# UNIVERSITY OF SOUTHAMPTON

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 UNIVERSITY OF SOUTHAMPTON PHYS1013W1 SEMESTER 2 EXAMINATION ENERGY AND MATTER Duration: 120 MINS (2 hours) This paper contains 8 questions. Answers to Section A and Section B must be in separate answer books Answer all questions in Section A and only two questions in Section B. Section A carries 1/3 of the total marks for the exam paper and you should aim to spend about 40 mins on it. Section B carries 2/3 of the total marks for the exam paper and you should aim to spend about 80 mins on it. An outline marking scheme is shown in brackets to the right of each question. A Sheet of Physical Constants is provided with this examination paper. Only university approved calculators may be used. A foreign language translation dictionary (paper version) is permitted provided it contains no notes, additions or annotations. Copyright 2015 c University of Southampton Page 1 of 15

2 2 PHYS1013W1 Useful formulae Conversions 0 K = C 1 atm = Pa = 760 Torr 1 Pa = 10 5 bar = atm = Torr Thermodynamic potentials Internal Energy: U Enthalpy: H = U + PV Helmhotz Free Energy: F = U TS Gibbs Free Energy: G = U TS + PV Availability: A = U T 0 S + P 0 V Atomic weights Hydrogen: 1 Helium: 4 Nitrogen: 14 Copyright 2015 c University of Southampton Page 2 of 15

3 Section A 3 PHYS1013W1 A1. The International Space Station has an internal volume V = 916 m 3 and is pressurised to P = kpa at a temperature of 20 C. What is the total mass and RMS velocity of the air contained (assuming air is molecular nitrogen N 2 which behaves as an ideal gas)? [ 6 ] Ideal gas: PV = Nk B T N = PV/(k B T) = M = N m = u = 1070 kg v RMS = 3k B T m = 510 m/ s A2. An ideal gas at pressure P 1, volume and temperature T 1 undergoes a free (Joule) expansion to volume V 2. Find the new temperature T 2 and pressure P 2. Define the terms adiabatic and isochoric and state whether either of these can be used to describe the Joule expansion. [ 4 ] In a free expansion, temperature does not change T 2 = T 1. For fixed temperature P 1 = P 2 V 2 [ 1 2 ] P 2 = ( /V 2 ) P 1 [ 1 2 ]. Adiabatic: no heat flow into or out of the gas [ 1 2 ]. Isochoric: no change in volume [ 1 2 ]. The Joule expansion is adiabatic, but not isochoric.. TURN OVER Copyright 2015 c University of Southampton Page 3 of 15

4 4 PHYS1013W1 A3. A reversible heat engine is used as a heat pump to run a domestic freezer. It consumes 20 W of electrical power and maintains the cold reservoir at 10 C in a room at +20 C. Draw a heat engine diagram depicting the flow of heat and work, find the efficiency of this engine, and calculate the rate at which it extracts heat from the cold reservoir. [ 5 ] Diagram Reversible efficiency η = 1 T cold T hot New question: η = [1 2 ]= 10% [1 2 ] η = Work Q H Q H = 20 W η = 200 W Q C + Work = Q H Q C = 200 W 20 W = 180 W A4. A cup of water at T initial cools to room temperature T room. Derive an expression for the change in entropy of 1) the water, and 2) the room. Comment on the sign of the total change in entropy. [ 5 ] Differential change in entropy of water: ds = dq T = C dt T is the heat capacity. S = C T room T initial dt T ( ) = C ln Troom T initial where C Entropy of room: (constant temperature) S = C T initial T room T room The total change in entropy is positive [ 1 2 ], as it must be for any irreversible process [ 1 2 ] Copyright 2015 c University of Southampton Page 4 of 15

5 Section B 5 PHYS1013W1 B1. (a) Write down the equation of state for an ideal gas of N particles. Derive an expression for the number density of particles n in terms of pressure and temperature. [ 3 ] PV = Nk B T n = N/V n = k B T/P (b) State the equipartition theorem and explain carefully what is meant by a degree of freedom. [ 4 ] The Classical Equipartition Theorem states that, for a system in thermal equilibrium at temperature T, the average energy per particle is 1 2 k BT per degree of freedom [2]. A degree of freedom is any dynamical variable which contributes a quadratic term to the total energy of the particle [2]. (c) List the degrees of freedom for a diatomic molecule. [ 3 ] Three translational kinetic ; two rotational ; two vibrational. (d) Explain why the molar heat capacity at constant volume of the diatomic molecule H 2 is 3R/2 below 100 K and 5R/2 above 200 K. [ 2 ] Below 100 K, thermal energies are not sufficient to excite the rotational degrees of freedom, and only translational degrees of freedom are excited. TURN OVER Copyright 2015 c University of Southampton Page 5 of 15

6 6 PHYS1013W1 (e) 1 mol of H 2 in a container of constant volume increases in temperature from 50 K to 300 K. Using the heat capacities discussed above, calculate the heat supplied by the environment to the gas. [ 3 ] Constant volume: dw = 0 du = dq. U initial = 3R/2 50 K, U final = 5R/2 300 K. Q = 675R = 5.6 kj. (Mark for either answer in terms of R or S.I.) (f) Calculate the RMS velocities of H 2 at 300 K and at 50 K. [ 3 ] 3k v RMS = B T m 50K: v RMS = m/ s = 790 m/ s [ ] 300K: v RMS = 1930 m/ s [ 1 2 ] (g) Find the ratio of the rate of effusion at the two temperatures given in part (f), noting that the volume remains constant. [ 2 ] Effusion flux: Φ = n s 4 T (because n is constant) 300 Hence, ratio is 50 = 6 = 2.45 Copyright 2015 c University of Southampton Page 6 of 15

