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Unit Eight:Thermal Properties of Matter

John Elberfeld

JElberfeld@itt-tech.edu

518 872 2082

GE253 Physics

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Schedule

• Unit 1 – Measurements and Problem Solving• Unit 2 – Kinematics• Unit 3 – Motion in Two Dimensions• Unit 4 – Force and Motion• Unit 5 – Work and Energy• Unit 6 – Linear Momentum and Collisions• Unit 7 – Solids and Fluids• Unit 8 – Temperature and Kinetic Theory• Unit 9 – Sound• Unit 10 – Reflection and Refraction of Light• Unit 11 – Final

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Chapter 8 Objectives• Distinguish between temperature and heat.• Explain how a temperature scale is constructed and

convert temperatures from one scale to another.• Describe the ideal gas law, explain how it is used to

determine absolute zero, and understand the Kelvin temperature scale.

• Understand and calculate the thermal expansions of solids and liquids.

• Relate kinetic theory and temperature and explain the process of diffusion.

• Understand the difference between monatomic and diatomic gases, the meaning of the equipartition theorem, and the expression for the internal energy of a diatomic gas.

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Reading Assignment

• Read and study College Physics, by Wilson and Buffa, Chapter 8, pages 259 to 281

• Be prepared for a quiz on this material

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Written Assignments

• Do the homework on the handout.• You must show all your work, and carry

through the units in all calculations• Use the proper number of significant

figures and, when reasonable, scientific notation

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Lesson Introduction

• Last week, we began our study of real liquids and solids.

• We now expand our topics to gases and to do this, we need to introduce the concept of temperature.

• Temperature is the way our brains interpret the electrical signals from the hot and cold sensory receptors in our skin; though, believe it or not, biologists aren’t sure about the identity of these receptors.

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Temperature

• The study of the thermal properties of matter is called thermodynamics, which is governed by the laws of thermodynamics.

• One of the key concepts in thermodynamics is temperature, and you will learn how it is measured.

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Temperature (cont.)

• In physics, temperature can be defined in two ways:– In terms of thermal equilibrium.– In terms of the kinetic energy of atoms

and molecules.

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Thermal Equilibrium

• When two hot and cold bodies come into contact, heat flows from the hotter to the colder body.

• When this heat flow stops, the bodies are said to have attained thermal equilibrium.

• The zeroth law of thermodynamics states that if two bodies, A and B, are each in thermal equilibrium with a third body, C, then A, and B are in thermal equilibrium with each other.

10 Temperature and the Kinetic Theory of Gases

• Temperature can be interpreted as the kinetic energy possessed by the atoms and molecules of an object.

• When the temperature of a gas increases, the atoms or molecules that constitute the gas, whiz around at a higher speed.

• The kinetic energy that these atoms and molecules possess is what we measure as the temperature of the gas.

• KE = mv2/2• Gasses at the same temperature

have the same average kinetic energy for their molecules

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Measurement of Temperature

• We will discuss the main temperature scales used to measure and specify temperature.

• This is done by using some reproducible phenomenon, such as the boiling and melting points of water, for the centigrade scale.

• The three main temperature scales used for measuring temperature are:– Celsius– Fahrenheit– Kelvin

12 Measurement of Temperature (cont.)

• On the Celsius scale, the freezing point of water is a temperature of 0°C, and the boiling point of water is a temperature of 100°C.

• On the Fahrenheit scale, the freezing point of water is 32°F, and the boiling point of water is 212°F.

• The reference point on the Kelvin scale is specified as the triple point of water, that is, liquid, ice, and vapour.

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Comparisons

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Kelvin and Celsius

• K and C degrees are the same size.– An INCREASE in 27º C is the same as

and INCREASE in 27º K

• K = C + 273

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Temperature

• The concept of temperature is based on your sense of touch because you can sense heat or cold.

• Temperature is something that is measured with a thermometer.

• The temperature of an object is determined by the average translational kinetic energy of the object’s molecules.

• Therefore, temperature provides a measurement of heat and an indication of the internal energy content of objects.

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Thermal Expansion

• With an increase in temperature, most objects expand.

• This means that the volume of the object increases.

• This phenomenon is called thermal expansion.

• Similarly, with a decrease in temperature, most objects contract.

• The amount of expansion or contraction is directly proportional to the change in temperature.

• One of the rare exceptions to this principle is water, which is denser at 4ºC than it is at 0ºC.

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Temperature

• Many types of thermometers work on the principle of thermal expansion.

• For example, atmospheric temperature is measured with using mercury thermometers, which have a column of mercury that expands and contracts as the temperature changes.

• The diagram below shows how another type of thermometer works.

• This thermometer has a bimetallic strip, which is particularly useful in measuring high temperatures.

