# Problem Set MIT Professor Gerbrand Ceder Fall 2003

Size: px
Start display at page:

Transcription

1 LEVEL 1 PROBLEMS Problem Set MIT Professor Gerbrand Ceder Fall 003 Problem 1.1 The internal energy per kg for a certain gas is given by U = T + C where U is in kj/kg, T is in Kelvin, and C is a constant. a) If the gas is heated in a rigid container (constant volume) from a temperature of 40 C to 315 C, compute the amount of work and heat flow into the system (per kg of gas). b) Compute the entropy change (per kg of gas) for the above change of state, under the assumption that the gas is ideal. molecular weight of the gas: 10 g/mol Problem 1. Two moles of an ideal gas undergo an equation of state that brings them from 0 C and 5 atm to 110 C and 45 atm. Calculate the entropy change of this gas. C p = 7/ R C v = 5/ R Molar mass of the gas: 3g/mol Problem 1.3 One hundred gram of iron is quenched from a temperature of 1100 C to 0 C by throwing it in a bucket of ice water (water + ice). a) What is the enthalpy change of the iron sample when it cools from 1100 C to 0 C? b) What is the minimal amount of ice (in grams) that has to be present to keep the bucket at 0 o C after it has equilibrated with the iron? You may assume that the bucket does not exchange heat with the environment (only with the iron). Above 91 C Fe is -Fe (fcc) ; below 91 C it is -Fe (bcc). H( -Fe) - H( -Fe) = 900 J/mole Heat capacity for -Fe: 34J/mol-K Heat capacity for -Fe: 38J/mol-K Enthalpy of melting for ice: kj/mol Molar mass for Fe: 56g/mole Molar mass for H O: 18g/mol Problem 1.4 One m 3 of diatomic ideal gas is first expanded from an initial state at 98K and 15 atm pressure to a final state at 1atm. During this expansion the gas is thermally insulated from the environment. After this expansion the insulation is removed and the gas is allowed to cool (or heat) back to 98K, while keeping the pressure constant at 1atm. What is the amount of work done on the gas in these two processes. It might be helpful if you draw the processes on an appropriate state diagram. 1

2 Problem 1.5 Consider the two differentials: df 1 = y (3 x + y )dx + x ( x + y )dy df = y (3 x + y ) dx + x x + y ) dy Integrate them between the points x = 0, y=0 and x=1, y=1, along the path y=x and along y=x. Which of the two differentials is an exact differential? In thermodynamics exact differentials correspond to properties of materials (statefunctions) such as internal energy and volume. Energy exchanges (flows) on the other hand are inexact differentials. They are path dependent. Problem 1.6 One mole of air is compressed isothermally at 300K from one atmosphere to fifteen atmospheres. a) Calculate the amount of work required in the compression. b) How much heat must be added or removed from the gas to maintain its temperature at 300K. c) Does the enthalpy of the gas change? If so, how much? d) Does the entropy of the gas change? If so, how much? 5 You may assume that air is an ideal gas with a constant volume heat capacity of R Problem 1.7 The heat of evaporation of water at 100 C and 1 atm is 61 J/g. (The density of water vapor at 100 C and 1 atm 3 pressure is kg/m.) (a) What percentage of that energy is used as work done by the vapor? (b) What is the internal energy change for the evaporation of water? Problem 1.8 The initial state of a quantity of monoatomic ideal gas is P=1 atm and V=1 liter and T=373 K. The gas is isothermally expanded to a volume of liters and then is cooled at constant pressure to the volume V. This volume is such that a reversible adiabatic compression to a pressure of 1 atm returns the system to its initial state. All of the changes of state are conducted reversibly. Calculate the value of V and the total workdone on or by the gas. Problem 1.9 Free expansion: Consider a chamber with a partition (see figure). One side of the chamber is filled with a gas and the other side is vacuum. Assume that both sides of the partition have a volume V (the chamber then has a volume V). Suddenly, the partition is broken and the gas expands to fill the whole chamber having final volume V. ( (i) What is the work performed by gas?