7 7 PHYS1013W1 B2. (a) Using two heat engine diagrams, describe the two processes which are forbidden according to the Clausius and Kelvin formulations of the Second Law of Thermodynamics. State these two formulations in words. [ 4 ] Diagrams: +. Clausius: No process is possible whose sole result is the transfer of heat from a colder to a hotter body. Kelvin: No process is possible whose sole result is the complete conversion of heat into work. (Marks given for meaning, not for verbatim recall.) TURN OVER Copyright 2015 c University of Southampton Page 7 of 15

8 8 PHYS1013W1 (b) (i) Draw a P V diagram for the Carnot cycle. [ 1 ] (ii) Label and describe each of the four stages in this cycle. [ 2 ] (iii) Indicate which feature of the diagram represents the per cycle work. [ 1 ] Axes labels [ 1 2 ]. Cyclic operation described using e.g. arrows [1 2 ]. Following 4 stages identified and which is which indicated on diagram: adiabatic compression [ 1 2 ], isothermal compression [1 2 ], adiabatic expansion [ 1 2 ], isothermal expansion [1 2 ]. Area inside loop identified as representing work per cycle. (iv) Draw a T S diagram for the Carnot cycle and indicate the correspondence between stages in the P V diagram. [ 2 ] Correctly drawn T S diagram [ 1 2 ]with axes labels [1 2 ]. Correspondence between all four stages correctly identified Copyright 2015 c University of Southampton Page 8 of 15

9 9 PHYS1013W1 (c) (i) Show that the work necessary to compress one mole of ideal gas adiabatically from volume and temperature T 1 to volume V 2 is [ W = RT (V2 ) 1 γ 1 1]. 1 γ Adiabatic: PV γ = constant = P 1 V γ 1 [ 5 ] W = V2 PdV = P 1 V γ 1 V2 V γ dv = P 1V γ [ ] 1 V 1 γ V 2 1 γ = P 1V γ ( ) 1 γ 2 γ 1 1 γ = P ( ) 1 1 γ Vγ 1 1 γ 2 γ 1 [ = RT (V2 ) 1 γ 1 1] 1 γ (ii) Find an expression for the work necessary to perform the same compression isothermally and explain whether the work is larger in the adiabatic or the isothermal case. [ 3 ] PV = RT P = RT/V (constant temperature) W = V2 = RT 1 V2 dv V = RT 1 ln [ V2 Work is larger for adiabatic case [ 1 2 ]because in isothermal case heat also contributes to increase in internal energy [ 1 2 ]. ] TURN OVER Copyright 2015 c University of Southampton Page 9 of 15

10 (iii) For a Joule expansion, describe qualitatively i. the change in entropy 10 PHYS1013W1 ii. the change in temperature. 1) Entropy increases [ 1 2 ]because there are more possible microscopic configurations [ 1 2 ] 2) Temperature stays constant [ 1 2 ]because no work is done by the gas [ 1 2 ] [ 2 ] Copyright 2015 c University of Southampton Page 10 of 15

11 11 PHYS1013W1 B3. (a) A blackbody spectrum is observed to be maximum at a wavelength of 800 nm and the total power output is measured to be 1 kw. What is the temperature and area of the emitter? [ 4 ] New question: Wien s law: T = m K/λ max = 3625 K [2] Stefan Boltzmann law: P/A = σt 4 A = P/(σT 4 ) = m 2 (b) The luminosity of the Sun is L = W. Treating Pluto (radius r = m) as a blackbody in equilibrium with the Sun, estimate its temperature at closest approach to the Sun (d = m). [ 6 ] Absorbing area of Pluto: πr 2 [ 1 2 ] Emitting area of Pluto: 4πr 2 [ 1 2 ] Solar intensity at Pluto: L 4πd 2 Blackbody power emitted by Pluto: 4πr 2 σt 4 Equating: Hence: T = 4πr 2 σt 4 = L 4πd 2πr2 ( ) 1/4 L = 51 K 16πd 2 σ (c) Explain what it means for entropy to be a function of state and write down the expression the change in entropy for a system at temperature T when a small amount of heat is added in a reversible process. [ 2 ] Entropy being a function of state means it represents a property of the system, regardless of how that state was reached ds = dq T TURN OVER Copyright 2015 c University of Southampton Page 11 of 15

12 12 PHYS1013W1 (d) State the Fundamental Equation of Thermodynamics and show that the differential change in entropy of an ideal gas is ds = c V dt T du = TdS PdV Using du = c V dt and PV = RT ds = 1 T du + P T dv = c v dt T + RdV V + RdV V [ 3 ] (e) Heat is delivered to a heat engine operating between T H = 500 K and T C = 300 K via a cylindrical steel rod (thermal conductivity κ = 400 W m 1 K 1 ) of area A = 0.1 m 2 and length L = 1 m. What is the maximum rate at which the engine can do work? [ 5 ] New question: Fourier s law: dq dt = Aκ dt dx dt dx = 200 K/ m [1 2 ] dq dt = ( ) W = 8 kw Engine maximum efficiency: η = 1 T C T H = 0.4 [ 1 2 ] Maximum work output: W = η dq dt = 3.2 kw Copyright 2015 c University of Southampton Page 12 of 15

