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Thermal Physics AP Physics B Lecture Notes x z

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Thermal Physics Temperature and the zeroth Law of Thermodynamics Thermometers and Temperature Scales Thermal Expansion of Solids and Liquids Microscopic Description of an Ideal Gas Topics The Kinetic Theory of Gases

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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. AB C Then A and B are in thermal equilibrium. If A is in thermal equilibrium with C and B is in thermal equilibrium with C The Zeroth Law of Thermodynamics

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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.

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

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Thermal Physics 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.

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CelsiusFahrenheitKelvin Boiling Point (H 2 O) Melting Point (H 2 O) Absolute Zero Temperature is generally measured using either the Kelvin, Celsius, or the Fahrenheit scale. Thermometers and Temperature Scales

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

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

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Thermal Physics 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 the plate's surface area. (C) always contract. (D) always expand.

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LoLo LL L L o T TT L = L o T L = L o (1+ T) Coefficient of linear expansion L L o = L o T Thermal Expansion of Solids and Liquids

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

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

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New Volume Initial Volume LoLo LoLo LoLo L o + L Volume Expansion L = L o T Thermal Expansion of Solids and Liquids

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Coefficient of Volume Expansion Thermal Expansion of Solids and Liquids

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

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PV = nRT Pressure (Pa) Volume (m 3 ) Absolute Temperature (K) Gas Constant (8.31 J/mol K) (L. atm)/(mol. K) 1.99 cal/(mol. K) Gas Quantity (mol) Microscopic Description of an Ideal Gas

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Thermal Physics ~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 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.

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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 H 2 has a mass of 2 g 1 mol Ne has a mass of 20 g 1 mol CO 2 has a mass of 44 g The number of moles in a certain number of particles: The number of moles in a certain mass of material: Microscopic Description of an Ideal Gas

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PV = NkT Pressure (Pa) Volume (m 3 ) Absolute Temperature (K) Boltzmann’s Constant (1.38 x J/K) Number of Molecules Microscopic Description of an Ideal Gas

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

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A gas is contained in an 8.0 x 10 3 m 3 vessel at 20 o C and a pressure of 9.0 x 10 5 N/m 2. (a) Determine the number of moles of gas in the vessel. Microscopic Description of an Ideal Gas (Problem)

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A gas is contained in an 8.0 x 10 3 m 3 vessel at 20 oC and a pressure of 9.0 x 10 5 N/m 2. (b) How many molecules are in the vessel? Microscopic Description of an Ideal Gas (Problem (con’t))

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Thermal Physics 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

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A cylinder with a moveable piston contains gas at a temperature of 27 o C, a volume of 1.5 m 3, and an absolute pressure of 0.20 x 10 5 Pa. 1.5 m 3 27 o C 0.20 x 10 5 Pa 0.70 m x 10 5 Pa Microscopic Description of an Ideal Gas

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What will be its final temperature if the gas is compressed to 0.70 m 3 and the absolute pressure increases to 0.80 x 10 5 Pa? 1.5 m 3 27 o C 0.20 x 10 5 Pa 0.70 m x 10 5 Pa Microscopic Description of an Ideal Gas (Problem)

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

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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

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

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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

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

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Thermal Physics 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.

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

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Thermal Physics 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

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

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Calculate the rms speed of a Nitrogen molecule (N 2 ) when the temperature is 100 o C. Mass of N 2 molecule: rms speed: The Kinetic Theory of Gases (Problem)

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If 2.0 mol of an ideal gas are confined to a 5.0 L vessel at a pressure of 8.0 x 10 5 Pa, what is the average kinetic energy of a gas molecule? Temperature of the gas: Kinetic energy: The Kinetic Theory of Gases (Problem)

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Thermal Physics 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

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Mean and rms Speed Mean Speed: rms Speed: The Kinetic Theory of Gases

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Thermal Physics 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

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Thermal Physics 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

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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.

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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: Summary

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