3 Assume that the walls of the chamber are insulating (adiabatic). (ii) What is then the change in internal energy of the gas after once it has equilibrated after the free expansion? (iii) If the gas is an ideal gas, does the temperature of the gas change? (iv) Does the temperature change if the gas is not ideal (i.e. U=U(T,V)) Assume that the walls of the chamber conduct heat. (v) If the gas is ideal, does the internal energy of the gas change? (vi) If the gas is not ideal (i.e. U=U(T,V)) does the internal energy of the gas change after the expansion? Is any heat exchanged with the environment and if so how much. LEVEL PROBLEMS Problem.1 Carefully consider the following situations and answer whether the entropy of the universe increases, decreases, or remains constant. a) ideal (frictionless) electrical motor pulling a weight. S >0 S <0 S = 0 b) ideal electrical heater S >0 S <0 S = 0 c) acceleration of an object in the gravity field of the earth (no air friction) S >0 S <0 S = 0 Problem. 3 One m of diatomic ideal gas is expanded from an initial state at 98K and 15atm pressure to a final state at atm and 98K. a) What is the volume of the gas after the expansion? b) What is the amount of work done by the gas if the temperature remained constant during the expansion. c) What is the amount of work done if the gas is thermally insulated from its environment during the expansion to atm and then allowed to cool (or warm) back to 98K, keeping the pressure constant at atm.? It might be helpful if you draw the processes on an appropriate state diagram. Problem.3 The energy of a system of one mole, is given by U = AP V where A is a positive constant of dimension [P] 1. Find the equation of the reversible adiabats in the P-V plane (Callen: problem 1.8-5). Problem.4 You are the head of a venture-capital firm that is trying to evaluate whether to put money into the commercial development of a new power generation device developed by Power&Heat Associates. The machine needs to generate electrical power at the rate of 1 MW. The engineers suggest a machine with the heat flows shown on the figure below: At 500 C 1.5MW of heat is delivered from a burner to a high temperature boiler. The machine also absorps 0.5 MW as heat from the burning of a low-grade fuel at 300 C. Cooling of the machine occurs in the environment at 5 C. a) Calculate the amount of heat that needs to be absorbed from the system at 5 C (cooling requirement) b) Can this machine operate as planned? Prove your answer! 3

4 Problem.5 Ten (10) moles of ideal gas at 500 C are adiabatically expanded in a turbine from a pressure of 100 atm to a pressure of atm. Because you are the King (or Queen) of Thermo you can compute that a reversible adiabatic expansion between these pressure can produce 108kJ of work. Unfortunately, the mechanical engineers that built the turbine mess up, and the expansion only produces 80kJ of work (but is still adiabatic). a) What is the final temperature of the gas coming out of the turbine? b) If the expansion were reversible the entropy change of the gas would be zero. What is the entropy change of the gas due to the mechanical engineer s mess up? Cp = 7/ R Cv = 5/ R Problem.6 An insulated tank contains a gas at 10atm pressure (fig a). When the valve on the tank is opened, air flows out of the tank while the air remaining in the tank cools down. T a is the temperature of the last air coming out of the tank (when the pressure inside has become equal to 1atm). Compare this now to the situation in figure b. A balloon originally filled so that the pressure inside is 10 atm is drained by slowly letting air out (similar to the flow through the valve in figure a). As the air flows out the balloon shrinks. T b is the temperature of the air in the balloon when it is deflated (when the pressure inside is 1 atm). What is the relation between T a and Tb? Chose one of the options below and briefly explain! You do not need to calculate the temperatures Ta or Tb You may assume that there are no heat flows through the balloon (process is adiabatic). Mark the correct result below and EXPLAIN BRIEFLY! Ta = Tb Ta < Tb Ta > Tb 4

5 Problem.7 A tank contains 50 liters of water at 80 C. An additional 10 liters needs to be added to this tank, keeping the total contents of the tank at 80 C. For this I have water available at 5 C and an electrical heater. Two different procedures for accomplishing this are suggested. I) The 10 liters at 5 C is first mixed with the 50 liters at 80 C and then the mixture is heated up to 80 C. II) The 10 liters is first heated from 5 C to 80 C and then mixed with the 50 liters at 80 C. Calculate for both scenarios a) the total amount of electrical energy required (in kwh) b) the total entropy change of the universe (system + surroundings). heat capacity for H O: 1cal/g-K M H0=18g/mole 1 liter of water = 1 kg All mixing and heating is done under constant atmospheric pressure. Problem.8 Consider a system at T 1, P 1,V 1 which is composed of one mole of a classical ideal gas for which PV=RT and U=A+BT. Let the system change in four steps. The first step is a very slow compression to P,V at a constant temperature of T 1. The second step is a quick compression to T 3, P 3, V 3. The third step is a very slow expansion to P 4, V 4 at a constant temperature T 3. The fourth step is a very quick expansion back to T 1, P 1, V 1. The second and fourth steps are so quick that there is no heat exchange. Calculate the relations between the total work, heat of the first step and the heat of the third step, expressing the results in terms of T 1 and T 3. (Hillert: problem 1.3.3) Problem.9 When an ideal gas undergoes a Joule-Thompson expansion its temperature remains constant. Show that this expansion is irreversible by showing that entropy of the universe (system + environment) increases. The Joule- Thompson expansion is an adiabatic flow through an insulated valve, i.e. the gas comes out a lower pressure than it goes in. For an ideal gas the temperature of the gas going out is identical to the temperature of the incoming gas, i.e. T = i T o 5

