Physics 161 Lecture 14 Kinetic Theory of Gas. October 18, 2018

Transcription

1 Physics 161 Lecture 14 Kinetic Theory of Gas October 18,

2 Exam 1, Thursday 18 Oct The exam will start promptly at 10:00pm. You will be permitted to open your exam at 10:00pm. You will have until 11:20pm to complete your exam. You must arrive five minutes early to find the exam that has your name (by section and alphabetic within section). DO NOT USE SOMEONE ELSES EXAM. The exam in some official lists may show to start at 9:40pm, because that is when we have been assigned the room. You will not be allowed to enter at that time, because we have to set up the room. Remember: no phones, no bags. If you are found with a phone during the exam, you will automatically receive a grade of 0% for the exam. 2

3 Exam-1 Topics (1) 1. Kinematic equations for constant acceleration: - one dimension - two dimensions - projectile motion 2. Newton s second law + third law 3. Friction and the normal force: - static friction - kinetic friction 4. Collisions - elastic - inelastic - perfectly inelastic 3

4 Exam-1 Topics (2) 5. Uniform circular motion - angular variables - angular-linear relations 6. Conservation of energy - kinetic energy - spring potential energy - gravitational potential energy - work done 7. Conservation of momentum - Collisions, elastic, inelastic, perfectly inelastic - impulse 4

5 Lecture 14: learning objectives Review from lecture 13 - Temperature, scales and how to measure. - Heat, internal energy, atomic/molecular picture. - Thermal expansion, specific heat, phase change. This lecture 14 We will state the properties of an ideal gas and apply the ideal gas law. A miracle that it works for all gases What are the assumptions of the kinetic theory of gases. We will relate the pressure and temperature to the average kinetic energy of atoms/molecules and define the internal energy of a gas. Sep. 1,

6 Back to Problem: gram of steam at 100 C is added to 50 gram of ice at 0 C. a)find the amount of ice melted and the final temperature. b)repeat with steam of mass 1.0 g and ice of mass 50 g. 6 Sep. 1, 2015

7 Problem: Condense 10 gram steam at 100 o C produces 22,600 J Melting 50 gram of ice at 0 o C requires 16,500 J. We end up with 50 gram of 0 o C water + 10 gram of 100 o C water + (22,600 16,500) J CONCLUSION: Final state will be 60 gram of water of final temperature T f. Heat required = Heat produced 16,000 + c w (T f 0) = c w (100 T f ) + 22,600 7 Sep. 1, 2015

8 iclicker question: temperature What describes temperature best? -a) Energy transferred from one object to another. NO -b) Heat transferred from one object to another. NO -c) Work done by one object on another. NO +d) Measure of kinetic energy of atoms/molecules. YES? +e) Can you feel the temperature by touching (hot or cold). YES? 8 9/29/1 5

9 iclicker question: feel surfaces Which surface has the greater temperature? a) The metal surface. b) The plastic surface. c) The surfaces are at the same temperature. 9 9/29/1 5

10 iclicker question: ice melting On which surface will the ice melt first? a) The metal surface. b) The plastic surface. c) The ice will melt equally fast on both. 10 9/29/1 5

11 What are Ideal gases Ideal gas: System containing a (very) large number of widelyseparated point particles that interact only through perfectly elastic collisions. NO FRICTION, NO INELASTIC COLLISIONS Most real gases closely approximate an ideal gas 11

12 Avogadro s number, N A Avogadro s number: The number of particles in one mole of a substance. Avogadro s number is given by N A = 6.02 x particles/mole Mole: One mole of any substance is that amount of the substance that contains as many particles (atoms, molecules) as there are atoms in 12 g of the isotope Carbon-12. What is the mass of one mole of He-4? 12

13 Ideal gas law (1) Ideal gas law: The product of the pressure P and volume V of an ideal gas is proportional to the number of moles n of gas times the Kelvin temperature T of the gas. Here R is the ideal gas constant, R = 8.31 J/ (mol.k) and n is the number of moles of gas. The Ideal gas law is an Equation of state that relates the pressure, volume and temperature of the gas. This follows from 3 experimental observations: - (1) gas pressure P is inversely proportional to volume V at fixed temperature (Boyle s law) - (2) volume V of the gas is proportional to the Kelvin temperature T at fixed pressure (Charles law) - (3) gas pressure P is directly proportional to the Kelvin 13 temperature T at fixed volume (Gay-Lussac s law)

14 Ideal gas law (2) Ideal gas law: The product of the pressure P and volume V of an ideal gas is proportional to the number of molecules N of gas times the Kelvin temperature T of the gas. Here R is the ideal gas constant, R = 8.31 J/ (mol.k) and n is the number of moles of gas. Here k B is Boltzmann s constant, k B = R/N A = 1.38 x J/ K and N = n x N A is the number of molecules in the gas. The temperature T must be measured in Kelvin! 14

15 Problem: Gas is confined in a tank at a pressure of 11.0 atm and a temperature of 25.0 C. If two-thirds of the gas is withdrawn and the temperature is raised to 75.0 C, what is the new pressure of the gas remaining in the tank? 15

16 Kinetic theory of gases The kinetic theory of gases is based on the following assumptions: 1. Number of molecules is large. 2. Molecules are separated by an average distance much larger than the molecular size. Molecules are treated as point particles. 3. Molecules obey Newton s laws of motion individually. 4. Molecules interact with each other only via shortrange forces during elastic collisions. 5. Molecules collide elastically with the container walls. 6. Molecules are all identical. 16

17 Pressure P and kinetic theory of gases MICROSCOPIC PICTURE: Pressure P of gas is caused by gas atoms knocking on the container wall Pressure in kinetic theory of gases: The pressure of an ideal gas is proportional to the number of molecules per unit volume, N/V, and to the average translational kinetic energy of a molecule. p

18 Temperature in the kinetic theory of gases Temperature (in microscopic picture): The temperature of an ideal gas is a direct measure of the average molecular kinetic energy of the gas. p. 340 The total kinetic energy of N molecules is p

19 Internal energy in the kinetic theory of gases Internal energy U in the kinetic theory of gases: The internal energy of a monatomic gas is given by the total kinetic energy of the molecules. p

20 iclicker WHAT ARE THE UNITS OF PV a) Pa x m 3 b) N x m c) Joule d) All of the above 20

21 Root-mean-square speed Root-mean-square speed: The square root of the average of the speed-squared of each molecule. p. 341 Here M is the molar mass in kilograms per mole. 21

22 Problem: Two gases in a mixture pass through a filter at rates proportional to the gases rms speeds. Find a) The ratio of speeds for the two isotopes of chlorine, 35 Cl and 37 Cl, as they pass through the filter. b) Which isotope moves faster? 22 9/29/1 5