13 13 PHYS1013W1 B4. Throughout this question you may assume the gas is ideal. (a) Starting with the availability A, find the appropriate thermodynamic potential for a process which is open to and in good thermal contact with the environment, and identify the name given to this potential from the list at the start of the examination paper. [ 4 ] P = P 0 and T = T 0 which implies dp = 0 and dt = 0 Hence da = du TdS + PdV = d(u TS + PV) Identify G = U TS + PV as Gibbs free energy (b) The molar heat capacity of a gas at constant pressure is observed to be c p = 5R/2, independent of temperature. Find the molar heat capacity at constant volume for this gas, and state the type of gas this is likely to be. [ 2 ] c v = c p R = 3R/2 This is likely to be a monatomic gas (c) One mole of monatomic gas undergoes Joule expansion from volume to V 2 >. It is then compressed isothermally back to. Show that the work done during this compression is W = RT ln [V 2 / ]. [ 3 ] dw = PdV P = RT/V W = RT V 2 dv V = +RT ln [V 2/ ] (d) By noting that the compression is isothermal and the gas is ideal, write down an expression for the heat flow into the gas during this compression. [ 2 ] Isothermal du = dq + dw = 0 Heat flow in Q = +RT ln [V 2 / ] TURN OVER Copyright 2015 c University of Southampton Page 13 of 15

14 14 PHYS1013W1 (e) A Stirling cycle uses isothermal and isochoric processes between volumes and V 2 and using reservoirs at temperatures T H and T C. Sketch and label a P V diagram for this cycle [ 4 ] P V diagram with correctly drawn and labelled isothermal and isochoric processes: Axes labels Isothermals drawn and labeled Isochorics drawn and labeled Hot and cold isothermals identified (f) Explain why the heat entering during isochoric heating is exactly equal to the heat leaving during isochoric cooling. [ 2 ] No work is done, so du = dq For ideal gas, U = c V T and isochoric processes are between the same isotherms Copyright 2015 c University of Southampton Page 14 of 15

15 15 PHYS1013W1 (g) Define efficiency in terms of heat and work, and use the results in this B question to derive an expression for the efficiency of a Stirling engine. [ 3 ] Efficiency η = W Q H Q H = RT H ln [V 2 / ] [ 1 2 ] W = RT H ln [V 2 / ] RT C ln [V 2 / ] [ 1 2 ] η = T H T C T H = 1 T C T H END OF PAPER Copyright 2015 c University of Southampton Page 15 of 15

### Speed Distribution at CONSTANT Temperature is given by the Maxwell Boltzmann Speed Distribution

Temperature ~ Average KE of each particle Particles have different speeds Gas Particles are in constant RANDOM motion Average KE of each particle is: 3/2 kt Pressure is due to momentum transfer Speed Distribution

### Physics 408 Final Exam

Physics 408 Final Exam Name You are graded on your work (with partial credit where it is deserved) so please do not just write down answers with no explanation (or skip important steps)! Please give clear,

### Chemistry. Lecture 10 Maxwell Relations. NC State University

Chemistry Lecture 10 Maxwell Relations NC State University Thermodynamic state functions expressed in differential form We have seen that the internal energy is conserved and depends on mechanical (dw)

### A) 2.0 atm B) 2.2 atm C) 2.4 atm D) 2.9 atm E) 3.3 atm

Name: Date: 1. On a cold day ( 3 C), the gauge pressure on a tire reads 2.0 atm. If the tire is heated to 27 C, what will be the absolute pressure of the air inside the tire? A) 2.0 atm B) 2.2 atm C) 2.4

### Chapter 19: The Kinetic Theory of Gases Questions and Example Problems

Chapter 9: The Kinetic Theory of Gases Questions and Example Problems N M V f N M Vo sam n pv nrt Nk T W nrt ln B A molar nmv RT k T rms B p v K k T λ rms avg B V M m πd N/V Q nc T Q nc T C C + R E nc

### Process Nature of Process

AP Physics Free Response Practice Thermodynamics 1983B. The pv-diagram above represents the states of an ideal gas during one cycle of operation of a reversible heat engine. The cycle consists of the following

### The Second Law of Thermodynamics (Chapter 4)

The Second Law of Thermodynamics (Chapter 4) First Law: Energy of universe is constant: ΔE system = - ΔE surroundings Second Law: New variable, S, entropy. Changes in S, ΔS, tell us which processes made

### THE SECOND LAW OF THERMODYNAMICS. Professor Benjamin G. Levine CEM 182H Lecture 5

THE SECOND LAW OF THERMODYNAMICS Professor Benjamin G. Levine CEM 182H Lecture 5 Chemical Equilibrium N 2 + 3 H 2 2 NH 3 Chemical reactions go in both directions Systems started from any initial state

### Chapter 2 Carnot Principle

Chapter 2 Carnot Principle 2.1 Temperature 2.1.1 Isothermal Process When two bodies are placed in thermal contact, the hotter body gives off heat to the colder body. As long as the temperatures are different,