6 Problem.10 For a particular system it is found that if the volume is kept constant at the value V o and the pressure is changed from P o to an arbitrary pressure P, the heat transfer to the system is Q = A ( P P o ) (A > 0) In addition it is known that the reversible adiabats of the system are of the form P V = constant ( > 0) Find the internal energy U(P,V) for an arbitrary point in the P-V plane, expressing U(P,V) in terms of P o,v o, A and (as well as P and V) (Callen: problem 1.8-6) LEVEL 3 PROBLEMS Problem 3.1 Ammonia gas (NH 3 ) in a pressure cylinder is quickly brought to a temperature of 100K by rapidly compressing it to 10 atm. At the end of the compression the piston is fixed so that the system remains at constant volume. At 100K NH 3 will start to decompose according to the reaction: NH 3 > N +3 H (1) Assume that no NH 3 has decomposed during the rapid compression. a) What is the pressure inside the system when all the NH 3 has decomposed at a constant temperature of 100K? b) Compute the heat one needs to supply/extract from the cylinder to keep the temperature at 100K during the decomposition of the ammonia in the cylinder? c) If the decomposition reaction occurred adiabatically, what would be the temperature of the system after complete decomposition H for reaction (1) at 100K: 87kJ/mol (per mole of N formed) C,N = 33J/mol-k p C,H = 33J/mol-k p C,NH 3 = 36J/mol-k p Assume that all gasses behave ideal. Some properties of ideal gasses: C p C v = R U =0 V T H =0 p 6 T

7 Problem 3. An insulated tank contains air at 0.5 atm pressure and 98K. The outside pressure is at 1atm pressure and 98K. A valve is opened and air is allowed to flow into the tank. What is the temperature of the gas in the tank after it is filled? Problem 3.3 In class, it was shown that ( Q) P =(dh) P is valid. This equality was derived only for infinitesimal and reversible processes. In general though, H = Q holds for any irreversible process between an initial equilibrium state and a final equilibrium state that occurs in an environment with constant pressure. Q is the heat exchanged between the system and the environment during the irreversible process and H is the enthalpy difference between the initial and final equilibrium states. The only requirement is that the process occurs at constant pressure. Consider a chamber with a moveable frictionless piston and diathermal walls. The chamber is divided by a partition as illustrated in the figure. On one side of the partition is a gas A and on the other side of the partition is a gas B. When the partition is removed, the two components react to form AB. This reaction proceeds under explosive conditions that is so far from equilibrium that the pressure in the chamber during the process cannot be defined. Furthermore, the piston moves up and down violently during the reaction. Show that the heat Q exchanged between the gas in the chamber and the environment is equal to the change in enthalpy of the gas (i.e. Q= H=H AB -H A -H B ). Assume that the change in volume during the reaction is DV. Problem 3.4 An evacuated (P=0), insulated tank is surrounded by a very large volume (assume infinite volume) of an ideal gas at a temperature To. The valve on the tank is opened and the surrounding gas is allowed to flow quickly into the tank until the pressure inside the tank equals the pressure outside. Assume that no heat flow takes place. What is the final temperature of the gas in the tank? The heat capacities of the gas, C p and C v, each may be assumed to be constant over the temperature range spanned by the experiment. Your answer may be left in terms of C p and C v. Hint: One way to approach the problem is to define the system as the gas that ends up in the tank. (Ragone: problem 1.5) 7

8 Problem 3.5 Two tanks with equal volume are connected with a Joule-Thompson valve. Tank I contains an ideal gas at 10 atm pressure and 300K while tank II is empty (P = 0). The valve is opened slowly so that gas can flow from tank I into tank II. The valve is closed once the pressure in tank I has reached 5 atm. a) What is the temperature of the gas in tank I when the pressure there is 5atm? b) What is the temperature of the gas in tank II when the pressure in tank I has reached 5 atm? c) Prove that this process is irreversible by calculating the total entropy change of the system. C p for the ideal gas is 7/ R C v for the ideal gas is 5/ R Note that pressure changes in the tank may be considered to be reversible processes. The expansion across the Joule-Thompson valve is irreversible but conserves enthalpy, as discussed in class.the complete enclosure of the tank is insulated so that no heat exchange with the environment occurs. 8

