Thermal Physics x z AP Physics B Lecture Notes

Thermal Physics Topics 10-01 Temperature and the zeroth Law of Thermodynamics 10-02 Thermometers and Temperature Scales 10-03 Thermal Expansion of Solids and Liquids 10-04 Microscopic Description of an Ideal Gas 10-05 The Kinetic Theory of Gases

A B C Temperature and the zeroth Law of Thermodynamics Two objects placed in thermal contact will eventually come to the same temperature. When they do, we say they are in thermal equilibrium. The Zeroth Law of Thermodynamics A B C If A is in thermal equilibrium with C and B is in thermal equilibrium with C Then A and B are in thermal equilibrium.

Thermometers and Temperature Scales Temperature is a measure of how hot or cold something is. Thermometers are instruments designed to measure temperature. In order to do this, they take advantage of some property of matter that changes with temperature. Most materials expand when heated.

Thermometers and Temperature Scales Common thermometers used today include the liquid-in-glass type and the bimetallic strip.

Thermal Physics 10-01 A bimetallic strip, consisting of metal G on the top and metal H on the bottom, is rigidly attached to a wall at the left as shown. In the diagram. The coefficient of linear thermal expansion for metal G is greater than that of metal H. If the strip is uniformly heated, it will (A) curve upward. (B) curve downward. (C) remain horizontal, but get longer. (D) bend in the middle.

Thermometers and Temperature Scales Temperature is generally measured using either the Kelvin, Celsius, or the Fahrenheit scale. Celsius Fahrenheit Kelvin Boiling Point (H2O) 373 100 212 Melting Point (H2O) 273 32 Absolute Zero -273 -459

Thermal Expansion of Solids and Liquids Expansion occurs when an object is heated. A steel washer is heated Does the hole increase or decrease in size?

Thermal Expansion of Solids and Liquids When the washer is heated The hole becomes larger

Thermal Physics 10-02 Consider a flat steel plate with a hole through its center as shown in the diagram. When the plate's temperature is increased, the hole will (A) expand only if it takes up more than half the plate's surface area. (B) contract if it takes up less than half (C) always contract. (D) always expand.

Thermal Expansion of Solids and Liquids Lo DL  LoDT DT DL = aLoDT L - Lo = aLoDT Coefficient of linear expansion L = Lo(1+aDT)

Thermal Expansion of Solids and Liquids (Problem) sleeve shaft D d A cylindrical brass sleeve is to be shrunk-fitted over a brass shaft whose diameter is 3.212 cm at 0 oC. The diameter of the sleeve is 3.196 cm at 0 oC. To what temperature must the sleeve be heated before it will slip over the shaft?

Thermal Expansion of Solids and Liquids (Problem) shaft sleeve D d To what temperature must the sleeve be heated before it will slip over the shaft?

Thermal Expansion of Solids and Liquids Volume Expansion Lo + DL Lo New Volume Initial Volume DL = aLoDT

Thermal Expansion of Solids and Liquids Coefficient of Volume Expansion

Thermal Expansion of Solids and Liquids (Problem) An automobile fuel tank is filled to the brim with 45 L of gasoline at 10 oC. Immediately afterward, the vehicle is parked in the Sun, where the temperature is 35 oC. How much gasoline overflows from the tank as a result of expansion? Change in volume of the steel gas tank Overflow Change in volume of the gasoline

Microscopic Description of an Ideal Gas Volume (m3) Pressure (Pa) Absolute Temperature (K) PV = nRT Gas Quantity (mol) Gas Constant (8.31 J/molK) 0.0821 (L.atm)/(mol.K) 1.99 cal/(mol.K)

Thermal Physics 10-03 Both the pressure and volume of a given sample of an ideal gas double. This means that its temperature in Kelvin must (A) double. (B) quadruple. (C) reduce to one-fourth its original value. (D) remain unchanged. ~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10 ~M9 ~M11 ~M12 ~M13 ~M14 ~M15 ~M16 ~M17 ~M18 ~M20 ~M19 ~M21 ~M22 ~M23 ~M24 ~M25 ~M26 ~M27 ~M28 ~M30 ~M29 ~M31 ~M32 ~M33 ~M34 ~M35 ~M36 ~M37 ~M38 ~M40 ~M39 ~M41 ~M42 ~M43 ~M44 ~M45 ~M46 ~M47 ~M48 ~M50 ~M49 ~M51 ~M52 ~M53 ~M54 ~M55 ~M56 ~M57 ~M58 ~M60 ~M59

Microscopic Description of an Ideal Gas A mole (mol) is defined as the number of grams of a substance that is numerically equal to the molecular mass of the substance: 1 mol H2 has a mass of 2 g 1 mol Ne has a mass of 20 g 1 mol CO2 has a mass of 44 g The number of moles in a certain mass of material: The number of moles in a certain number of particles:

Microscopic Description of an Ideal Gas Volume (m3) Pressure (Pa) PV = NkT Absolute Temperature (K) Number of Molecules Boltzmann’s Constant (1.38 x 10-23 J/K)

Microscopic Description of an Ideal Gas Boltzmann’s Constant Gas Constant Avogadro’s Number

Microscopic Description of an Ideal Gas (Problem) A gas is contained in an 8.0 x 10-3 m3 vessel at 20 oC and a pressure of 9.0 x 105 N/m2. (a) Determine the number of moles of gas in the vessel.