### Physics 4C Chapter 19: The Kinetic Theory of Gases

Physics 4C Chapter 19: The Kinetic Theory of Gases Whether you think you can or think you can t, you re usually right. Henry Ford The only thing in life that is achieved without effort is failure. Source

### Unit 05 Kinetic Theory of Gases

Unit 05 Kinetic Theory of Gases Unit Concepts: A) A bit more about temperature B) Ideal Gas Law C) Molar specific heats D) Using them all Unit 05 Kinetic Theory, Slide 1 Temperature and Velocity Recall:

### Version 001 HW 15 Thermodynamics C&J sizemore (21301jtsizemore) 1

Version 001 HW 15 Thermodynamics C&J sizemore 21301jtsizemore 1 This print-out should have 38 questions. Multiple-choice questions may continue on the next column or page find all choices before answering.

### 8.21 The Physics of Energy Fall 2009

MIT OpenCourseWare http://ocw.mit.edu 8.21 The Physics of Energy Fall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 8.21 Lecture 9 Heat Engines

### A thermodynamic system is taken from an initial state X along the path XYZX as shown in the PV-diagram.

AP Physics Multiple Choice Practice Thermodynamics 1. The maximum efficiency of a heat engine that operates between temperatures of 1500 K in the firing chamber and 600 K in the exhaust chamber is most

### Problem: Calculate the entropy change that results from mixing 54.0 g of water at 280 K with 27.0 g of water at 360 K in a vessel whose walls are

Problem: Calculate the entropy change that results from mixing 54.0 g of water at 280 K with 27.0 g of water at 360 K in a vessel whose walls are perfectly insulated from the surroundings. Is this a spontaneous

### Thermodynamic system is classified into the following three systems. (ii) Closed System It exchanges only energy (not matter) with surroundings.

1 P a g e The branch of physics which deals with the study of transformation of heat energy into other forms of energy and vice-versa. A thermodynamical system is said to be in thermal equilibrium when

### 1985B4. A kilogram sample of a material is initially a solid at a temperature of 20 C. Heat is added to the sample at a constant rate of 100

1985B4. A 0.020-kilogram sample of a material is initially a solid at a temperature of 20 C. Heat is added to the sample at a constant rate of 100 joules per second until the temperature increases to 60

### Atkins / Paula Physical Chemistry, 8th Edition. Chapter 3. The Second Law

Atkins / Paula Physical Chemistry, 8th Edition Chapter 3. The Second Law The direction of spontaneous change 3.1 The dispersal of energy 3.2 Entropy 3.3 Entropy changes accompanying specific processes

### Chem Lecture Notes 6 Fall 2013 Second law

Chem 340 - Lecture Notes 6 Fall 2013 Second law In the first law, we determined energies, enthalpies heat and work for any process from an initial to final state. We could know if the system did work or

### Lecture 25 Goals: Chapter 18 Understand the molecular basis for pressure and the idealgas

Lecture 5 Goals: Chapter 18 Understand the molecular basis for pressure and the idealgas law. redict the molar specific heats of gases and solids. Understand how heat is transferred via molecular collisions

### Phase Changes and Latent Heat

Review Questions Why can a person remove a piece of dry aluminum foil from a hot oven with bare fingers without getting burned, yet will be burned doing so if the foil is wet. Equal quantities of alcohol

### Thermodynamics 2013/2014, lecturer: Martin Zápotocký

Thermodynamics 2013/2014, lecturer: Martin Zápotocký 2 lectures: 1. Thermodynamic processes, heat and work, calorimetry, 1 st and 2 nd law of thermodynamics 2. Entropy, thermodynamic potentials, nonequilibrium

### Module 5 : Electrochemistry Lecture 21 : Review Of Thermodynamics

Module 5 : Electrochemistry Lecture 21 : Review Of Thermodynamics Objectives In this Lecture you will learn the following The need for studying thermodynamics to understand chemical and biological processes.

### Ch. 19: The Kinetic Theory of Gases

Ch. 19: The Kinetic Theory of Gases In this chapter we consider the physics of gases. If the atoms or molecules that make up a gas collide with the walls of their container, they exert a pressure p on

### ΔU = Q W. Tue Dec 1. Assign 13/14 Friday Final: Fri Dec 11 2:30PM WALTER 145. Thermodynamics 1st Law. 2 nd Law. Heat Engines and Refrigerators

Tue Dec 1 Thermodynamics 1st Law ΔU = Q W 2 nd Law SYS Heat Engines and Refrigerators Isobaric: W = PΔV Isochoric: W = 0 Isothermal: ΔU = 0 Adiabatic: Q = 0 Assign 13/14 Friday Final: Fri Dec 11 2:30PM

### Chapter 19. Heat Engines

Chapter 19 Heat Engines Thermo Processes Eint = Q+ W Adiabatic No heat exchanged Q = 0 and E int = W Isobaric Constant pressure W = P (V f V i ) and E int = Q + W Isochoric Constant Volume W = 0 and E

### CHAPTER - 12 THERMODYNAMICS

CHAPER - HERMODYNAMICS ONE MARK QUESIONS. What is hermodynamics?. Mention the Macroscopic variables to specify the thermodynamics. 3. How does thermodynamics differ from Mechanics? 4. What is thermodynamic

