ε tran ε tran = nrt = 2 3 N ε tran = 2 3 nn A ε tran nn A nr ε tran = 2 N A i.e. T = R ε tran = 2

Size: px
Start display at page:

Download "ε tran ε tran = nrt = 2 3 N ε tran = 2 3 nn A ε tran nn A nr ε tran = 2 N A i.e. T = R ε tran = 2"

Transcription

1 F1 (a) Since the ideal gas equation of state is PV = nrt, we can equate the right-hand sides of both these equations (i.e. with PV = 2 3 N ε tran )and write: nrt = 2 3 N ε tran = 2 3 nn A ε tran i.e. T = 2 3 nn A nr ε tran = 2 N A 3 R ε tran = 2 3k ε tran This provides a definition of the macroscopic temperature T in terms of the average of the microscopic translational kinetic energy. (b) We just rearrange the equation from (a): ε tran = 2 3 kt = JK K = J Note that if we know the temperature, we do not need the number of moles (or atoms) to calculate the mean kinetic energy per atom; we would need that information to calculate the total internal energy.

2 (c) For five degrees of freedom, the equipartition of energy theorem states that the internal energy will be 5 2 NkT or 5 2 nrt. So E int = mol J K 1 mol 1 295K = J (d) The specific heat at constant pressure is given by C P = C V + R = 2 5 R + R = 2 7 R = J K 1 mol 1 = J K 1 mol 1

3 F2 (a) n(v) v represents the number of atoms (or molecules) in the gas which have speeds in the small range v to (v + v), so it gives information on how the population of atoms is distributed among the range of possible speeds. (The area under a graph of n(v) against v, over the entire range of speeds, will just be the total number of atoms in the gas.) (b) The mass of one mole of molecular hydrogen is 2.021g, which means that the mass of an individual hydrogen molecule (which is what m in the equation represents) is 2.021g/( ) = g = kg. Then v rms = JK K kg = m 2 s 2 = ms 1 (c) Since their root-mean-squared speeds are the same, but their masses are different, their temperatures must be different as well. We can rewrite the equation as T = m 3k v 2 rms, so the molecule with the larger mass will have the higher temperature. The oxygen will be hotter. (Section 3 gives a fuller discussion of the Maxwell Boltzmann distribution.)

4 F3 (a) There are two differences between this equation and the ideal gas equation of state. First, instead of P we have the quantity [P + (a/v m2 )]. This correction to the ideal gas behaviour represents the effect of intermolecular interactions. (See Subsection 4.3 for a more detailed explanation.) The second difference is replacing the volume V m by the term (V m b). This is a correction for the finite size of the molecules (which are points in the ideal gas model) and accounts for the excluded volume arising from the volumes of all the other molecules. (See Subsection 4.2 for more detail.) (b) We rearrange the equation slightly and substitute in the given values: T = (P + av m 2 )(V m b) R = Pa Nm 4 mol 2 ( m 3 mol 1 ) 2 ( )m 3 mol J K 1 mol 1 = 435K (Make sure you understand the unit conversions above.)

5 (c) Again, we need to rearrange the equation to solve for P. P + i.e. P = a V m 2 = RT V m b RT V m b a V 2 m Now we substitute in the given values (remembering that V m (per mole) is five times the given value of V): J K 1 mol 1 438K P = m 3 mol m 3 mol Nm 4 mol 2 ( m 3 mol 1 ) 2 P = J mol m 3 mol Nm 4 mol m 6 mol 2 = Jm Nm 2 = Pa Again, make sure you understand the unit conversions.

6 Study comment Having seen the Fast track questions you may feel that it would be wiser to follow the normal route through the module and to proceed directly to Ready to study? in Subsection 1.3. Alternatively, you may still be sufficiently comfortable with the material covered by the module to proceed directly to the Closing items. If you have completed both the Fast track questions and the Exit test, then you have finished the module and may leave it here.

7 R1 (a) The average speed 1v1 is calculated by taking the ratio of the total distance travelled to the total time taken: 1v1 = (5 + 5)1m/101s = 11m1s 1 (b) The average velocity is calculated by taking the ratio of the net displacement to the total time taken for the displacement. Here the net displacement is zero and so 1v1 = 101 1m/101s with 1 1v1 1 = 01m1s 1 The average velocity is zero because the net displacement is zero since the particle returns to its starting point. (c) The average kinetic energy is m 1v 2 1 /2 = 31kg (11m1s 1 ) 2 /2 = 1.51J. (d) For the average magnitude of momentum, we take the product of the mass with the average speed: 1p1 = m 1v1 = 31kg 11m1s 1 = 31kg1m1s 1

8 (e) Taking the momentum to be positive in the initial direction of motion: momentum before the turnaround = p 1 = 31kg1m1s 1 in the initial direction momentum after turnaround = p 2 = 31kg1m1s 1 in the initial direction momentum change for particle is (1p 2 p 1 ) = 61kg1m1s 1 in the initial direction. (f) According to Newton s second law of motion, the average force exerted on the wall is equal to the rate of change of momentum, so F = (1p 2 p 1 )/ t = (6/ t)1kg1m1s 2 in the initial direction. Consult the relevant terms in the Glossary for further details.

9 T1 (a) Using the ideal gas law, PV = nrt, we find: n = PV ( Pa) 2.00 m 3 = RT J K 1 mol K n = Pa m J mol 1 = Nm = 155moles N m mol (b) The mass (in grams) of one mole of any substance is equal to its relative molecular mass, so for molecular hydrogen this is 2.021g. Thus, the system contains 2.021g 155 = 3131g = kg. The mass density is then ρ = M kg = = kg m 3 V 2.00 m3 (c) We have PV = constant, so if V increases by a factor of 2, P must decrease by a factor of 2. Thus, the new pressure is Pa.