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Bimetallic Strip

• This strip is used in mechanical thermostats to turn your furnace off and on

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Fahrenheit and Celsius

• Temperature is usually measured with either the Fahrenheit scale and the Celsius scale.

• According to the Fahrenheit scale, the freezing point of water is 32ºF and its boiling point is 212ºF.

• The Celsius scale, on the other hand, defines these two temperatures as 0ºC and 100ºC. The conversion equation between these two scales is:

• TF = (9/5)TC + 32• where TF is Temperature in the Fahrenheit scale

and TC is Temperature in the Celsius scale.

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Example

• What is the normal body temperature on the Celsius scale?

• TF = (9/5)TC + 32º

• TC = (5/9) (TF - 32º)

• When TF = 98.6º,

• TC = (5/9) (98.6º - 32º) = 37º

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Graphs

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Absolute Kelvin Temperature

• The lowest theoretically possible temperature is –273.15ºC, which is equal to –459.67ºF.

• This temperature is considered as absolute zero and can never actually be achieved.

• The absolute zero has given rise to the Kelvin temperature scale.

• Absolute 0 = 0ºK

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Kelvin Scale

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Kelvin Scale

• TK = TC + 273.15º• Calculate the following temperatures in

both Cº and Kº• Absolute 0 : –459.67ºF.• Very cold: - 40ºF• Ice Melts: 32ºF• Room Temperature: 68ºF• Body Temperature: 98.6ºF• Water boils: 212 ºF

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Common Temperatures

• Boil212º F, 100º C, 373º K

• Body98.6º F, 37º C, 310º K

• Room68º F, 20º C, 293º K

• Freeze32º F, 0º C, 273º K

• Absolute 0-459º F, -273º C, 0º K

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Combined Gas Law

• To describe the physical characteristics of a gas, you would state the pressure, volume, and temperature.

• Consider how you measure and change these characteristics: the volume of gas is equal to the volume of the container it is placed in.

• To change the volume of gas, change the volume of its container, for example by placing it in a cylinder that has a piston.

• To change the pressure of a gas, you can pump in more gas or force the gas into a smaller volume.

• The temperature of a gas is a variable because you can heat gas or cool it.

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Combined Gas Law

• Can we control physical characteristics of gasses? Yes and no!

• It turns out that, while we can control any of the gas’ physical characteristics, we cannot alter them independently.

• Changing any one the physical characteristics (variables) will cause a change in the others – the rest of the variables cannot remain constant.

• It has been proved that the product of the volume and pressure of a fixed amount of gas divided by its temperature is a constant.

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Charles’ and Boyle’s Laws

• This is known as the combined gas law :•

p1V1/T1 = p2V2/T2 = CONSTANT

where p is pressure, V is volume, and T is the temperature in KELVIN!!!.

• For processes where the temperature is constant, the combined gas law is called Boyle’s law.

• For processes where the pressure is constant, it is called Charles’ law.

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Use Kelvin in Gas Laws

• The combined gas law uses the Kelvin scale of measurements.

• In the combined gas law, the temperature must be expressed in units that will never be negative or else it would imply the pressure or volume can be negative!

• It is very important to always use the absolute temperature scale (Kelvin) in gas law calculations – your results will be very wrong otherwise – you could even calculate a negative volume.

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Example

• A gas placed in a rigid container is at room temperature (20ºC) and at pressure p1. If the gas is heated to a temperature of 60ºC, by what factor will its pressure change?

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Calculation

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Atomic Mass Units

• The constant in the combined gas law, pV/T = constant, depends on the quantity of gas.

• One measure of quantity is mass. • Is this the most useful measure of quantity when

applied to the gas law? • A better measure of quantity to use is the number

of particles. • Instead of using the actual number of particles or

counting them by hundreds or millions, a convenient measure of the quantity of gas is expressed in terms of a unit called mole.

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Moles

• The mole is based on a unit of mass called the atomic mass unit (a.m.u.), which measures the mass of individual atoms.

• This mass is given on the periodic table of the elements shown in the diagram.

• The mole is a very convenient measure because we can count out this number of atoms (or molecules) by weighing the whole sample of them instead of counting them individually.

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Mole

• A mole is one of the seven base SI units.• One mole is the number of atoms in a 12

g sample of carbon-12.• The experimentally determined value for

the number of atoms or molecules in a mole is:

• NA = 6.02 1023 atoms or molecules/mol

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Moles

• We have a mole of particles whenever we have a number of grams of it equal to its atomic or molecular weight in a.m.u.

• Thus, we have a mole of hydrogen (H) atoms when we weigh out 1 gram; a mole of hydrogen molecules (H2) is 2 grams; a mole of Carbon (C) is 12 grams.