### 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

### Lecture 6 Free Energy

Lecture 6 Free Energy James Chou BCMP21 Spring 28 A quick review of the last lecture I. Principle of Maximum Entropy Equilibrium = A system reaching a state of maximum entropy. Equilibrium = All microstates

### Specific Heat of Diatomic Gases and. The Adiabatic Process

Specific Heat of Diatomic Gases and Solids The Adiabatic Process Ron Reifenberger Birck Nanotechnology Center Purdue University February 22, 2012 Lecture 7 1 Specific Heat for Solids and Diatomic i Gasses

Enthalpy and Adiabatic Changes Chapter 2 of Atkins: The First Law: Concepts Sections 2.5-2.6 of Atkins (7th & 8th editions) Enthalpy Definition of Enthalpy Measurement of Enthalpy Variation of Enthalpy

### The Laws of Thermodynamics

MME 231: Lecture 06 he Laws of hermodynamics he Second Law of hermodynamics. A. K. M. B. Rashid Professor, Department of MME BUE, Dhaka oday s opics Relation between entropy transfer and heat Entropy change

### Identify the intensive quantities from the following: (a) enthalpy (b) volume (c) refractive index (d) none of these

Q 1. Q 2. Q 3. Q 4. Q 5. Q 6. Q 7. The incorrect option in the following table is: H S Nature of reaction (a) negative positive spontaneous at all temperatures (b) positive negative non-spontaneous regardless

### T ice T water T water = T ice =0 0 C. e =1

Given 1 kg of water at 100 0 C and a very large (very very large) block of ice at 0 0 C. A reversible heat engine absorbs heat from the water and expels heat to the ice until work can no longer be extracted

### Entropy in Macroscopic Systems

Lecture 15 Heat Engines Review & Examples p p b b Hot reservoir at T h p a a c adiabats Heat leak Heat pump Q h Q c W d V 1 V 2 V Cold reservoir at T c Lecture 15, p 1 Review Entropy in Macroscopic Systems

### Honors Physics. Notes Nov 16, 20 Heat. Persans 1

Honors Physics Notes Nov 16, 20 Heat Persans 1 Properties of solids Persans 2 Persans 3 Vibrations of atoms in crystalline solids Assuming only nearest neighbor interactions (+Hooke's law) F = C( u! u

### Preliminary Examination - Day 2 May 16, 2014

UNL - Department of Physics and Astronomy Preliminary Examination - Day May 6, 04 This test covers the topics of Thermodynamics and Statistical Mechanics (Topic ) and Mechanics (Topic ) Each topic has

### 19-9 Adiabatic Expansion of an Ideal Gas

19-9 Adiabatic Expansion of an Ideal Gas Learning Objectives 19.44 On a p-v diagram, sketch an adiabatic expansion (or contraction) and identify that there is no heat exchange Q with the environment. 19.45

### PY2005: Thermodynamics

ome Multivariate Calculus Y2005: hermodynamics Notes by Chris Blair hese notes cover the enior Freshman course given by Dr. Graham Cross in Michaelmas erm 2007, except for lecture 12 on phase changes.

### Final Exam, Chemistry 481, 77 December 2016

1 Final Exam, Chemistry 481, 77 December 216 Show all work for full credit Useful constants: h = 6.626 1 34 J s; c (speed of light) = 2.998 1 8 m s 1 k B = 1.387 1 23 J K 1 ; R (molar gas constant) = 8.314

### Irreversible Processes

Irreversible Processes Examples: Block sliding on table comes to rest due to friction: KE converted to heat. Heat flows from hot object to cold object. Air flows into an evacuated chamber. Reverse process

### 7.3 Heat capacities: extensive state variables (Hiroshi Matsuoka)

7.3 Heat capacities: extensive state variables (Hiroshi Matsuoka) 1 Specific heats and molar heat capacities Heat capacity for 1 g of substance is called specific heat and is useful for practical applications.

### 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 - 8 Introduction to Vapour Power Cycle Today, we will continue

### Last Name: First Name ID

Last Name: First Name ID This is a set of practice problems for the final exam. It is not meant to represent every topic and is not meant to be equivalent to a 2-hour exam. These problems have not been

### Adiabatic Expansion (DQ = 0)

Adiabatic Expansion (DQ = 0) Occurs if: change is made sufficiently quickly and/or with good thermal isolation. Governing formula: PV g = constant where g = C P /C V Adiabat P Isotherms V Because PV/T

### Chapter 3. Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc.

Chapter 3 Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc. Concepts Energy functions F and G Chemical potential, µ Partial Molar properties

### Thermodynamics is the Science of Energy and Entropy

Definition of Thermodynamics: Thermodynamics is the Science of Energy and Entropy - Some definitions. - The zeroth law. - Properties of pure substances. - Ideal gas law. - Entropy and the second law. Some

### The Direction of Spontaneous Change: Entropy and Free Energy

The Direction of Spontaneous Change: Entropy and Free Energy Reading: from Petrucci, Harwood and Herring (8th edition): Required for Part 1: Sections 20-1 through 20-4. Recommended for Part 1: Sections

### CHEMICAL THERMODYNAMICS

DEPARTMENT OF APPLIED CHEMISTRY LECTURE NOTES 6151- ENGINEERING CHEMISTRY-II UNIT II CHEMICAL THERMODYNAMICS Unit syllabus: Terminology of thermodynamics - Second law: Entropy - entropy change for an ideal