10 T2 (a) Using Equation 1 PV = nrt with n = 11mol and R = J1K 1 1mol 1, we find the volume of the gas V = nrt P = 1mol J K 1 mol K Nm 2 = m 3 (Eqn 1) (b) The volume occupied by the molecules themselves is: N 4 A 3 πr3 = mol 1 4 π ( m) 3 = m 3 mol 1 3 = m 3 for n = 1mol So, 1 mole of molecules occupies m 3, which is less than 0.1% of the total gas volume. Therefore Assumption 5 is justified.

11 (c) The number of molecules per unit volume is nn A V = 1mol mol m 3 = m 3 (d) If molecules have an average separation d, then each volume d0 3 contains on average one molecule. Total gas volume V = nn A d0 3 so d 3 = m 3 1mol mol and d = 2 m = m = 3.46 nm The ratio d r = m m = 17 So, the average molecular separation is 17 times the molecular radius.

12 Alternatively, we could have obtained the value for d0 3 from the answer to part (c). If the number of molecules per volume is x then d 3 = 1 x = 1m

13 T3 From Equation 9, T = 2 N A 3 R ε tran (Eqn 9) for both gases ε tran = J K 1 mol K mol 1 = J To calculate the speed, use Equation 12, v rms = 3kT m For helium, m is kg, so v rms = JK K = 1.37 km s 1 kg For argon, m = kg, so v rms = 4341m1s 1 Notice that although the average kinetic energies are the same, the helium atoms travel faster because they are lighter.

14 T4 11eV corresponds to an energy, in SI units, of J. From Equation 10 For the monatomic gas ε tran = 2 3 kt (Eqn 10) we have ε tran = 3 2 kt so T = 2 ε tran 3k so T = 2 ε tran J = 3k JK 1 = K For hydrogen molecules (m = kg), at this temperature, Equation 12 gives: v rms = 3kT m = JK K kg = 9.85 km s 1

15 T5 For the two samples each containing one mole we have energy added = E int = 3 2 = 5 2 Nk ( T ) monatomic Nk ( T ) diatomic where N = N A 11mol in each case, so ( T ) diatomic = 3 5 ( T ) monatomic So the monatomic system reaches the higher temperature. This is because in the monatomic molecule the temperature corresponds only to the amount of translational kinetic energy in the system; in the case of the diatomic molecule, the energy is shared out between translational and rotational kinetic energy.

16 T6 Using Equations 18 and 22, C V = q 2 N Ak = q R 2 (Eqn 18) C P C V = R (Eqn 22) we have the generalization: C P = q 2 R + R = q + 2 R 2

17 T7 The values for C V, C P, (C P C V ) and γ, as given in Table 2, are determined from Equations 18, 22, 23 and 24. C V = q 2 N Ak = q R (Eqn 18) 2 C P C V = R (Eqn 22) γ = C P C V = 1 + R = 1 + R 2 = 1 + C V q 2 R q C P = 1 + q 2 (Eqn 23) R (Eqn 24) Table 23See Answer T7. q C V = qr/2 C P = (1 + q/2)r (C P C V ) = R γ = C P /C V = 1 + 2/q 3 3R/2 5R/2 R 5/3 5 5R/2 7R/2 R 7/5 7 7R/2 9R/2 R 9/7

18 T8 If we substitute the figures from Question T2 into Equation 28 (i.e. an ideal gas at T = 3001K and at a pressure of Pa. ) 1 λ = (Eqn 28) 4 2πr 2 n ρ we find: 1 λ = 4 2 π ( ) 2 m = 58 nm 3 m This is equivalent to about 145 molecular diameters and is about 17 times the intermolecular separation.

19 T9 Yes, they are consistent. The first estimate is that there will be another molecule within about 8.75 diameters in some direction, while the second value is estimating how far the molecule will have to travel in a particular direction before colliding with another molecule. The second value depends on the size of the targets but the first does not. For the mean free path, we are essentially asking how long a cylinder with twice the diameter of a molecule must be to have the same volume as the cube that, on average, contains one molecule.

20 T10 The exponential function in Equation m f (v) v = 4π v 2πkT 2 exp ( mv 2 2kT ) v (Eqn 30) is dimensionless and has no units. The units of v 2 are (m 2 1s 2 ), so we just need to work out the units of the factor 32 m. 2πkT We know kt has the units of energy (k = J1K 1 ), so its units are kg1m 2 1s 2. The ratio then has units (kg/kg1m 2 1s 2 ) = m 2 1s 2, which is equivalent to 1/v 2. This, taken to the power of 3/2, produces a factor with the dimensions of 1/v 3. Finally then, the dimensions of the terms on the right-hand side apart from v are those of 1/v, which must be the dimensions of f1(v), as required.

21 T11 We know that heating the gas adds translational kinetic energy and so molecular speeds, on average, must increase1 1so the peak must shift to a higher speed. We also know that the effect of increasing T is to reduce the quantity A(T) and to reduce the exponentially decaying factor in 32 m f (v) = 4π v 2 exp( mv 2 2kT) = AT ( )v 2 exp( mv 2 2kT) 2πkT The curve for the higher temperature must rise less rapidly at low speeds (as A(T) is less) and fall less rapidly at high speeds (as the exponential factor is less negative). This implies that the curve is broadened, i.e. there are a wider range of speeds. The area under the whole curve is unity (as the probability for a molecule to have a speed somewhere within the full range is unity). So if the area under the curve stays constant but it is broadened it follows that the curve must reach a lower peak.

22 T12 The average speed for the five molecules is: v = v 1 + v 2 + v 3 + v 4 + v 5 = = 12 = 2.40 (in the arbitrary units of the question) For this very simple distribution the most probable speed, v prob, is 2. The root-mean-squared (rms) speed is given by Equation 6: where v rms = v 2 v 2 = v v v v v = = 34 5 = 6.80 We find v rms = 6.80 = 2.61, which confirms the claim,v rms > 1v1 > v prob. It can be seen from the averaging processes above that the evaluation of v rms gives additional weight to the higher values of v as compared to the lower values of v (by squaring the numbers); in contrast, the calculation of 1v1 treats large and small speeds equally. It follows that v rms > 1v1 is true for any distribution (unless all molecules have the same speed).

