Chapters 16, 17

Temperature, Heat, and the Thermal Behavior of Matter

Temperature

• Thermodynamics – branch of physics studying thermal energy of systems

• Temperature (T), a scalar – measure of the thermal (internal) energy of a system

• SI unit: K (Kelvin)

• Kelvin scale has a lower limit (absolute zero) and has no upper limit

William Thomson(Lord Kelvin)

(1824 - 1907)

Kelvin scale

• Kelvin scale is defined by the temperature of the triple point of pure water

• Triple point – set of pressure and temperature values at which solid, liquid, and gas phases can coexist

• International convention:T of the triple point of water is

KT 16.2733

The zeroth law of thermodynamics

• If two (or more) bodies in contact don’t change their internal energy with time, they are in thermal equilibrium

• 0th law of thermodynamics: if bodies are in thermal equilibrium, their temperatures are equal

Measuring temperature

• Temperature measurement principle: if 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 (and their temperatures are equal)

• The standard temperature for the Kelvin scale is measured by the constant-volume gas thermometer

Constant-volume gas thermometer

ghPP 0

CPT

33 CPT

33 P

PTT

3

16.273P

PK

Celsius and Fahrenheit scales

• Celsius scale:

• Fahrenheit scale:

Anders Cornelius Celsius

(1701 - 1744)

Gabriel DanielFahrenheit

(1686 - 1736)

15.273TTC

325

9CF TT

Temperature and heat

• Heat (Q): energy transferred between a system and its environment because of a temperature difference that exists between them

• SI Unit: Joule

• Alternative unit: calorie (cal): Jcal 1868.4 1

Absorption of heat

• Specific heat (c): heat capacity per unit mass

• Common states (phases) of matter: solid, liquid, gas

• Latenet heat (L): the amount of energy per unit mass transferred during a phase change (boiling, condensation, melting, freezing, etc.)

)( if TTcmTcmQ

LmQ

Q Q

Absorption of heat

Q Q

Absorption of heat

Absorption of heat

Chapter 17Problem 25

How much energy does it take to melt a 65-g ice cube?

Heat transfer mechanisms

• Thermal conduction

• Conduction rate:

• Thermal resistance:

• Conduction through a composite rod:

L

TTkA

t

Q chcond

H

2211 // kLkL

TTA chcond

H

k

LR Thermal conductivity

21 RR

TTA ch

Absorption of heat

Heat transfer mechanisms

• Thermal radiation

• Radiation rate:

• Stefan-Boltzmann constant:

• Absorption rate:

4eATrad P

4envabs eATP

428 /1067.5 KmW

)( 44 TTeA env Josef Stefan(1835-1893)

radabsnet PPP

Emissivity

Heat transfer mechanisms

• Convection

Heat transfer mechanisms

Chapter 16Problem 35

An oven loses energy at the rate of 14 W per °C temperature difference between its interior and the 20°C temperature of the kitchen. What average power must be supplied to maintain the oven at 180°C?

Avogadro’s number

• Mole – amount of substance containing a number of atoms (molecules) equal to the number of atoms in a 12 g sample of 12C

• This number is known as Avogadro’s number (NA):

NA = 6.02 x 1023 mol -1

• The number of moles in a sample

N – total number of atoms (molecules)m – total mass of a sample, m0 – mass of a single atom (molecule); M – molar mass

Amedeo Avogadro(1776 -1856)

M

m

Nm

m

N

Nn

AA

0

Ideal gases

• Ideal gas – a gas obeying the ideal gas law:

R – gas constant

R = 8.31 J/mol ∙ K

kB – Boltzmann constant

kB = 1.38 x 1023 J/K

nRTPV

nRTPV RTNN A )/( TNRN A )/( TNkB

TNkPV B

Ludwig EduardBoltzmann

(1844-1906)

Ideal gases

• The gas under consideration is a pure substance

• All molecules are identical

• Macroscopic properties of a gas: P, V, T

• The number of molecules in the gas is large, and the average separation between the molecules is large compared with their dimensions – the molecules occupy a negligible volume within the container

• The molecules obey Newton’s laws of motion, but as a whole they move randomly (any molecule can move in any direction with any speed)

Ideal gases

• The molecules interact only by short-range forces during elastic collisions

• The molecules make elastic collisions with the walls and these collisions lead to the macroscopic pressure on the walls of the container

• At low pressures the behavior of molecular gases approximate that of ideal gases quite well

Ideal gases

xixixixi vmvmvmvm 0000 2)()()(

t

vm xi

)( 0

xi

xi

vd

vm

/2

2 0d

vm xi2

0 )(xiF

A

FP x

21

d

FN

ixi

2

1

20 /)(

d

dvmN

ixi

31

20 )(

d

vmN

ixi

N

vv

N

ixi

x

1

2

2

)(V

vNm x2

0V

vnNm A

3

20

22222 3 xzyx vvvvv

Ideal gases

• Root-mean-square (RMS) speed:

V

vnNmP A

3

20

3

20 vNm

nPV A nRT

RTvNm A

3

20

Arms Nm

RTvv

0

2 3

Translational kinetic energy

• Average translational kinetic energy:

• At a given temperature, ideal gas molecules have the same average translational kinetic energy

• Temperature is proportional to the average translational kinetic energy of a gas

2

20vm

Kavg 2

20 vm

2

20 rmsvm

2

3

00

ANmRT

m

AN

RT

2

3

TkK Bavg 2

3

Internal energy

• For the sample of n moles, the internal energy:

• Internal energy of an ideal gas is a function of gas temperature only

avgA KnNE )(int kTnN A 2

3 nRT

2

3

nRTE2

3int

James Clerk Maxwell(1831-1879)

Distribution of molecular speeds

• Not all the molecules have the same speed

• Maxwell’s speed distribution law:

Nvdv – fraction of molecules with speeds in the range

from v to v + dv

Tk

vm

Bv

BevTk

mNN 22

2/3

0

20

24

Distribution of molecular speeds

• Distribution function is normalized to 1:

• Average speed:

• RMS speed:

• Most probablespeed:

1)(0

dvvNv

M

RTdvvvNv vavg

8)(

0

M

RTdvvNvv vrms

3)(

0

2

0mpv v

dv

dN

M

RTvmp

2

Thermal expansion

• Thermal expansion: increase in size with an increase of a temperature

• Linear expansion:

• Volume expansion:

TL

L

3

TV

V

Thermal expansion

Chapter 17Problem 30

A copper wire is 20 m long on a winter day when the temperature is - 12°C. By how much does its length increase on a 26°C summer day?

Questions?

Answers to the even-numbered problems

Chapter 16

Problem 222500 J/(kg K)

Answers to the even-numbered problems

Chapter 16

Problem 402.0 × 102 Pa/K

Answers to the even-numbered problems

Chapter 17

Problem 183.2 × 1023

Answers to the even-numbered problems

Chapter 17

Problem 3611 L