9 LEVEL 4 PROBLEMS Problem 4.1 The above picture shows two identical ideal gasses separated by a movable insulated piston. The two gasses are at the same temperature but different pressure. The compartments are fully insulated from the environment. In the initial state, the volumes of the two compartments are both equal to V o. What is the final temperature and pressure after the piston is slowly allowed to equilibrate? (so that process is reversible)? What will happen if the process is irreversible? 9

### 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

### 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

### 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

### 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

### 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

### 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

### Chapter 10 Temperature and Heat

Chapter 10 Temperature and Heat What are temperature and heat? Are they the same? What causes heat? What Is Temperature? How do we measure temperature? What are we actually measuring? Temperature and Its

### 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

### 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

### The Second Law of Thermodynamics

The Second aw of Thermodynamics The second law of thermodynamics asserts that processes occur in a certain direction and that the energy has quality as well as quantity. The first law places no restriction

### Exergy: the quality of energy N. Woudstra

Exergy: the quality of energy N. Woudstra Introduction Characteristic for our society is a massive consumption of goods and energy. Continuation of this way of life in the long term is only possible if

### 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

### Module 5: Combustion Technology. Lecture 34: Calculation of calorific value of fuels

1 P age Module 5: Combustion Technology Lecture 34: Calculation of calorific value of fuels 2 P age Keywords : Gross calorific value, Net calorific value, enthalpy change, bomb calorimeter 5.3 Calculation

### The Gas Laws. Our Atmosphere. Pressure = Units of Pressure. Barometer. Chapter 10

Our Atmosphere The Gas Laws 99% N 2 and O 2 78% N 2 80 70 Nitrogen Chapter 10 21% O 2 1% CO 2 and the Noble Gases 60 50 40 Oxygen 30 20 10 0 Gas Carbon dioxide and Noble Gases Pressure Pressure = Force

### The First Law of Thermodynamics

The First aw of Thermodynamics Q and W are process (path)-dependent. (Q W) = E int is independent of the process. E int = E int,f E int,i = Q W (first law) Q: + heat into the system; heat lost from the

### 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

### ES-7A Thermodynamics HW 1: 2-30, 32, 52, 75, 121, 125; 3-18, 24, 29, 88 Spring 2003 Page 1 of 6

Spring 2003 Page 1 of 6 2-30 Steam Tables Given: Property table for H 2 O Find: Complete the table. T ( C) P (kpa) h (kj/kg) x phase description a) 120.23 200 2046.03 0.7 saturated mixture b) 140 361.3

### 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,

### Thermodynamics. Thermodynamics 1

Thermodynamics 1 Thermodynamics Some Important Topics First Law of Thermodynamics Internal Energy U ( or E) Enthalpy H Second Law of Thermodynamics Entropy S Third law of Thermodynamics Absolute Entropy

### Introduction to the Ideal Gas Law

Course PHYSICS260 Assignment 5 Consider ten grams of nitrogen gas at an initial pressure of 6.0 atm and at room temperature. It undergoes an isobaric expansion resulting in a quadrupling of its volume.

### Chapter 8 Maxwell relations and measurable properties

Chapter 8 Maxwell relations and measurable properties 8.1 Maxwell relations Other thermodynamic potentials emerging from Legendre transforms allow us to switch independent variables and give rise to alternate

### 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

### Bomb Calorimetry. Example 4. Energy and Enthalpy

Bomb Calorimetry constant volume often used for combustion reactions heat released by reaction is absorbed by calorimeter contents need heat capacity of calorimeter q cal = q rxn = q bomb + q water Example

### 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.

### 39th International Physics Olympiad - Hanoi - Vietnam - 2008. Theoretical Problem No. 3

CHANGE OF AIR TEMPERATURE WITH ALTITUDE, ATMOSPHERIC STABILITY AND AIR POLLUTION Vertical motion of air governs many atmospheric processes, such as the formation of clouds and precipitation and the dispersal

### Temperature. Number of moles. Constant Terms. Pressure. Answers Additional Questions 12.1

Answers Additional Questions 12.1 1. A gas collected over water has a total pressure equal to the pressure of the dry gas plus the pressure of the water vapor. If the partial pressure of water at 25.0