23 T13 We use Equations 32, 33 and 12, the most probable speed v prob = the average speed v = the root-mean-squared speed v rms = with the helium mass substituted: v prob = v = v rms = 2kT m 8kT πm 3kT m 2kT m = J K K kg 8kT πm = J K K π kg 3kT m = J K K kg = 1.12 km s 1 = 1.26 km s 1 = 1.37 km s 1 (Eqn 32) (Eqn 33) (Eqn 12)

24 T14 To be dimensionally consistent, the terms within any set of brackets must have the same units. Thus, the units of b must be m 3 1mol 1 and a/v m 2 must be in Pa (= N1m 2 ). Table 13Values of van der Waals constants a and b for various gases. a/10 1 1m 6 1Pa1mol 2 b/10 5 1m 3 1mol 1 helium (He) nitrogen (N 2 ) oxygen (O 2 ) xenon (Xe) So a must have the units of P V m 2 and since V m 2 has units of m 6 1mol 2, this means that the units of a are N1m 2 m 6 1mol 2, or N1m 4 1mol 2. Therefore the units given in Table 1 are correct.

25 T15 Perhaps surprisingly, the answer is that there is no effect at all1 1whatever the details of the force! For simplicity, consider an attractive force which comes into play only very near the wall. This force will accelerate the molecules into the collision but decelerate them after the collision. The net change of momentum of the molecules will be the same as in the no force situation and it will be as if no force were operating.

Chapter 18 Thermal Properties of Matter

Chapter 18 Thermal Properties of Matter Chapter 18 Thermal Properties of Matter In this section we define the thermodynamic state variables and their relationship to each other, called the equation of state. The system of interest (most of the

More information

Rate of Heating and Cooling

Rate of Heating and Cooling Rate of Heating and Cooling 35 T [ o C] Example: Heating and cooling of Water E 30 Cooling S 25 Heating exponential decay 20 0 100 200 300 400 t [sec] Newton s Law of Cooling T S > T E : System S cools

More information

Chapter 15 Thermal Properties of Matter

Chapter 15 Thermal Properties of Matter Chapter 15 Thermal Properties of Matter To understand the mole and Avogadro's number. To understand equations of state. To study the kinetic theory of ideal gas. To understand heat capacity. To learn and

More information

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

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

More information

Ch. 19: The Kinetic Theory of Gases

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

More information

(2) The volume of molecules is negligible in comparison to the volume of gas. (3) Molecules of a gas moves randomly in all direction.

(2) The volume of molecules is negligible in comparison to the volume of gas. (3) Molecules of a gas moves randomly in all direction. 9.1 Kinetic Theory of Gases : Assumption (1) The molecules of a gas are identical, spherical and perfectly elastic point masses. (2) The volume of molecules is negligible in comparison to the volume of

More information

Lecture 24. Ideal Gas Law and Kinetic Theory

Lecture 24. Ideal Gas Law and Kinetic Theory Lecture 4 Ideal Gas Law and Kinetic Theory Today s Topics: Ideal Gas Law Kinetic Theory of Gases Phase equilibria and phase diagrams Ideal Gas Law An ideal gas is an idealized model for real gases that

More information

KINETIC THEORY OF GASES

KINETIC THEORY OF GASES KINETIC THEORY OF GASES VERY SHORT ANSWER TYPE QUESTIONS ( MARK). Write two condition when real gases obey the ideal gas equation ( nrt). n number of mole.. If the number of molecule in a container is

More information

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

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

More information

Handout 11: Ideal gas, internal energy, work and heat. Ideal gas law

Handout 11: Ideal gas, internal energy, work and heat. Ideal gas law Handout : Ideal gas, internal energy, work and heat Ideal gas law For a gas at pressure p, volume V and absolute temperature T, ideal gas law states that pv = nrt, where n is the number of moles and R

More information

Physics 2 week 7. Chapter 3 The Kinetic Theory of Gases

Physics 2 week 7. Chapter 3 The Kinetic Theory of Gases Physics week 7 Chapter 3 The Kinetic Theory of Gases 3.1. Ideal Gases 3.1.1. Experimental Laws and the Equation of State 3.1.. Molecular Model of an Ideal Gas 3.. Mean Free Path 3.3. The Boltzmann Distribution

More information

Handout 11: Ideal gas, internal energy, work and heat. Ideal gas law

Handout 11: Ideal gas, internal energy, work and heat. Ideal gas law Handout : Ideal gas, internal energy, work and heat Ideal gas law For a gas at pressure p, volume V and absolute temperature T, ideal gas law states that pv = nrt, where n is the number of moles and R

More information

PhysicsAndMathsTutor.com 1 2 (*) (1)

PhysicsAndMathsTutor.com 1 2 (*) (1) PhysicsAndMathsTutor.com 1 1. (a) pressure (*) Pa or N m volume m (*) (*) (not allow kpa) number of moles mol (or none) molar gas constant J K 1 mol 1 (mol 1 implies molar) temperature K 4 (b) (i) W(=

More information

Chapter 14. The Ideal Gas Law and Kinetic Theory

Chapter 14. The Ideal Gas Law and Kinetic Theory Chapter 14 The Ideal Gas Law and Kinetic Theory 14.1 Molecular Mass, the Mole, and Avogadro s Number To facilitate comparison of the mass of one atom with another, a mass scale know as the atomic mass

More information

Homework: 13, 14, 18, 20, 24 (p )

Homework: 13, 14, 18, 20, 24 (p ) Homework: 13, 14, 18, 0, 4 (p. 531-53) 13. A sample of an ideal gas is taken through the cyclic process abca shown in the figure below; at point a, T=00 K. (a) How many moles of gas are in the sample?