### Thermodynamics Boltzmann (Gibbs) Distribution Maxwell-Boltzmann Distribution Second Law Entropy

Thermodynamics Boltzmann (Gibbs) Distribution Maxwell-Boltzmann Distribution Second Law Entropy Lana Sheridan De Anza College May 8, 2017 Last time modeling an ideal gas at the microscopic level pressure,

### Thermodynamics and Phase Transitions in Minerals

Studiengang Geowissenschaften M.Sc. Wintersemester 2004/05 Thermodynamics and Phase Transitions in Minerals Victor Vinograd & Andrew Putnis Basic thermodynamic concepts One of the central themes in Mineralogy

### Chapter 19 The First Law of Thermodynamics

Chapter 19 The First Law of Thermodynamics Lecture by Dr. Hebin Li Assignment Due at 11:59pm on Sunday, December 7 HW set on Masteringphysics.com Final exam: Time: 2:15pm~4:15pm, Monday, December 8. Location:

### Pressure Volume Temperature Relationship of Pure Fluids

Pressure Volume Temperature Relationship of Pure Fluids Volumetric data of substances are needed to calculate the thermodynamic properties such as internal energy and work, from which the heat requirements

### Unit 7 (B) Solid state Physics

Unit 7 (B) Solid state Physics hermal Properties of solids: Zeroth law of hermodynamics: If two bodies A and B are each separated in thermal equilibrium with the third body C, then A and B are also in

### Reading Assignment #13 :Ch.23: (23-3,5,6,7,8), Ch24: (24-1,2,4,5,6) )] = 450J. ) ( 3x10 5 Pa) ( 1x10 3 m 3

Ph70A Spring 004 Prof. Pui Lam SOLUTION Reading Assignment #3 :h.3: (3-3,5,6,7,8), h4: (4-,,4,5,6) Homework #3: First Law and Second of Thermodynamics Due: Monday 5/3/004.. A monatomic ideal gas is allowed

### Chapter 7. Entropy: A Measure of Disorder

Chapter 7 Entropy: A Measure of Disorder Entropy and the Clausius Inequality The second law of thermodynamics leads to the definition of a new property called entropy, a quantitative measure of microscopic

### CHAPTER 3 LECTURE NOTES 3.1. The Carnot Cycle Consider the following reversible cyclic process involving one mole of an ideal gas:

CHATER 3 LECTURE NOTES 3.1. The Carnot Cycle Consider the following reversible cyclic process involving one mole of an ideal gas: Fig. 3. (a) Isothermal expansion from ( 1, 1,T h ) to (,,T h ), (b) Adiabatic

### Application of the First Law of Thermodynamics to Adiabatic, Isothermal, Isobaric, and Isochoric Processes; Heat Engine and Engine Cycles

Application of the First Law of Thermodynamics to Adiabatic, Isothermal, Isobaric, and Isochoric Processes; Heat Engine and Engine Cycles by SHS Encoder 3 on February 05, 2018 lesson duration of 0 minutes

### Review of classical thermodynamics

Review of classical thermodynamics Fundamental Laws, Properties and Processes (2) Entropy and the Second Law Concepts of equilibrium Reversible and irreversible processes he direction of spontaneous change

### Outline. 1. Work. A. First Law of Thermo. 2. Internal Energy. 1. Work continued. Category: Thermodynamics. III. The Laws of Thermodynamics.

ategory: hermodynamics Outline III. he Laws of hermodynamics A. First Law of hermo B. Second Law of hermo (Entropy). Statistical Mechanics D. References Updated: 04jan A. First Law of hermo. Work 4 Stored

### 3. Basic Concepts of Thermodynamics Part 2

3. Basic Concepts of Thermodynamics Part 2 Temperature and Heat If you take a can of cola from the refrigerator and leave it on the kitchen table, its temperature will rise-rapidly at first but then more

### FIRST PUBLIC EXAMINATION SUBJECT 3: PHYSICAL CHEMISTRY

CCHE 4273 FIRST PUBLIC EXAMINATION Trinity Term 2005 Preliminary Examination in Chemistry SUBJECT 3: PHYSICAL CHEMISTRY Wednesday June 8 th 2005, 9:30am Time allowed: 2 ½ hours Candidates should answer

### Thermal and Statistical Physics Department Exam Last updated November 4, L π

Thermal and Statistical Physics Department Exam Last updated November 4, 013 1. a. Define the chemical potential µ. Show that two systems are in diffusive equilibrium if µ 1 =µ. You may start with F =

### 140a Final Exam, Fall 2006., κ T 1 V P. (? = P or V ), γ C P C V H = U + PV, F = U TS G = U + PV TS. T v. v 2 v 1. exp( 2πkT.

