Thermal Physics AP Physics B Lecture Notes x z. Thermal Physics 10-01 Temperature and the zeroth Law of Thermodynamics 10-02 Thermometers and Temperature

Thermal Physics

AP Physics BLecture Notes

x

z

Thermal Physics

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

Topics

10-05 The Kinetic Theory of Gases

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.

A B

C

Then A and B are in thermal equilibrium.

If A is in thermal equilibrium with Cand B is in thermal equilibrium with C

The Zeroth Law of Thermodynamics

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.

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.

0 -273 -459

Celsius FahrenheitKelvin

273 0 32

373 100 212

Boiling

Point (H2O)

Melting

Point (H2O)

Absolute Zero

Temperature is generally measured using either the Kelvin, Celsius, or the Fahrenheit scale.


Thermal Expansion of Solids and Liquids

A steel washeris heated

Does the hole increase or decrease in size?

Expansion occurs when an object is heated.

When the washeris heated

The hole becomeslarger



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.

LoL

L LoT

TL = LoT

L = Lo(1+T)

Coefficient oflinear expansion

L Lo = LoT


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.

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)

To what temperature must the sleeve be heated before it will slip over the shaft?

shaft sleeve

D d

C/1 10 x 19 o6

TLL i

ddD

Tf

C0T

cm 196.3dcm 212.3D

oi

cm 3.196C/1 10x 19

cm 3.196cm 3.212o6 C 263 o

dDL

if TTddD

fdTdD


32o

2o

3o LLL3LL3LV

New Volume

3o LLV

Initial Volume

3oo LV

TL3V 3o

Lo

Lo

Lo

Lo + L

Lo + L

Lo + LVolume Expansion

L = LoT

LL3VVV 2oo

TLL3V o2o

TV3V o


TV3V o

3

TVV o

TVVV oo

T1VV o

Coefficientof

VolumeExpansion


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?

SG VVV

TVV oSG

2545 10 x 3310 x 6.9 V 64

L 04.1V

Overflow

Change in volumeof the gasoline

Change in volumeof the steelgas tank

TVTVV oSoG


PV = nRT

Pressure(Pa)

Volume(m3)

AbsoluteTemperature

(K)

Gas Constant(8.31 J/molK)

0.0821 (L.atm)/(mol.K)

1.99 cal/(mol.K)

Gas Quantity(mol)

Microscopic Description of an Ideal Gas


~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.

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 g1 mol Ne has a mass of 20 g1 mol CO2 has a mass of 44 g

mol/g mass molecular

grams massmol n Μ

mn

mol/particlesnumber svogadro'A)(particles molecules

mol n AN

Nn

The number of moles in a certain number of particles:

The number of moles in a certain mass of material:


PV = NkT

Pressure(Pa)

Volume(m3)

AbsoluteTemperature

(K)

Boltzmann’sConstant

(1.38 x 10-23 J/K)

Number ofMolecules


Boltzmann’s Constant

nRTPV NkT

NnR

k

nNR

k

GasConstant

Avogadro’sNumber


A gas is contained in an 8.0 x 103 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.

nRTPV

RTPV

n K 293Kmol/J 31.8

m10 x 0.8N/m 10 x 0.9 2325

mol 0.3n

Microscopic Description of an Ideal Gas (Problem)

A gas is contained in an 8.0 x 103 m3 vessel at 20 oC

and a pressure of 9.0 x 105 N/m2.

(b) How many molecules are in the vessel?

AnNN

mol 0.3n

mol

molecules23 10 x 02.6mol 0.3

molecules 10 x 8.1N 24

Microscopic Description of an Ideal Gas (Problem (con’t))


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

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

0.20 x 105 Pa

0.70 m3

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

0.20 x 105 Pa

0.70 m3

0.80 x 105 Pa

nRTPV constantnRT

PV

i

ii

f

ffTVP

TVP

ii

ffif VP

VPTT

35

35

m 5.1 Pa 10 x 2.0

m 7.0 Pa 10 x 8.0K 300 K 560

273

C 287 o

Microscopic Description of an Ideal Gas (Problem)

K 300C 27 o

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

x

y

z

v

L

AThe force exerted on the wall by the collision of one molecule of mass m is

tΔ

mvΔF

x

x

vL2mv2

L

mv2x

Then the average force due to N molecules colliding with that wall is

2xvN

Lm

F


The averages of the squares of the speeds in all three directions are equal:

So the pressure on the wall is:

AF

P AL

vNm 2

31

VvNm 2

31

LvmN

F2

31x

y

z

v

L

A

2xvN

Lm

F


Rewriting,

so

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

221

32 vm NPV NkT

kTvm 221

32

kTvmEK 232

21

VvNm

P2

31


Molecular Kinetic Energy

Temperature is a measure of the averagemolecular kinetic energy.

2kT3

KE

mkT3

v rms

2vm 2

2kT3

2vm 2



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.


The absolute temperature of an ideal gas is directly proportional to which of the following?

(A) speed

(B) momentum

(C) kinetic energy

(D) mass


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

What is the total random kinetic energy of all themolecules in one mole of hydrogen at a temperatureof 300 K.

kT

23

NK A

Avogadro’snumber

Kinetic energy per molecule

J 3740K

K 003 KJ

10 x 38.1 23

molecules 10 x 02.6K 2323

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:

kg 10 x .654 26

kg 10 x .654

K 373 J/K 10 x .381326

23

m

kT3v rms

m/s 576v rms

rms speed:

molemolecules/ 10 x .026

kg/mole 10 x 0.28m

23

3


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 kineticenergy of a gas molecule?

Temperature of the gas:

nRTPV

nRPV

T

KmolJ

31.8mol 0.2

m 10 x 0.5Pa 10 x 0.8

335K 442

Kinetic energy:

kT23

K K 244KJ

10 x 38.123 23

molecule

Jx 2110 05.5



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

Mean and rms Speed5

2

3

6 2

61

4Mean Speed:

852362461

8

52362461 22222222

rms Speed:

m/s 4.0v rms

m/s 3.6v mean



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


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.

nRTPV 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:

kTvmEK 232

21

Summary

Documents

Thermal Physics AP Physics B Lecture Notes x z. Thermal Physics 10-01 Temperature and the zeroth Law of Thermodynamics 10-02 Thermometers and Temperature