More information

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)

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

More information

Although different gasses may differ widely in their chemical properties, they share many physical properties

Although different gasses may differ widely in their chemical properties, they share many physical properties IV. Gases (text Chapter 9) A. Overview of Chapter 9 B. Properties of gases 1. Ideal gas law 2. Dalton s law of partial pressures, etc. C. Kinetic Theory 1. Particulate model of gases. 2. Temperature and

More information

14 The IDEAL GAS LAW. and KINETIC THEORY Molecular Mass, The Mole, and Avogadro s Number. Atomic Masses

14 The IDEAL GAS LAW. and KINETIC THEORY Molecular Mass, The Mole, and Avogadro s Number. Atomic Masses 14 The IDEAL GAS LAW and KINETIC THEORY 14.1 Molecular Mass, The Mole, and Avogadro s Number Atomic Masses The SI Unit of mass: An atomic mass unit is de ned as a unit of mass equal to 1/12 of the mass

More information

Atomic Mass and Atomic Mass Number. Moles and Molar Mass. Moles and Molar Mass

Atomic Mass and Atomic Mass Number. Moles and Molar Mass. Moles and Molar Mass Atomic Mass and Atomic Mass Number The mass of an atom is determined primarily by its most massive constituents: protons and neutrons in its nucleus. The sum of the number of protons and neutrons is called

More information

Module 5: Rise and Fall of the Clockwork Universe. You should be able to demonstrate and show your understanding of:

Module 5: Rise and Fall of the Clockwork Universe. You should be able to demonstrate and show your understanding of: OCR B Physics H557 Module 5: Rise and Fall of the Clockwork Universe You should be able to demonstrate and show your understanding of: 5.2: Matter Particle model: A gas consists of many very small, rapidly

More information

Lecture 24. Ideal Gas Law and Kinetic Theory

Lecture 24. Ideal Gas Law and Kinetic Theory Lecture 4 Ideal Gas Law and Kinetic Theory Today s Topics: Ideal Gas Law Kinetic Theory of Gases Phase equilibria and phase diagrams Ideal Gas Law An ideal gas is an idealized model for real gases that

More information

Web Resource: Ideal Gas Simulation. Kinetic Theory of Gases. Ideal Gas. Ideal Gas Assumptions

Web Resource: Ideal Gas Simulation. Kinetic Theory of Gases. Ideal Gas. Ideal Gas Assumptions Web Resource: Ideal Gas Simulation Kinetic Theory of Gases Physics Enhancement Programme Dr. M.H. CHAN, HKBU Link: http://highered.mheducation.com/olcweb/cgi/pluginpop.cgi?it=swf::00%5::00%5::/sites/dl/free/003654666/7354/ideal_na.swf::ideal%0gas%0law%0simulation

More information

KINETICE THEROY OF GASES

KINETICE THEROY OF GASES INTRODUCTION: Kinetic theory of gases relates the macroscopic properties of gases (like pressure, temperature, volume... etc) to the microscopic properties of the gas molecules (like speed, momentum, kinetic

More information

Chapter 14 Kinetic Theory

Chapter 14 Kinetic Theory Chapter 14 Kinetic Theory Kinetic Theory of Gases A remarkable triumph of molecular theory was showing that the macroscopic properties of an ideal gas are related to the molecular properties. This is the

More information

Physics 4C Chapter 19: The Kinetic Theory of Gases

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

More information

Physics 231 Topic 12: Temperature, Thermal Expansion, and Ideal Gases Alex Brown Nov

Physics 231 Topic 12: Temperature, Thermal Expansion, and Ideal Gases Alex Brown Nov Physics 231 Topic 12: Temperature, Thermal Expansion, and Ideal Gases Alex Brown Nov 18-23 2015 MSU Physics 231 Fall 2015 1 homework 3 rd midterm final Thursday 8-10 pm makeup Friday final 9-11 am MSU

More information

Chapter 14. The Ideal Gas Law and Kinetic Theory

Chapter 14. The Ideal Gas Law and Kinetic Theory Chapter 14 The Ideal Gas Law and Kinetic Theory 14.1 Molecular Mass, the Mole, and Avogadro s Number To facilitate comparison of the mass of one atom with another, a mass scale know as the atomic mass

More information

Temperature, Thermal Expansion and the Gas Laws

Temperature, Thermal Expansion and the Gas Laws Temperature, Thermal Expansion and the Gas Laws z x Physics 053 Lecture Notes Temperature,Thermal Expansion and the Gas Laws Temperature and Thermometers Thermal Equilibrium Thermal Expansion The Ideal

More information

Physics 160 Thermodynamics and Statistical Physics: Lecture 2. Dr. Rengachary Parthasarathy Jan 28, 2013

Physics 160 Thermodynamics and Statistical Physics: Lecture 2. Dr. Rengachary Parthasarathy Jan 28, 2013 Physics 160 Thermodynamics and Statistical Physics: Lecture 2 Dr. Rengachary Parthasarathy Jan 28, 2013 Chapter 1: Energy in Thermal Physics Due Date Section 1.1 1.1 2/3 Section 1.2: 1.12, 1.14, 1.16,

More information

Ideal Gas Behavior. NC State University

Ideal Gas Behavior. NC State University Chemistry 331 Lecture 6 Ideal Gas Behavior NC State University Macroscopic variables P, T Pressure is a force per unit area (P= F/A) The force arises from the change in momentum as particles hit an object

More information

Gases and Kinetic Theory

Gases and Kinetic Theory Gases and Kinetic Theory Chemistry 35 Fall 2000 Gases One of the four states of matter Simplest to understand both physically and chemically Gas Properties Low density Fluid Can be defined by their: 1.