### Standard Free Energies of Formation at 298 K. Average Bond Dissociation Energies at 298 K

1 Thermodynamics There always seems to be at least one free response question that involves thermodynamics. These types of question also show up in the multiple choice questions. G, S, and H. Know what

### 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

### 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

### 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

### CO 2 41.2 MPa (abs) 20 C

comp_02 A CO 2 cartridge is used to propel a small rocket cart. Compressed CO 2, stored at a pressure of 41.2 MPa (abs) and a temperature of 20 C, is expanded through a smoothly contoured converging nozzle

### So T decreases. 1.- Does the temperature increase or decrease? For 1 mole of the vdw N2 gas:

1.- One mole of Nitrogen (N2) has been compressed at T0=273 K to the volume V0=1liter. The gas goes through the free expansion process (Q = 0, W = 0), in which the pressure drops down to the atmospheric

### 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

### 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.

### Gas Laws. The kinetic theory of matter states that particles which make up all types of matter are in constant motion.

Name Period Gas Laws Kinetic energy is the energy of motion of molecules. Gas state of matter made up of tiny particles (atoms or molecules). Each atom or molecule is very far from other atoms or molecules.

### Thermochemistry. r2 d:\files\courses\1110-20\99heat&thermorans.doc. Ron Robertson

Thermochemistry r2 d:\files\courses\1110-20\99heat&thermorans.doc Ron Robertson I. What is Energy? A. Energy is a property of matter that allows work to be done B. Potential and Kinetic Potential energy

### Chem 1A Exam 2 Review Problems

Chem 1A Exam 2 Review Problems 1. At 0.967 atm, the height of mercury in a barometer is 0.735 m. If the mercury were replaced with water, what height of water (in meters) would be supported at this pressure?

### QUESTIONS THERMODYNAMICS PRACTICE PROBLEMS FOR NON-TECHNICAL MAJORS. Thermodynamic Properties

QUESTIONS THERMODYNAMICS PRACTICE PROBLEMS FOR NON-TECHNICAL MAJORS Thermodynamic Properties 1. If an object has a weight of 10 lbf on the moon, what would the same object weigh on Jupiter? ft ft -ft g

Chapter 18 Homework Answers 18.22. 18.24. 18.26. a. Since G RT lnk, as long as the temperature remains constant, the value of G also remains constant. b. In this case, G G + RT lnq. Since the reaction

### Chapter 6 The first law and reversibility

Chapter 6 The first law and reversibility 6.1 The first law for processes in closed systems We have discussed the properties of equilibrium states and the relationship between the thermodynamic parameters

### 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

### Final Exam CHM 3410, Dr. Mebel, Fall 2005

Final Exam CHM 3410, Dr. Mebel, Fall 2005 1. At -31.2 C, pure propane and n-butane have vapor pressures of 1200 and 200 Torr, respectively. (a) Calculate the mole fraction of propane in the liquid mixture

### SUPPLEMENTARY TOPIC 3 ENERGY AND CHEMICAL REACTIONS

SUPPLEMENTARY TOPIC 3 ENERGY AND CHEMICAL REACTIONS Rearranging atoms. In a chemical reaction, bonds between atoms in one or more molecules (reactants) break and new bonds are formed with other atoms to

### CHAPTER 7 THE SECOND LAW OF THERMODYNAMICS. Blank

CHAPTER 7 THE SECOND LAW OF THERMODYNAMICS Blank SONNTAG/BORGNAKKE STUDY PROBLEM 7-1 7.1 A car engine and its fuel consumption A car engine produces 136 hp on the output shaft with a thermal efficiency

### States of Matter CHAPTER 10 REVIEW SECTION 1. Name Date Class. Answer the following questions in the space provided.

CHAPTER 10 REVIEW States of Matter SECTION 1 SHORT ANSWER Answer the following questions in the space provided. 1. Identify whether the descriptions below describe an ideal gas or a real gas. ideal gas

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Given: 4 NO2(g) + O2(g) 2 N2O5(g) ΔH = -110.2 kj find ΔH for N2O5(g) 2 NO2(g) + 1/2 O2(g).