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Atomic Mass Units

• A mole of a substance, abbreviated mol, is expressed as the sum of the atomic masses of the atoms that constitute it.

• It is expressed in grams and not in atomic mass units.

• Therefore, a mole of hydrogen gas (H2) has a mass of 2 grams, and a mole of ammonia (NH4) has a mass of 18 grams.

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Ideal Gas Law

• If n is the number of moles of a gas, you can write the combined gas law as follows:

• pV = nRT • where R is the universal gas constant and

has the following value:• R= 8.31 J / (mol Kº)• When the combined gas law is written in

this form, it is called the ideal gas law, and a gas that follows this law is called an ideal gas.

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Ideal Gas Equation

• PV = nRT

• P = Pressure in Pa or N/M

• V = Volume in m3

• n = number of Moles

• R = Universal gas constant

• T = Temperature in Kelvin degrees

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Relationships

• If the amount of gas is unchanged, then nR is constant

• PV/T = nR• P1V1/T1 = P2V2/T2

• If T increases, P, V or both must increase to maintain a constant ratio

• If P increases, T must increase or V must decrease, or both, to maintain a constant ratio

• If V increases, T must increase or P must decrease, or both, to maintain a constant ratio

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Demo

• As the gas heats up, it expands

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Practice

• If the Standard temperature and pressure (STP) of a gas are 0ºC and 1 atm (one atmosphere of pressure), what is the volume of one mole of oxygen at STP?

• Because the equation is easy, they make you convert units!

• The universal gas constant (R) is 8.31 J / (mol.K).

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Calculations

• pV = nRT• TK = TC + 273.15º• 0ºC = 273.15º K• 1 atm = 1.01 x 105N/m2

• V = nRT/p• V= 1 mol 8.31 J/(mol Kº) 273.15º K / 1.01 x

105N/m2

• V = 2.24 x 10-2 m3

• V = 22.4 Liters using an older volume measurement

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R is a CONSTANT

• The gas constant, R, has the same value for oxygen, hydrogen, and all other gases.

This fact indicates that there are no or little molecular forces between the molecules of a gas.

• If molecular forces were present between gas molecules, they would vary for different gases and each gas would have its own gas constant.

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Lesson Introduction

• In previous lessons – as when we dealt with inelastic collisions and nonconservative forces – the law of conservation of energy has not always appeared to be valid.

• In this lesson, we will introduce the concept of internal energy, which will enable us to reconcile conservation of energy with kinetic energy losses.

• We will also explain the difference between diffusion and osmosis, which are two processes necessary for the metabolism of organisms.

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Thermal Expansion

• Increasing the temperature of ideal gases increases the speed of their molecules.

• Although molecules of solids and liquids are strongly bound together, their speed also increases with an increase in temperature.

• While a solid will not expand as much as a gas (under constant pressure), solids do generally expand with increasing temperature because the average distance between the molecules increases, as shown in the diagram.

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• With increasing temperature, the solid has more internal energy so the atoms vibrate over greater distances.

• With wider vibrations in all dimensions, the solid expands as a whole.

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Thermal Expansion

• When the temperature of a long rod of length Lo is increased from To to T, the length of the rod increases to L.

• The change in length, L- Lo, or ΔL is directly proportional to L and to the change in temperature, ΔT

• The constant of proportionality is the coefficient of thermal expansion, α

• ΔL =α L Δ T• The thermal expansion of a sheet of material acts

as linear expansion along two dimensions, and the thermal expansion of a solid block acts as a linear expansion along three dimensions.

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Expansions

• ΔL = α L Δ T

• ΔA = 2α A Δ T

• ΔV = 3α V Δ T

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Practice

• A steel beam is 5.0 m long at a temperature of 20ºC. On a hot day, the temperature rises to 40ºC. What is the change in the beam’s length?

• The coefficient of expansion for steel is 12 x 10–6 /  ºC.

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Calculations

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Thermal Expansion of a Fluid

• Since a liquid or a gas does not retain its shape, linear and area thermal expansion do not apply.

• However, due to change in volume, there is volume expansion and a coefficient of volume expansion:

• ΔV = β V Δ T• A table giving the coefficients of

expansion is shown in the graphic. • A curious exception is seen in the case of

water, which reaches its maximum density at 4ºC. This is why ice floats.

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Table

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Water

• Water is an exception

• What would happen if ice sank?!?!

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Practice

• A steel block is exactly 1m by 3m by 2m at 20º C.

• What is the volume of the block?

• The coefficient of linear expansion is 11x10-6 /ºC

• Compute the new length, the new width, and new height at 60º C.

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More practice

• What is the new volume based on the last three calculations?

• Using ΔV=V0β(ΔT) where β= 3α

• What is the % difference between your two calculation?

