Chapter 13 Temperature and Kinetic - Siena Sciencerfinn/courses/phys110/temp-ideal-gas.pdf · Chapter 13 Temperature and Kinetic ... •atomic nature of matter ... relevant for liquids

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Chapter 13

Temperature and KineticTheory

13-1 Atomic Theory of Matter

• Atomic mass unit (u)•This unit is defined so carbon-12 has amass of exactly 12.0000 u. Expressed inkilograms:

Brownian motion is the resultof collisions with individualwater molecules.

13-1 Atomic Theory of Matter

•atomic nature of matter•Democritus - atom•Brownian motion (Robert Brown, 1827)

•the result of collisions with individualwater molecules•quantified by Einstein (1905)

13-1 Atomic Theory of Matter

On a microscopic scale, the arrangements ofmolecules in solids (a), liquids (b), and gases (c)are quite different.

13-2 Temperature and ThermometersTemperature is a measure of how hot or coldsomething is.

Most materials expand when heated.

13-2 Temperature and ThermometersThermometers are instruments designed tomeasure temperature. In order to do this, they takeadvantage of some property of matter thatchanges with temperature.

Early thermometers:

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13-2 Temperature and Thermometers

Common thermometers used today include theliquid-in-glass type and the bimetallic strip.

13-2 Temperature and Thermometers

•Most common temp scales:Fahrenheit and Celsius

•Defined by phase change of waterat atmospheric pressure

•freezing point of water

•0°C or 32°F

•boiling point of water

• 100°C or 212°F.

Chapter 13: Problem 3(a)

• Room temperature is 680F. What is this inCelsius?

13-3 Thermal Equilibrium and the ZerothLaw of Thermodynamics

•Two objects placed in thermal contact willeventually come to the same temperature.When they do, we say they are in thermalequilibrium.

•zeroth law of thermodynamics:if two objects are each in equilibrium with athird object, they are also in thermal equilibriumwith each other.

13-4 Thermal Expansion

Linear expansionoccurs when an objectis heated.

(13-1b)

Here, α is the coefficient of linearexpansion.

Ch 13: Problem 7

• A concrete highway is built of slabs 12 mlong (200C). How wide should theexpansion cracks between the slabs be (at200C) to prevent buckling if the range oftemperature is -300C and +500C?

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13-4 Thermal Expansion

Volume expansion is similar, except that it isrelevant for liquids and gases as well as solids:

(13-2)

Here, β is the coefficient of volumeexpansion.

For uniform solids,

13-4 Thermal Expansion

13-4 Thermal Expansion•Water behaves differently from most other solids – itsminimum volume occurs when its temperature is 4°C. As itcools further, it expands.

•Maximum density at 4 C.

13-6 The Gas Laws and Absolute Temperature

Equation of state:relationship between the volume, pressure,temperature, and mass of a gas

Boyle’s Law: the volume of agiven amount of gas is inverselyproportional to the pressure aslong as the temperature isconstant.

13-6 The Gas Laws and Absolute Temperature

The volume is linearly proportional to thetemperature, as long as the temperature issomewhat above the condensation point andthe pressure is constant:

Extrapolating, the volume becomes zero at−273.15°C; this temperature is called absolutezero.

13-6 The Gas Laws and Absolute Temperature

•Kelvin scale:

•0 K at absolute zero

•molecules stop moving!

•same temp per degree as the Celsius scale

•the freezing point of water is 273.15 K

•the boiling point is 373.15 K.

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13-7 The Ideal Gas Law

A mole (mol) is defined as the number of gramsof a substance that is numerically equal to themolecular 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 ofmaterial:

13-7 The Ideal Gas Law

ideal gas law:(13-3)

where n is the number of moles andR is the universal gas constant.

13-8 Problem Solving with the Ideal Gas Law

Useful facts and definitions:

• Standard temperature and pressure (STP)

• Volume of 1 mol of an ideal gas is 22.4 L

• If the amount of gas does not change:

• Always measure T in kelvins

• P must be the absolute pressure

Ch 13: Problem 29

• If 3.00 m3 of a gas initially at STP is placedunder a pressure of 3.20 atm, thetemperature of the gas rises to 38.00C.What is the volume?

13-9 Ideal Gas Law in Terms of Molecules:Avogadro’s Number

Avogadro’s number: the number of moleculesin one mole

The number of molecules in a gas is thenumber of moles times Avogadro’s number:

13-9 Ideal Gas Law in Terms of Molecules:Avogadro’s Number

Therefore we can write:

where k is called Boltzmann’s constant.

(13-4)

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Ch13: Problem 42

• How many moles of water are there is1.000 L? How many molecules?

13-10 Kinetic Theory and the MolecularInterpretation of Temperature

Assumptions of kinetic theory:

• large number of molecules, moving in randomdirections with a variety of speeds

• molecules are far apart, on average

• molecules obey laws of classical mechanicsand interact only when colliding

• collisions are perfectly elastic

13-10 Kinetic Theory and the MolecularInterpretation of Temperature

(13-8)

The average translational kinetic energy ofthe molecules in an ideal gas is directlyproportional to the temperature of the gas.

13-10 Kinetic Theory and the MolecularInterpretation of Temperature

We can invert this to find the average speed ofmolecules in a gas as a function oftemperature:

(13-9)

Ch 13: Problem 47

• Calculate the rms speed of helium atomsnear the surface of the Sun at atemperature of about 6000 K.