40a Final Exam, Fall 2006 Data: P 0 0 5 Pa, R = 8.34 0 3 J/kmol K = N A k, N A = 6.02 0 26 particles/kilomole, T C = T K 273.5. du = TdS PdV + i µ i dn i, U = TS PV + i µ i N i Defs: 2 β ( ) V V T ( )

### 1. Second Law of Thermodynamics

1. Second Law of hermodynamics he first law describes how the state of a system changes in response to work it performs and heat absorbed. However, the first law cannot explain certain facts about thermal

### Chap. 3. The Second Law. Law of Spontaneity, world gets more random

Chap. 3. The Second Law Law of Spontaneity, world gets more random Kelvin - No process can transform heat completely into work Chap. 3. The Second Law Law of Spontaneity, world gets more random Kelvin

### Alternate Midterm Examination Physics 100 Feb. 20, 2014

Alternate Midterm Examination Physics 100 Feb. 20, 2014 Name/Student #: Instructions: Formulas at the back (you can rip that sheet o ). Questions are on both sides. Calculator permitted. Put your name

### CH341 Test 2 Physical Chemistry Test 2 Fall 2011, Prof. Shattuck

Physical Chemistry Test 2 Fall 2011, Prof. Shattuck Name 1 Constants: R = 8.3145 J K -1 mol -1 = 0.083145 L bar K -1 mol -1 R = 0.08206 L atm K -1 mol -1 1 F = 96485 C mol -1 1 atm = 1.01325 bar 1 bar

### Chapter 17. Work, Heat, and the First Law of Thermodynamics Topics: Chapter Goal: Conservation of Energy Work in Ideal-Gas Processes

Chapter 17. Work, Heat, and the First Law of Thermodynamics This false-color thermal image (an infrared photo) shows where heat energy is escaping from a house. In this chapter we investigate the connection

### 1 mol ideal gas, PV=RT, show the entropy can be written as! S = C v. lnt + RlnV + cons tant

1 mol ideal gas, PV=RT, show the entropy can be written as! S = C v lnt + RlnV + cons tant (1) p, V, T change Reversible isothermal process (const. T) TdS=du-!W"!S = # "Q r = Q r T T Q r = \$W = # pdv =

### P340: Thermodynamics and Statistical Physics, Exam#2 Any answer without showing your work will be counted as zero

P340: hermodynamics and Statistical Physics, Exam#2 Any answer without showing your work will be counted as zero 1. (15 points) he equation of state for the an der Waals gas (n = 1 mole) is (a) Find (

### 140a Final Exam, Fall 2007., κ T 1 V P. (? = P or V ), γ C P C V H = U + PV, F = U TS G = U + PV TS. T v. v 2 v 1. exp( 2πkT.

4a Final Exam, Fall 27 Data: P 5 Pa, R = 8.34 3 J/kmol K = N A k, N A = 6.2 26 particles/kilomole, T C = T K 273.5. du = TdS PdV + i µ i dn i, U = TS PV + i µ i N i Defs: 2 β ( ) V V T ( ) /dq C? dt P?

### Chemical thermodynamics the area of chemistry that deals with energy relationships

Chemistry: The Central Science Chapter 19: Chemical Thermodynamics Chemical thermodynamics the area of chemistry that deals with energy relationships 19.1: Spontaneous Processes First law of thermodynamics

### Answers to Assigned Problems from Chapter 2

Answers to Assigned Problems from Chapter 2 2.2. 1 mol of ice has a volume of 18.01 g/0.9168 g cm 3 = 19.64 cm 3 1 mol of water has a volume of 18.01 g/0.9998 g cm 3 = 18.01 cm 3 V(ice water) = 1.63 cm

### Properties of Entropy

Properties of Entropy Due to its additivity, entropy is a homogeneous function of the extensive coordinates of the system: S(λU, λv, λn 1,, λn m ) = λ S (U, V, N 1,, N m ) This means we can write the entropy

### Chapter 17 Temperature & Kinetic Theory of Gases 1. Thermal Equilibrium and Temperature

Chapter 17 Temperature & Kinetic Theory of Gases 1. Thermal Equilibrium and Temperature Any physical property that changes with temperature is called a thermometric property and can be used to measure

### Spring_#7. Thermodynamics. Youngsuk Nam.

Spring_#7 Thermodynamics Youngsuk Nam ysnam1@khu.ac.kr You can t connect the dots looking forward; you can only connect them looking backwards. So you have to trust that the dots will somehow connect in

### Chapter 5. Simple Mixtures Fall Semester Physical Chemistry 1 (CHM2201)

Chapter 5. Simple Mixtures 2011 Fall Semester Physical Chemistry 1 (CHM2201) Contents The thermodynamic description of mixtures 5.1 Partial molar quantities 5.2 The thermodynamic of Mixing 5.3 The chemical

### THERMODYNAMICS I. TERMS AND DEFINITIONS A. Review of Definitions 1. Thermodynamics = Study of the exchange of heat, energy and work between a system

THERMODYNAMICS I. TERMS AND DEFINITIONS A. Review of Definitions 1. Thermodynamics = Study of the exchange of heat, energy and work between a system and its surroundings. a. System = That part of universe

### The Kinetic Theory of Gases

chapter 1 The Kinetic Theory of Gases 1.1 Molecular Model of an Ideal Gas 1. Molar Specific Heat of an Ideal Gas 1.3 Adiabatic Processes for an Ideal Gas 1.4 The Equipartition of Energy 1.5 Distribution

### The laws of Thermodynamics. Work in thermodynamic processes

The laws of Thermodynamics ork in thermodynamic processes The work done on a gas in a cylinder is directly proportional to the force and the displacement. = F y = PA y It can be also expressed in terms

### People s Physics book 3e

The Big Ideas Heat is a form of energy transfer. It can change the kinetic energy of a substance. For example, the average molecular kinetic energy of gas molecules is related to temperature. A heat engine

### Phys102 First Major- 161 Code: 20 Coordinator: Dr. A. Naqvi Saturday, October 29, 2016 Page: 1

Coordinator: Dr. A. Naqvi Saturday, October 29, 2016 Page: 1 Q1. FIGURE 1 shows three waves that are separately sent along the same unstretchable string that is kept under constant tension along an x-axis.