Microscopic Description of an Ideal Gas (Problem (con’t)) A gas is contained in an 8.0 x 10-3 m3 vessel at 20 oC and a pressure of 9.0 x 105 N/m2. (b) How many molecules are in the vessel?

Thermal Physics 10-04 A container of an ideal gas at 1 atm is compressed to one-third its volume, with the temperature held constant. What is its final pressure? (A) 1/3 atm (B) 1 atm (C) 3 atm (D) 9 atm

Microscopic Description of an Ideal Gas 0.20 x 105 Pa 0.80 x 105 Pa A cylinder with a moveable piston contains gas at a temperature of 27 oC, a volume of 1.5 m3, and an absolute pressure of 0.20 x 105 Pa. 1.5 m3 27 oC 0.70 m3

Microscopic Description of an Ideal Gas (Problem) 0.20 x 105 Pa 0.80 x 105 Pa What will be its final temperature if the gas is compressed to 0.70 m3 and the absolute pressure increases to 0.80 x 105 Pa? 1.5 m3 27 oC 0.70 m3

The Kinetic Theory of Gases Assumptions of kinetic theory: 1) large number of molecules, moving in random directions with a variety of speeds 2) molecules are far apart, on average 3) molecules obey laws of classical mechanics and interact only when colliding 4) collisions are perfectly elastic

The Kinetic Theory of Gases x y z v L A The force exerted on the wall by the collision of one molecule of mass m is Then the average force due to N molecules colliding with that wall is

The Kinetic Theory of Gases x y z v L A The averages of the squares of the speeds in all three directions are equal: So the pressure on the wall is:

The Kinetic Theory of Gases Rewriting, so The average translational kinetic energy of the molecules in an ideal gas is directly proportional to the temperature of the gas.

The Kinetic Theory of Gases Molecular Kinetic Energy Temperature is a measure of the average molecular kinetic energy.

Thermal Physics 10-05 According to the ideal gas Law, PV = constant for a given temperature. As a result, an increase in volume corresponds to a decrease in pressure. This happens because the molecules (A) collide with each other more frequently. (B) move slower on the average. (C) strike the container wall less often. (D) transfer less energy to the walls of the container each time they strike it.

Thermal Physics 10-06 The absolute temperature of an ideal gas is directly proportional to which of the following? (A) speed (B) momentum (C) kinetic energy (D) mass

Thermal Physics 10-07 Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, the average molecular kinetic energy of oxygen, compared to hydrogen (A) is greater. (B) is less. (C) is the same. (D) cannot be determined since pressure and volume are not given

The Kinetic Theory of Gases (Problem) What is the total random kinetic energy of all the molecules in one mole of hydrogen at a temperature of 300 K. Kinetic energy per molecule Avogadro’s number

The Kinetic Theory of Gases (Problem) Calculate the rms speed of a Nitrogen molecule (N2) when the temperature is 100 oC. Mass of N2 molecule: rms speed:

The Kinetic Theory of Gases (Problem) If 2.0 mol of an ideal gas are confined to a 5.0 L vessel at a pressure of 8.0 x 105 Pa, what is the average kinetic energy of a gas molecule? Temperature of the gas: Kinetic energy:

Thermal Physics 10-08 A container holds N molecules of an ideal gas at a given temperature. If the number of molecules in the container is increased to 2N with no change in temperature or volume, the pressure in the container (A) doubles. (B) remains constant. (C) is cut in half. (D) none of the above

The Kinetic Theory of Gases 5 2 3 6 1 4 Mean and rms Speed Mean Speed: rms Speed:

Thermal Physics 10-09 A sample of an ideal gas is slowly compressed to one-half its original volume with no change in temperature. What happens to the average speed of the molecules in the sample? (A) It does not change. (B) It doubles. (C) It halves. (D) none of the above

Thermal Physics 10-10 A mole of diatomic oxygen molecules and a mole of diatomic nitrogen molecules at STP have (A) the same average molecular speeds. (B) the same number of molecules. (C) the same diffusion rates. (D) all of the above

Summary Temperature is a measure of how hot or cold something is, and is measured by thermometers. There are three temperature scales in use: Celsius, Fahrenheit, and Kelvin. When heated, a solid will get longer by a fraction given by the coefficient of linear expansion. The fractional change in volume of gases, liquids, and solids is given by the coefficient of volume expansion.

Summary Ideal gas law: One mole of a substance is the number of grams equal to the atomic or molecular mass. Each mole contains Avogadro’s number of atoms or molecules. The average kinetic energy of molecules in a gas is proportional to the temperature:

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