temperature and pressure. Here we see how the temperature and

More information

Chapter 6 Thermodynamics: The First Law

Chapter 6 Thermodynamics: The First Law Key Concepts 6.1 Systems Chapter 6 Thermodynamics: The First Law Systems, States, and Energy (Sections 6.1 6.8) thermodynamics, statistical thermodynamics, system, surroundings, open system, closed system,

More information

Next, solid silicon is separated from other solid impurities by treatment with hydrogen chloride at 350 C to form gaseous trichlorosilane (SiCl 3 H):

Next, solid silicon is separated from other solid impurities by treatment with hydrogen chloride at 350 C to form gaseous trichlorosilane (SiCl 3 H): University Chemistry Quiz 5 2014/12/25 1. (5%) What is the coordination number of each sphere in (a) a simple cubic cell, (b) a body-centered cubic cell, and (c) a face-centered cubic cell? Assume the

More information