Physics 231 Lecture 29 Some slides relevant to Wed. Lecture. The notes for the lecture given by Dr. Nagy can be found at

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1 Physics 231 Lecture 29 Some slides relevant to Wed. Lecture. he notes for the lecture given by Dr. Nagy can be found at Main points : emperature and thermometers hermal expansion ΔL αδl; ΔA γa Δ; ΔV βvδ Ideal gas Law: PV nr Nk B

Heating something increases its thermal energy Every body of matter (solid, liquid or gas) consists of atoms in rapid motion Heating increases the random motion of these particles.

2 Heating something increases its thermal energy Every body of matter (solid, liquid or gas) consists of atoms in rapid motion Heating increases the random motion of these particles. his additional random motion adds to the thermal energy part of the kinetic and potential energies of the individual molecules/atoms making up the matter Solids Individual particles locked in place/connected to neighbors via spring like bonds Vibrate about equilibrium position (kinetic + potential energy) emperature is the observable quantity associated with thermal motion

Zeroth Law of hermodynamics If objects A and B are in thermal equilibrium with a third object, C, then A and B are in thermal equilibrium with each other.

3 Zeroth Law of hermodynamics If objects A and B are in thermal equilibrium with a third object, C, then A and B are in thermal equilibrium with each other. his will mean that these objects are at the same temperature, an abstract concept that we will now make more concrete with examples of thermometers that change their properties with temperature.

4 Different emperature Scales hree different temperature scales are commonly in use: Fahrenheit Celsius Kelvin Celsius define such that the freezing point of water is at a temperature of about o C and boiling temperature is at about 1 o C. he conversions from Celcius to Farenheit and to Kelvin are as follows: F K 9 5 C C At K, molecules in gas are nearly at rest and many material have unusual properties. What is this temperature in Fahrenheit? a) F b) -273 F c) 46 F d) -923 F C K C F 9 5 C ( ) F

hermometers While we know what is hot or cold. Much of what we think is simply perception: Wind makes day feel colder because moving air strips away the insulating layer of warm air next to our skin.

5 hermometers While we know what is hot or cold. Much of what we think is simply perception: Wind makes day feel colder because moving air strips away the insulating layer of warm air next to our skin. Cold metal feels colder than equally cold wood. Humid winter days feel colder than dry winter days. How do we construct a reliable thermometer? Need a quantity that has a unique dependence on temperature. Example the length of a column of mercury in a thermometer grows linearly with temperature. Δ L αl Δ Many solids and liquids expand linearly with : Example: A aluminum rod which is 1. m long at C. What is its length at 1 C? (α Al 23x1-6 / C) a).9989 m L αl 23x1 6 / o C 1.m 1 o C b) 1.11 m Δ L.23m c) 1.23 m L L +ΔL 1.23m d) 1.45 m Δ Δ ( )( )( )

6 emperature and hermal Expansion Slide 12-42

7 y Area and Volume expansion he areas and volumes of many objects also expand with temperature. Example: Calculation of the area expansion coefficient! for a rectangular aluminum plate. xy x + Δx y + Δy ; Δx αx Δ; Δy αy x A f ( )( ) Δ ( x + αx Δ )( y + αy Δ ) x y ( 1+ αδ )( 1+ αδ ) A f A f A 1+ 2α Δ + α 2 Δ 2 ( ) ΔA A f A 2α ΔA ΔA γ ΔA where γ 2α By analogy, the volume expansion coefficient β3α for a uniform material, where: Quiz: A swimming pool contains 11 m 3 ( about 3, gal of water). he sun heats the water from 17 to 27 C. What is the change in the volume of the water? β2.7x1-4 / C. a).8 m 3 b).13 m 3 c).17 m 3 d).23 m 3 V ΔV βδv 3 11m Δ V VβΔ ( )( ) -4 o β 2.7x1 / C Δ V 11m 2.7x1 / C 1 C.228m 3-4 o o 3

8 Example A brass ring of inner diameter 1. cm at 2. C is heated and slipped over an aluminum rod of outer diameter 1.1 cm at 2. C. Assuming the average coefficients of linear expansion are constant, to what temperature must this combination be cooled to separate them? (α Al 24x1-6 / o C, α Br 19x1-6 / o C) Want D Br > D Al DBr DBr, +ΔD Br; DAl DAl, +ΔDAl DBr, +Δ D Br > DAl, +ΔDAl DBr, DAl, > ΔDAl ΔDBr D D > αal AlΔ αbr BrΔ ( αal Al αbr Br ) D D Δ ( ) > Δ Δ (24x x1 1.) 5.x1.1 5.x1 2 C +Δ C>Δ 5 f 199 C >Δ 179 C

9 he special case of Ice Many material contract when changing from liquid to solid. Ice is an exception. he lowest energy configuration of the solid occupies a larger volume than the same mass of liquid. he fact is key to spread of life across the planet because it means that ice is on the surface of large bodies of water where it will melt during summer rather than on the bottom.

10 Phases of Matter Slide 12-16

11 Reading Quiz 2. A sample of nitrogen gas is in a sealed container with a constant volume. Heat is added to the gas. he pressure A. increases B. stays the same C. decreases D. can t be determined with the information given Slide 12-8

12 Ideal gas pressure depends linearly on temperature. nr P a + b K V If is measuredin Kelvin Ideal gas pressure depends linearly on temperature. Here nnumber of moles of the gas. here are N A 6.2x1 23 molecules or atoms (if the atoms don t combine into molecules) per mole. One mole.224 m 3 of gas at o C and P1 atm. R8.31 J/(moleK) Ideal gas Example: A molecular gas is contained in an 8.-L vessel at a temperature of 2 C and a pressure of 9. atm. (a) Determine the number of moles of gas in the vessel. (b) How many molecules are in the vessel? PV ( 5 )( 3) a) n 9 1.1x1 Pa.8m R 3. moles 8.31J / K 293K b) N nn A ( )( ) x x1 molecules

13 Example Gas is confined in a tank at a pressure of 1. atm and a temperature of 15. C. If half of the gas is withdrawn and the temperature is raised to 65. C, what is the ratio of the final density over the initial density? 1 Nm Nm Nm f ρ ρ f 2 1 V V V 2 ρ What is the new pressure in the tank? P N V k B P N V k f f B f P P f Pf Nf k B f V N V k B Nf N f atm 5.9atm.59

Chapter 10: Thermal Physics

Chapter 10: Thermal Physics Chapter 10: hermal Physics hermal physics is the study of emperature, Heat, and how these affect matter. hermal equilibrium eists when two objects in thermal contact with each other cease to echange energy.