More information

CHAPTER III: Kinetic Theory of Gases [5%]

CHAPTER III: Kinetic Theory of Gases [5%] CHAPTER III: Kinetic Theory of Gases [5%] Introduction The kinetic theory of gases (also known as kinetic-molecular theory) is a law that explains the behavior of a hypothetical ideal gas. According to

More information

Kinetic theory. Collective behaviour of large systems Statistical basis for the ideal gas equation Deviations from ideality

Kinetic theory. Collective behaviour of large systems Statistical basis for the ideal gas equation Deviations from ideality Kinetic theory Collective behaviour of large systems Statistical basis for the ideal gas equation Deviations from ideality Learning objectives Describe physical basis for the kinetic theory of gases Describe

More information

Lecture 3. The Kinetic Molecular Theory of Gases

Lecture 3. The Kinetic Molecular Theory of Gases Lecture 3. The Kinetic Molecular Theory of Gases THE IDEAL GAS LAW: A purely empirical law solely the consequence of experimental observations Explains the behavior of gases over a limited range of conditions

More information

Thermal Properties of Matter (Microscopic models)

Thermal Properties of Matter (Microscopic models) Chapter 18 Thermal Properties of Matter (Microscopic models) PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 6_18_2012

More information

Example Problems: 1.) What is the partial pressure of: Total moles = 13.2 moles 5.0 mol A 7.0 mol B 1.2 mol C Total Pressure = 3.

Example Problems: 1.) What is the partial pressure of: Total moles = 13.2 moles 5.0 mol A 7.0 mol B 1.2 mol C Total Pressure = 3. 5.6 Dalton s Law of Partial Pressures Dalton s Law of Partial Pressure; The total pressure of a gas is the sum of all its parts. P total = P 1 + P + P 3 + P n Pressures are directly related to moles: n

More information

Chapter 1 - The Properties of Gases. 2. Knowledge of these defines the state of any pure gas.

Chapter 1 - The Properties of Gases. 2. Knowledge of these defines the state of any pure gas. Chapter 1 - The Properties of Gases I. The perfect gas. A. The states of gases. (definition) 1. The state variables: volume=v amount of substance, moles = n pressure = p temperature = T. Knowledge of these

More information

PHYSICS - CLUTCH CH 19: KINETIC THEORY OF IDEAL GASSES.

PHYSICS - CLUTCH CH 19: KINETIC THEORY OF IDEAL GASSES. !! www.clutchprep.com CONCEPT: ATOMIC VIEW OF AN IDEAL GAS Remember! A gas is a type of fluid whose volume can change to fill a container - What makes a gas ideal? An IDEAL GAS is a gas whose particles

More information

KINETIC THEORY OF GASES

KINETIC THEORY OF GASES LECTURE 8 KINETIC THEORY OF GASES Text Sections 0.4, 0.5, 0.6, 0.7 Sample Problems 0.4 Suggested Questions Suggested Problems Summary None 45P, 55P Molecular model for pressure Root mean square (RMS) speed

More information

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

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

More information

= mol NO 2 1 mol Cu Now we use the ideal gas law: atm V = mol L atm/mol K 304 K

= mol NO 2 1 mol Cu Now we use the ideal gas law: atm V = mol L atm/mol K 304 K CHEM 101A ARMSTRONG SOLUTIONS TO TOPIC C PROBLEMS 1) This problem is a straightforward application of the combined gas law. In this case, the temperature remains the same, so we can eliminate it from the

More information

Ideal Gases. 247 minutes. 205 marks. theonlinephysicstutor.com. facebook.com/theonlinephysicstutor. Name: Class: Date: Time: Marks: Comments:

Ideal Gases. 247 minutes. 205 marks. theonlinephysicstutor.com. facebook.com/theonlinephysicstutor. Name: Class: Date: Time: Marks: Comments: Ideal Gases Name: Class: Date: Time: 247 minutes Marks: 205 marks Comments: Page 1 of 48 1 Which one of the graphs below shows the relationship between the internal energy of an ideal gas (y-axis) and

More information

Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature

Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature OpenStax-CNX module: m55236 1 Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature OpenStax This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution

More information

Part I: Basic Concepts of Thermodynamics

Part I: Basic Concepts of Thermodynamics Part I: Basic Concepts of Thermodynamics Lecture 3: Heat and Work Kinetic Theory of Gases Ideal Gases 3-1 HEAT AND WORK Here we look in some detail at how heat and work are exchanged between a system and

More information

QuickCheck. Collisions between molecules. Collisions between molecules

QuickCheck. Collisions between molecules. Collisions between molecules Collisions between molecules We model molecules as rigid spheres of radius r as shown at the right. The mean free path of a molecule is the average distance it travels between collisions. The average time

More information

(a) (i) One of the assumptions of the kinetic theory of gases is that molecules make elastic collisions. State what is meant by an elastic collision.

(a) (i) One of the assumptions of the kinetic theory of gases is that molecules make elastic collisions. State what is meant by an elastic collision. 1 (a) (i) One of the assumptions of the kinetic theory of gases is that molecules make elastic collisions. State what is meant by an elastic collision. State two more assumptions that are made in the kinetic

More information

Molecular Motion and Gas Laws

Molecular Motion and Gas Laws Molecular Motion and Gas Laws What is the connection between the motion of molecules (F = ma and K = mv 2 /2) and the thermodynamics of gases (pv = nrt and U = 3nRT/2)? In this lab, you will discover how

More information

PV = n R T = N k T. Measured from Vacuum = 0 Gauge Pressure = Vacuum - Atmospheric Atmospheric = 14.7 lbs/sq in = 10 5 N/m

PV = n R T = N k T. Measured from Vacuum = 0 Gauge Pressure = Vacuum - Atmospheric Atmospheric = 14.7 lbs/sq in = 10 5 N/m PV = n R T = N k T P is the Absolute pressure Measured from Vacuum = 0 Gauge Pressure = Vacuum - Atmospheric Atmospheric = 14.7 lbs/sq in = 10 5 N/m V is the volume of the system in m 3 often the system

More information

Downloaded from

Downloaded from Chapter 13 (Kinetic Theory) Q1. A cubic vessel (with face horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of500 ms in vertical direction.