### Saeid Rahimi. Effect of Different Parameters on Depressuring Calculation Results. 01-Nov-2010. Introduction. Depressuring parameters

Effect of Different Parameters on Depressuring Calculation Results Introduction Saeid Rahimi 01-Nov-2010 Emergency depressuring facilities are utilized to accomplish at least one of the following objectives:

### UNIT 2 REFRIGERATION CYCLE

UNIT 2 REFRIGERATION CYCLE Refrigeration Cycle Structure 2. Introduction Objectives 2.2 Vapour Compression Cycle 2.2. Simple Vapour Compression Refrigeration Cycle 2.2.2 Theoretical Vapour Compression

### CHAPTER 14 THE CLAUSIUS-CLAPEYRON EQUATION

CHAPTER 4 THE CAUIU-CAPEYRON EQUATION Before starting this chapter, it would probably be a good idea to re-read ections 9. and 9.3 of Chapter 9. The Clausius-Clapeyron equation relates the latent heat

### Thermodynamics - Example Problems Problems and Solutions

Thermodynamics - Example Problems Problems and Solutions 1 Examining a Power Plant Consider a power plant. At point 1 the working gas has a temperature of T = 25 C. The pressure is 1bar and the mass flow

### 5. Which temperature is equal to +20 K? 1) 253ºC 2) 293ºC 3) 253 C 4) 293 C

1. The average kinetic energy of water molecules increases when 1) H 2 O(s) changes to H 2 O( ) at 0ºC 3) H 2 O( ) at 10ºC changes to H 2 O( ) at 20ºC 2) H 2 O( ) changes to H 2 O(s) at 0ºC 4) H 2 O( )

### APPLIED THERMODYNAMICS. TUTORIAL No.3 GAS TURBINE POWER CYCLES. Revise gas expansions in turbines. Study the Joule cycle with friction.

APPLIED HERMODYNAMICS UORIAL No. GAS URBINE POWER CYCLES In this tutorial you will do the following. Revise gas expansions in turbines. Revise the Joule cycle. Study the Joule cycle with friction. Extend

### When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.

Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs

### Technical Thermodynamics

Technical Thermodynamics Chapter 2: Basic ideas and some definitions Prof. Dr.-Ing. habil. Egon Hassel University of Rostock, Germany Faculty of Mechanical Engineering and Ship Building Institute of Technical

### The final numerical answer given is correct but the math shown does not give that answer.

Note added to Homework set 7: The solution to Problem 16 has an error in it. The specific heat of water is listed as c 1 J/g K but should be c 4.186 J/g K The final numerical answer given is correct but

### Unit 5 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Name: Class: Date: Unit 5 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1) The internal energy of a system is always increased by. A) adding

### vap H = RT 1T 2 = 30.850 kj mol 1 100 kpa = 341 K

Thermodynamics: Examples for chapter 6. 1. The boiling point of hexane at 1 atm is 68.7 C. What is the boiling point at 1 bar? The vapor pressure of hexane at 49.6 C is 53.32 kpa. Assume that the vapor

### How To Calculate The Performance Of A Refrigerator And Heat Pump

THERMODYNAMICS TUTORIAL 5 HEAT PUMPS AND REFRIGERATION On completion of this tutorial you should be able to do the following. Discuss the merits of different refrigerants. Use thermodynamic tables for

### Heat of Combustion PCh 6-99

UMR ChemLabs Heat of Combustion PCh 6-99 Gary L. Bertrand, Professor of Chemistry A calorimeter (calor L = heat + metron Gr = measure) should be literally a device to measure heat. In reality, most calorimeters

### Name Class Date. In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question.

Assessment Chapter Test A Chapter: States of Matter In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question. 1. The kinetic-molecular

### ENTHALPY CHANGES FOR A CHEMICAL REACTION scaling a rxn up or down (proportionality) quantity 1 from rxn heat 1 from Δ r H. = 32.

CHEMISTRY 103 Help Sheet #10 Chapter 4 (Part II); Sections 4.6-4.10 Do the topics appropriate for your lecture Prepared by Dr. Tony Jacob http://www.chem.wisc.edu/areas/clc (Resource page) Nuggets: Enthalpy

### Chapter 1 Classical Thermodynamics: The First Law. 1.2 The first law of thermodynamics. 1.3 Real and ideal gases: a review

Chapter 1 Classical Thermodynamics: The First Law 1.1 Introduction 1.2 The first law of thermodynamics 1.3 Real and ideal gases: a review 1.4 First law for cycles 1.5 Reversible processes 1.6 Work 1.7

### 1. Thermite reaction 2. Enthalpy of reaction, H 3. Heating/cooling curves and changes in state 4. More thermite thermodynamics

Chem 105 Fri 10-23-09 1. Thermite reaction 2. Enthalpy of reaction, H 3. Heating/cooling curves and changes in state 4. More thermite thermodynamics 10/23/2009 1 Please PICK UP your graded EXAM in front.