### Not so black. Black Hole Thermodynamics. Nobel Prize 2017: Rainer Weiss, Kip Thorne, and Barry Barish.

Not so black Nobel Prize 2017: Rainer Weiss, Kip Thorne, and Barry Barish. Black Hole Thermodynamics Zeroth Law of thermodynamics requires that black holes are round *. First law of thermodynamics requires

### ...Thermodynamics. Entropy: The state function for the Second Law. Entropy ds = d Q. Central Equation du = TdS PdV

...Thermodynamics Entropy: The state function for the Second Law Entropy ds = d Q T Central Equation du = TdS PdV Ideal gas entropy s = c v ln T /T 0 + R ln v/v 0 Boltzmann entropy S = klogw Statistical

### Some properties of the Helmholtz free energy

Some properties of the Helmholtz free energy Energy slope is T U(S, ) From the properties of U vs S, it is clear that the Helmholtz free energy is always algebraically less than the internal energy U.

### Physics 53. Thermal Physics 1. Statistics are like a bikini. What they reveal is suggestive; what they conceal is vital.

Physics 53 Thermal Physics 1 Statistics are like a bikini. What they reveal is suggestive; what they conceal is vital. Arthur Koestler Overview In the following sections we will treat macroscopic systems

### This is a statistical treatment of the large ensemble of molecules that make up a gas. We had expressed the ideal gas law as: pv = nrt (1)

1. Kinetic Theory of Gases This is a statistical treatment of the large ensemble of molecules that make up a gas. We had expressed the ideal gas law as: pv = nrt (1) where n is the number of moles. We

### [S R (U 0 ɛ 1 ) S R (U 0 ɛ 2 ]. (0.1) k B

Canonical ensemble (Two derivations) Determine the probability that a system S in contact with a reservoir 1 R to be in one particular microstate s with energy ɛ s. (If there is degeneracy we are picking

### 2. Under conditions of constant pressure and entropy, what thermodynamic state function reaches an extremum? i

1. (20 oints) For each statement or question in the left column, find the appropriate response in the right column and place the letter of the response in the blank line provided in the left column. 1.

### First Law showed the equivalence of work and heat. Suggests engine can run in a cycle and convert heat into useful work.

0.0J /.77J / 5.60J hermodynamics of Biomolecular Systems 0.0/5.60 Fall 005 Lecture #6 page he Second Law First Law showed the euivalence of work and heat U = + w, du = 0 for cyclic process = w Suggests

### Thermodynamics Qualifying Exam Study Material

Thermodynamics Qualifying Exam Study Material The candidate is expected to have a thorough understanding of undergraduate engineering thermodynamics topics. These topics are listed below for clarification.

### PHYSICS 149: Lecture 26

PHYSICS 149: Lecture 26 Chapter 14: Heat 14.1 Internal Energy 14.2 Heat 14.3 Heat Capacity and Specific Heat 14.5 Phase Transitions 14.6 Thermal Conduction 14.7 Thermal Convection 14.8 Thermal Radiation

### On my honor as a Texas A&M University student, I will neither give nor receive unauthorized help on this exam.

Physics 201, Exam 4 Name (printed) On my honor as a Texas A&M University student, I will neither give nor receive unauthorized help on this exam. Name (signed) The multiple-choice problems carry no partial

### !W "!#U + T#S, where. !U = U f " U i and!s = S f " S i. ! W. The maximum amount of work is therefore given by =!"U + T"S. !W max

1 Appendix 6: The maximum wk theem (Hiroshi Matsuoka) 1. Question and answer: the maximum amount of wk done by a system Suppose we are given two equilibrium states of a macroscopic system. Consider all

### Gases. T boil, K. 11 gaseous elements. Rare gases. He, Ne, Ar, Kr, Xe, Rn Diatomic gaseous elements H 2, N 2, O 2, F 2, Cl 2

Gases Gas T boil, K Rare gases 11 gaseous elements He, Ne, Ar, Kr, Xe, Rn 165 Rn 211 N 2 O 2 77 F 2 90 85 Diatomic gaseous elements Cl 2 238 H 2, N 2, O 2, F 2, Cl 2 H 2 He Ne Ar Kr Xe 20 4.4 27 87 120

### Solutions Midterm Exam 3 December 12, Match the above shown players of the best baseball team in the world with the following names:

Problem 1 (2.5 points) 1 2 3 4 Match the above shown players of the best baseball team in the world with the following names: A. Derek Jeter B. Mariano Rivera C. Johnny Damon D. Jorge Posada 1234 = a.

### Lecture 30. Chapter 21 Examine two wave superposition (-ωt and +ωt) Examine two wave superposition (-ω 1 t and -ω 2 t)

To do : Lecture 30 Chapter 21 Examine two wave superposition (-ωt and +ωt) Examine two wave superposition (-ω 1 t and -ω 2 t) Review for final (Location: CHEM 1351, 7:45 am ) Tomorrow: Review session,