More information

Collisions between molecules

Collisions between molecules Collisions between molecules We model molecules as rigid spheres of radius r as shown at the right. The mean free path of a molecule is the average distance it travels between collisions. The average time

More information

Chapter 14. The Ideal Gas Law and Kinetic Theory

Chapter 14. The Ideal Gas Law and Kinetic Theory Chapter 14 The Ideal Gas Law and Kinetic Theory 14.1 Molecular Mass, the Mole, and Avogadro s Number The atomic number of an element is the # of protons in its nucleus. Isotopes of an element have different

More information

CHAPTER 21 THE KINETIC THEORY OF GASES-PART? Wen-Bin Jian ( 簡紋濱 ) Department of Electrophysics National Chiao Tung University

CHAPTER 21 THE KINETIC THEORY OF GASES-PART? Wen-Bin Jian ( 簡紋濱 ) Department of Electrophysics National Chiao Tung University CHAPTER 1 THE KINETIC THEORY OF GASES-PART? Wen-Bin Jian ( 簡紋濱 ) Department of Electrophysics National Chiao Tung University 1. Molecular Model of an Ideal Gas. Molar Specific Heat of an Ideal Gas. Adiabatic

More information

Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature

Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature Bởi: OpenStaxCollege We have developed macroscopic definitions of pressure and temperature. Pressure is the force divided by

More information

Chemical Thermodynamics : Georg Duesberg

Chemical Thermodynamics : Georg Duesberg The Properties of Gases Kinetic gas theory Maxwell Boltzman distribution, Collisions Real (non-ideal) gases fugacity, Joule Thomson effect Mixtures of gases Entropy, Chemical Potential Liquid Solutions

More information

Kinetic theory of the ideal gas

Kinetic theory of the ideal gas Appendix H Kinetic theory of the ideal gas This Appendix contains sketchy notes, summarizing the main results of elementary kinetic theory. The students who are not familiar with these topics should refer

More information

KINETIC THEORY OF GASES

KINETIC THEORY OF GASES KINETIC THEORY OF GASES Boyle s Law: At constant temperature volume of given mass of gas is inversely proportional to its pressure. Charle s Law: At constant pressure volume of a given mass of gas is directly

More information

Chapter 19 Entropy Pearson Education, Inc. Slide 20-1

Chapter 19 Entropy Pearson Education, Inc. Slide 20-1 Chapter 19 Entropy Slide 20-1 Ch 19 & 20 material What to focus on? Just put out some practice problems for Ch. 19/20 Ideal gas how to find P/V/T changes. How to calculate energy required for a given T

More information

Chapter 10. Thermal Physics. Thermodynamic Quantities: Volume V and Mass Density ρ Pressure P Temperature T: Zeroth Law of Thermodynamics

Chapter 10. Thermal Physics. Thermodynamic Quantities: Volume V and Mass Density ρ Pressure P Temperature T: Zeroth Law of Thermodynamics Chapter 10 Thermal Physics Thermodynamic Quantities: Volume V and Mass Density ρ Pressure P Temperature T: Zeroth Law of Thermodynamics Temperature Scales Thermal Expansion of Solids and Liquids Ideal

More information

Physics 231 Lecture 30. Main points of today s lecture: Ideal gas law:

Physics 231 Lecture 30. Main points of today s lecture: Ideal gas law: Physics 231 Lecture 30 Main points of today s lecture: Ideal gas law: PV = nrt = Nk BT 2 N 1 2 N 3 3 V 2 3 V 2 2 P = m v = KE ; KE KE = kbt Phases of Matter Slide 12-16 Ideal Gas: properties Approximate

More information

An ideal gas. Ideal gas equation.

An ideal gas. Ideal gas equation. S t r o n a 1 Autor: Ryszard Świda An ideal gas. Ideal gas equation. To facilitate the application of physical theories, various physicals models are created and used. A physical model is a hypothetical

More information

There are three phases of matter: Solid, liquid and gas

There are three phases of matter: Solid, liquid and gas FLUIDS: Gases and Liquids Chapter 4 of text There are three phases of matter: Solid, liquid and gas Solids: Have form, constituents ( atoms and molecules) are in fixed positions (though they can vibrate

More information

Chapter 14 Thermal Physics: A Microscopic View

Chapter 14 Thermal Physics: A Microscopic View Chapter 14 Thermal Physics: Microscopic View The main focus of this chapter is the application of some of the basic principles we learned earlier to thermal physics. This will give us some important insights

More information

The Kinetic Theory of Gases

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

More information

Chapter 12. Answers to examination-style questions. Answers Marks Examiner s tips

Chapter 12. Answers to examination-style questions. Answers Marks Examiner s tips (a) v esc = gr = (.6 740 0 3 ) ½ = 400 m s (370 m s to 3 sig figs) (b) (i) Mean kinetic energy = 3_ kt =.5.38 0 3 400 = 8.3 0 J (ii) Mass of an oxygen molecule m= molar mass/n A 0.03 = kg 6.0 0 3 Rearranging

More information

CHEM 101A EXAM 1 SOLUTIONS TO VERSION 1

CHEM 101A EXAM 1 SOLUTIONS TO VERSION 1 CHEM 101A EXAM 1 SOLUTIONS TO VERSION 1 Multiple-choice questions (3 points each): Write the letter of the best answer on the line beside the question. Give only one answer for each question. B 1) If 0.1

More information

Kinetic Theory. 84 minutes. 62 marks. theonlinephysicstutor.com. facebook.com/theonlinephysicstutor. Name: Class: Date: Time: Marks: Comments:

Kinetic Theory. 84 minutes. 62 marks. theonlinephysicstutor.com. facebook.com/theonlinephysicstutor. Name: Class: Date: Time: Marks: Comments: Kinetic Theory Name: Class: Date: Time: 84 minutes Marks: 62 marks Comments: Page 1 of 19 1 Which one of the following is not an assumption about the properties of particles in the simple kinetic theory?