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Solution

• Original volume = L x W x H = 6m3

• ΔL = L0α(ΔT)• ΔL1 = 1m 11x10-6 /ºC (40 ºC) = 4.4x10-4m• ΔL2 = 2m 11x10-6 /ºC (40 ºC) = 8.8x10-4m• ΔL3 = 3m 11x10-6 /ºC (40 ºC) = 13.2x10-4m• New dimensions• L = 1m + 4.4x10-4m = 1.00044m• W = 2m + 8.8x10-4m = 2.00088m• H = 3m + 13.2x10-4m = 3.00132m• New Volume = 6.0079234 m3

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Use another formula

• ΔV = V0β(ΔT) where β = 3α

• β = 3 x 11x10-6 /ºC = 33 x10-6 /ºC

• ΔV = 6m3 x 33 x10-6 /ºC (40 ºC) = .00792m3

• Total New Volume = 6.00792 m3

• %difference = • (6.0079234- 6.00792) m3/6.0079234m3

• .00005% error – so β = 3α is a good approximation

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Heat Energy

• Heat is energy in a thermal form.

• Heat is measured in the units of energy (joules).

• A calorie is defined as the amount of heat required to raise the temperature of 1 g of water by 1° C.– 1 cal = 4.186 J– Both cal and J measure energy

59 Heat Absorption by Solids and Liquids

• The quantity of heat that an object or material absorbs (or loses) when heated is determined by heat capacity or the specific heat of an object.

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Heat and Temperature

• In a gas, the temperature depends on the average kinetic energy of the gas molecules.

• Gasses at the same temperature have the same average kinetic energy for their molecules

• The more molecules you have, the more heat energy you have, and the more work you can do with that energy

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Sources of Heat Energy

• Mechanical energy can be converted into heat energy

• Friction generates heat

• When non-conservative forces act, mechanical energy is lost and converted to heat energy.

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Heat

• The chart on the screen shows that internal energy consists of kinetic energy and molecular potential energy. There is no general formula for molecular potential energy. The symbol used for the internal energy of a system or object is U.

• Note that only the translational portion of the internal kinetic energy contributes to the temperature.

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Energy of Particles

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Ideal Gasses

• Gas molecules collide with the container walls in perfectly elastic collisions so no heat is generated

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Diffusion

• If you are standing at one end of a room and your friend cuts open an orange at the other end, you will smell the orange in a few moments.

• The molecules of the orange are concentrated initially at one place.

• However, the random motion of the molecules of air distributes the molecules evenly around the room.

• This process is called diffusion.

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Diffusion• Diffusion occurs rapidly in liquids and

gases because the atoms or molecules have no fixed position and can easily move over large distances in fluid.

• It occurs very slowly in solids because most of the atoms or molecules have a fixed position in the material.

• The figure below shows the diffusion of blue ink.

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Diffusion

• The rate of diffusion depends on the average speed of the molecules being diffused.

• The average speed depends on the average kinetic energy, which is directly proportional to the temperature of the gas.

• For example, in a mixture of oxygen (O2) and carbon dioxide (CO2), the average kinetic energy is the same, but the average speed of the oxygen molecules is greater because their mass is less than that of the carbon dioxide molecules.

• KE = mV2/2

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Osmosis

• Osmosis, an important process in biology, is a form of diffusion. In this process, uniform concentration is achieved when water molecules are transported through a semi-permeable membrane.

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Diffusion

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Heat of Transformation

• When solids and liquids change their state to liquids and gases, the change requires energy.

• Such transformations are called phase transformations, and the heat absorbed or given out by a unit mass of the substance to undergo this transformation is called the heat of transformation .

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Change of State

• During a change of state, there is NO change in temperature– All the heat energy goes into breaking

the molecules apart, not making them move faster

– A change in temperature requires faster moving molecules

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Heat Transfer

• All bodies exchange heat with their environment.

• Heat is transferred by the following processes:– Conduction– Convection– Radiation

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Conduction

• When one end of a metal rod is heated, the other end of the rod also becomes warm. – This is because heat energy is

conducted along the length of the rod.

• The SI unit of thermal conductivity is W/(m K)

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• Convection is the process that involves heat transfer by the physical movement of a fluid.

• In convection, the material itself is transported and carries the heat energy with it.

• Convection currents in a liquid being heated are shown below

Convection

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Radiation

• All objects emit electromagnetic radiation.

• The total amount of energy radiated per unit time per unit surface area of the body is proportional to the fourth power of the absolute temperature of the body.

• Solar energy, in the form of electromagnetic waves or radiation, is shown below:

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Summary

• What is the difference between temperature and heat?

• How do thermometers work?• What is the ideal gas law and the Kelvin

temperature scale?• Do all substances expand when heated?

Why and why not?• What is the kinetic theory of matter and

what phenomena does it explain?