### CHEM 105 HOUR EXAM III 28-OCT-99. = -163 kj/mole determine H f 0 for Ni(CO) 4 (g) = -260 kj/mole determine H f 0 for Cr(CO) 6 (g)

CHEM 15 HOUR EXAM III 28-OCT-99 NAME (please print) 1. a. given: Ni (s) + 4 CO (g) = Ni(CO) 4 (g) H Rxn = -163 k/mole determine H f for Ni(CO) 4 (g) b. given: Cr (s) + 6 CO (g) = Cr(CO) 6 (g) H Rxn = -26

### Thermochemical equations allow stoichiometric calculations.

CHEM 1105 THERMOCHEMISTRY 1. Change in Enthalpy ( H) Heat is evolved or absorbed in all chemical reactions. Exothermic reaction: heat evolved - heat flows from reaction mixture to surroundings; products

### APPLIED THERMODYNAMICS TUTORIAL 1 REVISION OF ISENTROPIC EFFICIENCY ADVANCED STEAM CYCLES

APPLIED THERMODYNAMICS TUTORIAL 1 REVISION OF ISENTROPIC EFFICIENCY ADVANCED STEAM CYCLES INTRODUCTION This tutorial is designed for students wishing to extend their knowledge of thermodynamics to a more

### Engineering Problem Solving as Model Building

Engineering Problem Solving as Model Building Part 1. How professors think about problem solving. Part 2. Mech2 and Brain-Full Crisis Part 1 How experts think about problem solving When we solve a problem

### 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

### The value of a state function is independent of the history of the system.

1 THERMODYNAMICS - The study of energy in matter - Thermodynamics allows us to predict whether a chemical reaction occurs or not. - Thermodynamics tells us nothing about how fast a reaction occurs. - i.

### Chemistry 110 Lecture Unit 5 Chapter 11-GASES

Chemistry 110 Lecture Unit 5 Chapter 11-GASES I. PROPERITIES OF GASES A. Gases have an indefinite shape. B. Gases have a low density C. Gases are very compressible D. Gases exert pressure equally in all

### 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.

### We will study the temperature-pressure diagram of nitrogen, in particular the triple point.

K4. Triple Point of Nitrogen I. OBJECTIVE OF THE EXPERIMENT We will study the temperature-pressure diagram of nitrogen, in particular the triple point. II. BAKGROUND THOERY States of matter Matter is made

### CHEM 36 General Chemistry EXAM #1 February 13, 2002

CHEM 36 General Chemistry EXAM #1 February 13, 2002 Name: Serkey, Anne INSTRUCTIONS: Read through the entire exam before you begin. Answer all of the questions. For questions involving calculations, show

### Introductory Chemistry, 3 rd Edition Nivaldo Tro. Roy Kennedy Massachusetts Bay Community College Wellesley Hills, Maqqwertd ygoijpk[l

Introductory Chemistry, 3 rd Edition Nivaldo Tro Quantities in Car an octane and oxygen molecules and carbon dioxide and water Chemical Reactions Roy Kennedy Massachusetts Bay Community College Wellesley

### Type: Single Date: Homework: READ 12.8, Do CONCEPT Q. # (14) Do PROBLEMS (40, 52, 81) Ch. 12

Type: Single Date: Objective: Latent Heat Homework: READ 12.8, Do CONCEPT Q. # (14) Do PROBLEMS (40, 52, 81) Ch. 12 AP Physics B Date: Mr. Mirro Heat and Phase Change When bodies are heated or cooled their

### 7. 1.00 atm = 760 torr = 760 mm Hg = 101.325 kpa = 14.70 psi. = 0.446 atm. = 0.993 atm. = 107 kpa 760 torr 1 atm 760 mm Hg = 790.

CHATER 3. The atmosphere is a homogeneous mixture (a solution) of gases.. Solids and liquids have essentially fixed volumes and are not able to be compressed easily. have volumes that depend on their conditions,

### Experiment 12E LIQUID-VAPOR EQUILIBRIUM OF WATER 1

Experiment 12E LIQUID-VAPOR EQUILIBRIUM OF WATER 1 FV 6/26/13 MATERIALS: PURPOSE: 1000 ml tall-form beaker, 10 ml graduated cylinder, -10 to 110 o C thermometer, thermometer clamp, plastic pipet, long

### State Newton's second law of motion for a particle, defining carefully each term used.

5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

### Thermodynamics 2nd year physics A. M. Steane 2000, revised 2004, 2006

Thermodynamics 2nd year physics A. M. Steane 2000, revised 2004, 2006 We will base our tutorials around Adkins, Equilibrium Thermodynamics, 2nd ed (McGraw-Hill). Zemansky, Heat and Thermodynamics is good