More information

The Kinetic Theory of Gases

The Kinetic Theory of Gases PHYS102 Previous Exam Problems CHAPTER 19 The Kinetic Theory of Gases Ideal gas RMS speed Internal energy Isothermal process Isobaric process Isochoric process Adiabatic process General process 1. Figure

More information

CHEM1100 Summary Notes Module 2

CHEM1100 Summary Notes Module 2 CHEM1100 Summary Notes Module 2 Lecture 14 Introduction to Kinetic Theory & Ideal Gases What are Boyle s and Charles Laws? Boyle s Law the pressure of a given mass of an ideal gas is inversely proportional

More information

AP Chemistry Ch 5 Gases

AP Chemistry Ch 5 Gases AP Chemistry Ch 5 Gases Barometer - invented by Evangelista Torricelli in 1643; uses the height of a column of mercury to measure gas pressure (especially atmospheric) Manometer- a device for measuring

More information

Revision Guide for Chapter 13

Revision Guide for Chapter 13 Matter: very simple Revision Guide for Chapter Contents Student s Checklist Revision Notes Ideal gas... Ideal gas laws... Assumptions of kinetic theory of gases... 5 Internal energy... 6 Specific thermal

More information

CH301 Unit 1 GAS LAWS, KINETIC MOLECULAR THEORY, GAS MIXTURES

CH301 Unit 1 GAS LAWS, KINETIC MOLECULAR THEORY, GAS MIXTURES CH301 Unit 1 GAS LAWS, KINETIC MOLECULAR THEORY, GAS MIXTURES Goals for Our Second Review Your first exam is in about 1 week! Recap the ideal gas law Kinetic Molecular Theory 3 important relationships

More information

Physics 1501 Lecture 35

Physics 1501 Lecture 35 Physics 1501: Lecture 35 Todays Agenda Announcements Homework #11 (Dec. 2) and #12 (Dec. 9): 2 lowest dropped Honors students: see me after the class! Todays topics Chap.16: Temperature and Heat» Latent

More information

1 Points to Remember Subject: Chemistry Class: XI Chapter: States of matter Top concepts 1. Intermolecular forces are the forces of attraction and repulsion between interacting particles (atoms and molecules).

More information

Chapter 19 Entropy Pearson Education, Inc. Slide 20-1

Chapter 19 Entropy Pearson Education, Inc. Slide 20-1 Chapter 19 Entropy Slide 20-1 Ch 19 & 20 material What to focus on? Just put out some practice problems Ideal gas how to find P/V/T changes. E.g., gas scaling, intro to the ideal gas law, pressure cooker,

More information

Chapter 11. Molecular Composition of Gases

Chapter 11. Molecular Composition of Gases Chapter 11 Molecular Composition of Gases PART 1 Volume-Mass Relationships of Gases Avogadro s Law Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Recall

More information

For more info visit

For more info visit Kinetic Theory of Matter:- (a) Solids:- It is the type of matter which has got fixed shape and volume. The force of attraction between any two molecules of a solid is very large. (b) Liquids:- It is the

More information

Kinetic Theory of Aether Particles

Kinetic Theory of Aether Particles Chapter 2 Kinetic Theory of Aether Particles 2.1 Basic Concepts and Assumptions This chapter will derive energy density and pressure from particles collision on a surface based on kinetic theory. Kinetic

More information

Atoms, electrons and Solids

Atoms, electrons and Solids Atoms, electrons and Solids Shell model of an atom negative electron orbiting a positive nucleus QM tells that to minimize total energy the electrons fill up shells. Each orbit in a shell has a specific

More information

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

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

More information

Chapter 13: Temperature, Kinetic Theory and Gas Laws

Chapter 13: Temperature, Kinetic Theory and Gas Laws Chapter 1: Temperature, Kinetic Theory and Gas Laws Zeroth Law of Thermodynamics (law of equilibrium): If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in

More information

MP203 Statistical and Thermal Physics. Jon-Ivar Skullerud and James Smith

MP203 Statistical and Thermal Physics. Jon-Ivar Skullerud and James Smith MP203 Statistical and Thermal Physics Jon-Ivar Skullerud and James Smith October 3, 2017 1 Contents 1 Introduction 3 1.1 Temperature and thermal equilibrium.................... 4 1.1.1 The zeroth law of

More information

Unit 05 Kinetic Theory of Gases

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:

More information

The Kinetic-Molecular Theory of Gases

The Kinetic-Molecular Theory of Gases The Kinetic-Molecular Theory of Gases kinetic-molecular theory of gases Originated with Ludwig Boltzman and James Clerk Maxwell in the 19th century Explains gas behavior on the basis of the motion of individual

More information

Lecture Presentation. Chapter 10. Gases. James F. Kirby Quinnipiac University Hamden, CT Pearson Education

Lecture Presentation. Chapter 10. Gases. James F. Kirby Quinnipiac University Hamden, CT Pearson Education Lecture Presentation Chapter 10 2015 Pearson Education James F. Kirby Quinnipiac University Hamden, CT Characteristics of Physical properties of gases are all similar. Composed mainly of nonmetallic elements

More information

Gases: Their Properties & Behavior. Chapter 09 Slide 1

Gases: Their Properties & Behavior. Chapter 09 Slide 1 9 Gases: Their Properties & Behavior Chapter 09 Slide 1 Gas Pressure 01 Chapter 09 Slide 2 Gas Pressure 02 Units of pressure: atmosphere (atm) Pa (N/m 2, 101,325 Pa = 1 atm) Torr (760 Torr = 1 atm) bar

