PHY 2048C General Physics I with lab Spring 2011 CRNs 11154, & Dr. Derrick Boucher Assoc. Prof. of Physics Session 24, Chapter 18

Chapter 17 Homework Due Wednesday midnight (was Tues 4/12) Chapter 18 Homework Due Sunday midnight Chapter 17 Homework Due Wednesday midnight (was Tues 4/12) Chapter 18 Homework Due Sunday midnight Chapter 19 (LAST HOMEWORK) Due Wed midnight

Chapter 18 Practice Problems 1, 5, 13, 19, 21, 25, 31, 39, 41 Unless otherwise indicated, all practice material is from the “Exercises and Problems” section at the end of the chapter. (Not “Questions.”)

Chapter 17. Quiz Get your clickers ready

What quantities appear in the first law of thermodynamics? A. force, mass, acceleration B. inertia, torque, angular momentum C. work, heat, thermal energy D. work, heat, entropy E. enthalpy, entropy, heat

What was the original unit for measuring heat? A. BTU B. Watt C. Joule D. Pascal E. Calorie

What is the name of an ideal-gas process in which no heat is transferred? A. Isochoric B. Isentropic C. Isothermal D. Isobaric E. Adiabatic

Heat is A. the amount of thermal energy in an object. B. the energy that moves from a hotter object to a colder object. C. a fluid-like substance that flows from a hotter object to a colder object. D. both A and B. E. both B and C.

The thermal behavior of water is characterized by the value of its A. heat density. B. heat constant. C. specific heat. D. thermal index.

Chapter 18. The Micro/Macro Connection Heating the air in a hot-air balloon increases the thermal energy of the air molecules. This causes the gas to expand, lowering its density and allowing the balloon to float in the cooler surrounding air. Chapter Goal: To understand the properties of a macroscopic system in terms of the microscopic behavior of its molecules.

Topics: Molecular Speeds and Collisions Pressure in a Gas Temperature Thermal Energy and Specific Heat Thermal Interactions and Heat Irreversible Processes and the Second Law of Thermodynamics Chapter 18. The Micro/Macro Connection

Molecular Speeds and Collisions

Mean Free Path If a molecule has N coll collisions as it travels distance L, the average distance between collisions, which is called the mean free path λ (lowercase Greek lambda), is

EXAMPLE 18.1 The mean free path at room temperature QUESTION:

EXAMPLE 18.1 The mean free path at room temperature

Pressure in a Gas The pressure on the wall of a container due to all the molecular collisions is This expresses the macroscopic pressure in terms of the microscopic physics. The pressure depends on the density of molecules in the container and on how fast, on average, the molecules are moving.

Anticipating the ideal gas law It seems like T is related, proportional to, mv 2

Temperature in a Gas The thing we call temperature measures the average translational kinetic energy of molecules in a gas. A higher temperature corresponds to a larger value of є avg and thus to higher molecular speeds. Absolute zero is the temperature at which є avg and all molecular motion ceases. By definition, є avg = ½mv rms 2, where v rms is the root mean squared molecular speed. Using the ideal-gas law, we found є avg = 3/2 k B T. By equating these expressions we find that the rms speed of molecules in a gas is

Monatomic and Diatomic Gases The thermal energy of a monatomic gas of N atoms is A diatomic gas has more thermal energy than a monatomic gas at the same temperature because the molecules have rotational as well as translational kinetic energy.

Degrees of Freedom Molecules can have kinetic energy in many ways Each way is called a “degree of freedom” The more DOF, the more energy a gas of such molecules can absorb for a given T change (specific heat)

Degrees of Freedom

Classical physics cannot explain this graph Quantum mechanics (c. 1920s) explains this in terms of the minimum energy needed to increase rotation or vibration Essentially, you can’t add arbitrarily small amounts of energy to systems, only minimum sized chunks called “quanta”

Thermal Interactions and Heat Consider a rigid, insulated container divided into two sections by a very thin, stiff membrane. The left side, which we’ll call system 1, has N 1 atoms at an initial temperature T 1i. System 2 on the right has N 2 atoms at an initial temperature T 2i. The membrane is so thin that atoms can collide at the boundary as if the membrane were not there, yet it is a barrier that prevents atoms from moving from one side to the other. System 1 and system 2 begin with thermal energies

Thermal Interactions and Heat

The condition for thermal equilibrium is that the average translational kinetic energies of the atoms in both systems are equal. Because the average energies are directly proportional to the final temperatures, thermal equilibrium is characterized by the macroscopic condition as follows: Thermal Interactions and Heat The final thermal energies of the two systems are

Order, Disorder, and Entropy Scientists and engineers use a state variable called entropy to measure the probability that a macroscopic state will occur spontaneously. It is often said that entropy measures the amount of disorder in a system.

The Second Law of Thermodynamics Establishing the “arrow of time” is one of the most profound implications of the second law of thermodynamics.

Simulation: The finite gas and the repetition of history Key ideas here: Arrow of Time, Boltzmann’s paradox How can reversible atomic collisions lead to irreversible macroscopic phenomena? Also see the text, section (No, really, it’s GOOD!)

2 nd Law Implications #1 : Our sense of “normal” is based on probability We know when we are viewing a video backwards…but how? We have a sense of the “way things work” but that is really how they are likely to work. E.g. We know that a hot drink cooling down on a cold countertop will NEVER spontaneously heat up again. But actually, it is only VERY VERY UNLIKELY to heat up again…so unlikely that nobody will ever see it during several lifetimes of the universe.

Simulation: A bouncing “ball” Key ideas here: A rubber ball will never bounce as high as the dropping point…why? The initial mechanical energy (all piled up in one type of energy) is finally dissipated into the vibrations of all the ball’s degrees of freedom…NEVER to return to a useful energy form again. Q: will the ball ever bounce up again, if all the parts vibrate in JUST the right way to push against the floor?

2 nd Law Implications #2 : Useful energy is never as much as the total energy In any system, energy that is initially potential or kinetic tends to get turned into thermal energy which is less useful for systems that USE energy: Motors Machines Living organisms Stars Etc., etc., etc. There is always some energy wasted as heat transferred somewhere.

Chapter 18. Summary Slides

General Principles

Important Concepts

Applications