### Practice Test. 4) The planet Earth loses heat mainly by A) conduction. B) convection. C) radiation. D) all of these Answer: C

Practice Test 1) Increase the pressure in a container of oxygen gas while keeping the temperature constant and you increase the A) molecular speed. B) molecular kinetic energy. C) Choice A and choice B

### Review - After School Matter Name: Review - After School Matter Tuesday, April 29, 2008

Name: Review - After School Matter Tuesday, April 29, 2008 1. Figure 1 The graph represents the relationship between temperature and time as heat was added uniformly to a substance starting at a solid

### The Second Law of Thermodynamics

Objectives MAE 320 - Chapter 6 The Second Law of Thermodynamics The content and the pictures are from the text book: Çengel, Y. A. and Boles, M. A., Thermodynamics: An Engineering Approach, McGraw-Hill,

### 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.

### = 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

### 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

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

General Chemistry PHS 1015 Practice Exam 4 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Which of the following statements about pressure

### TEACHER BACKGROUND INFORMATION THERMAL ENERGY

TEACHER BACKGROUND INFORMATION THERMAL ENERGY In general, when an object performs work on another object, it does not transfer all of its energy to that object. Some of the energy is lost as heat due to

### Thermodynamics. Chapter 13 Phase Diagrams. NC State University

Thermodynamics Chapter 13 Phase Diagrams NC State University Pressure (atm) Definition of a phase diagram A phase diagram is a representation of the states of matter, solid, liquid, or gas as a function

### Sheet 5:Chapter 5 5 1C Name four physical quantities that are conserved and two quantities that are not conserved during a process.

Thermo 1 (MEP 261) Thermodynamics An Engineering Approach Yunus A. Cengel & Michael A. Boles 7 th Edition, McGraw-Hill Companies, ISBN-978-0-07-352932-5, 2008 Sheet 5:Chapter 5 5 1C Name four physical

### Calorimetry: Heat of Vaporization

Calorimetry: Heat of Vaporization OBJECTIVES INTRODUCTION - Learn what is meant by the heat of vaporization of a liquid or solid. - Discuss the connection between heat of vaporization and intermolecular

### 1. What is the molecular formula of a compound with the empirical formula PO and a gram-molecular mass of 284 grams?

Name: Tuesday, May 20, 2008 1. What is the molecular formula of a compound with the empirical formula PO and a gram-molecular mass of 284 grams? 2 5 1. P2O 5 3. P10O4 2. P5O 2 4. P4O10 2. Which substance

### Unit 3: States of Matter Practice Exam

Page 1 Unit 3: States of Matter Practice Exam Multiple Choice. Identify the choice that best completes the statement or answers the question. 1. Two gases with unequal masses are injected into opposite

### 87 16 70 20 58 24 44 32 35 40 29 48 (a) graph Y versus X (b) graph Y versus 1/X

HOMEWORK 5A Barometer; Boyle s Law 1. The pressure of the first two gases below is determined with a manometer that is filled with mercury (density = 13.6 g/ml). The pressure of the last two gases below

### 1.4.6-1.4.8 Gas Laws. Heat and Temperature

1.4.6-1.4.8 Gas Laws Heat and Temperature Often the concepts of heat and temperature are thought to be the same, but they are not. Perhaps the reason the two are incorrectly thought to be the same is because

### 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

### LECTURE 28 to 29 ACCUMULATORS FREQUENTLY ASKED QUESTIONS

LECTURE 28 to 29 ACCUMULATORS FREQUENTLY ASKED QUESTIONS 1. Define an accumulator and explain its function A hydraulic accumulator is a device that stores the potential energy of an incompressible fluid

CHEM 366 II-1 Adiabatic Bomb Calorimetry Introduction Obtaining energy in the form of heat from the combustion or oxidation of thermodynamically unstable (and often kinetically inert) hydrocarbons and

### OUTCOME 2 INTERNAL COMBUSTION ENGINE PERFORMANCE. TUTORIAL No. 5 PERFORMANCE CHARACTERISTICS

UNIT 61: ENGINEERING THERMODYNAMICS Unit code: D/601/1410 QCF level: 5 Credit value: 15 OUTCOME 2 INTERNAL COMBUSTION ENGINE PERFORMANCE TUTORIAL No. 5 PERFORMANCE CHARACTERISTICS 2 Be able to evaluate