More information

Chapter 10 Notes: Gases

Chapter 10 Notes: Gases Chapter 10 Notes: Gases Watch Bozeman Videos & other videos on my website for additional help: Big Idea 2: Gases 10.1 Characteristics of Gases Read p. 398-401. Answer the Study Guide questions 1. Earth

More information

CHEMISTRY XL-14A GASES. August 6, 2011 Robert Iafe

CHEMISTRY XL-14A GASES. August 6, 2011 Robert Iafe CHEMISTRY XL-14A GASES August 6, 2011 Robert Iafe Chemistry in the News 2 Polymer nicotine trap is composed of a porphyrin derivative (black), in which amide pincers (green) are attached to the zinc (violet)

More information

Why study gases? A Gas 10/17/2017. An understanding of real world phenomena. An understanding of how science works.

Why study gases? A Gas 10/17/2017. An understanding of real world phenomena. An understanding of how science works. Kinetic Theory and the Behavior of Ideal & Real Gases Why study gases? n understanding of real world phenomena. n understanding of how science works. Gas Uniformly fills any container. Mixes completely

More information

A Gas Uniformly fills any container. Easily compressed. Mixes completely with any other gas. Exerts pressure on its surroundings.

A Gas Uniformly fills any container. Easily compressed. Mixes completely with any other gas. Exerts pressure on its surroundings. Chapter 5 Gases Chapter 5 A Gas Uniformly fills any container. Easily compressed. Mixes completely with any other gas. Exerts pressure on its surroundings. Copyright Cengage Learning. All rights reserved

More information

10/15/2015. Why study gases? An understanding of real world phenomena. An understanding of how science works.

10/15/2015. Why study gases? An understanding of real world phenomena. An understanding of how science works. 0/5/05 Kinetic Theory and the Behavior of Ideal & Real Gases Why study gases? An understanding of real world phenomena. An understanding of how science works. 0/5/05 A Gas fills any container. completely

More information

Understanding KMT using Gas Properties and States of Matter

Understanding KMT using Gas Properties and States of Matter Understanding KMT using Gas Properties and States of Matter Learning Goals: Students will be able to describe matter in terms of particle motion. The description should include Diagrams to support the

More information

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)

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

More information

C H E M 1 CHEM 101-GENERAL CHEMISTRY CHAPTER 5 GASES INSTR : FİLİZ ALSHANABLEH

C H E M 1 CHEM 101-GENERAL CHEMISTRY CHAPTER 5 GASES INSTR : FİLİZ ALSHANABLEH C H E M 1 CHEM 101-GENERAL CHEMISTRY CHAPTER 5 GASES 0 1 INSTR : FİLİZ ALSHANABLEH CHAPTER 5 GASES Properties of Gases Pressure History and Application of the Gas Laws Partial Pressure Stoichiometry of

More information

Section A Q1 Which of the following least resembles an ideal gas? A ammonia B helium C hydrogen D trichloromethane

Section A Q1 Which of the following least resembles an ideal gas? A ammonia B helium C hydrogen D trichloromethane Section A Q1 Which of the following least resembles an ideal gas? A ammonia B helium C hydrogen D trichloromethane Q2 The density of ice is 1.00 g cm 3. What is the volume of steam produced when 1.00 cm3

More information

Thermodynamics: Microscopic vs. Macroscopic (Chapters 16, )

Thermodynamics: Microscopic vs. Macroscopic (Chapters 16, ) Thermodynamics: Microscopic vs. Macroscopic (Chapters 16, 18.1-5 ) Matter and Thermal Physics Thermodynamic quantities: Volume V and amount of substance Pressure P Temperature T: Ideal gas Zeroth Law of

More information

Pressure. Pressure Units. Molecular Speed and Energy. Molecular Speed and Energy

Pressure. Pressure Units. Molecular Speed and Energy. Molecular Speed and Energy Pressure is defined as force per unit area. Pressure Pressure is measured with a device called a barometer. A mercury barometer uses the weight of a column of Hg to determine the pressure of gas pushing

More information

Kinetic Model of Gases

Kinetic Model of Gases Kinetic Model of Gases Section 1.3 of Atkins, 6th Ed, 24.1 of Atkins, 7th Ed. 21.1 of Atkins, 8th Ed., and 20.1 of Atkins, 9th Ed. Basic Assumptions Molecular Speeds RMS Speed Maxwell Distribution of Speeds

More information

Gases. Characteristics of Gases. Unlike liquids and solids, gases

Gases. Characteristics of Gases. Unlike liquids and solids, gases Gases Characteristics of Gases Unlike liquids and solids, gases expand to fill their containers; are highly compressible; have extremely low densities. 1 Pressure Pressure is the amount of force applied

More information

Videos 1. Crash course Partial pressures: YuWy6fYEaX9mQQ8oGr 2. Crash couse Effusion/Diffusion:

Videos 1. Crash course Partial pressures:   YuWy6fYEaX9mQQ8oGr 2. Crash couse Effusion/Diffusion: Videos 1. Crash course Partial pressures: https://youtu.be/jbqtqcunyza?list=pl8dpuualjxtphzz YuWy6fYEaX9mQQ8oGr 2. Crash couse Effusion/Diffusion: https://youtu.be/tlrzafu_9kg?list=pl8dpuualjxtph zzyuwy6fyeax9mqq8ogr

More information

Calculations In Chemistry * * * * * Module 19 Kinetic Molecular Theory

Calculations In Chemistry * * * * * Module 19 Kinetic Molecular Theory Calculations In Chemistry Module 19 Kinetic Molecular Theory Module 19 Kinetic Molecular Theory...487 Lesson 19A: Squares and Square Roots... 487 Lesson 19B: Kinetic Molecular Theory... 495 Lesson 19C:

More information