Chapter 10 Thermal Physics. Temperature Thermodynamics – branch of physics studying thermal energy of systems Temperature ( T ), a scalar – measure of.

Chapter 10

Thermal Physics

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

Chapter 10Problem 3

Convert the following temperatures to their values on the Fahrenheit and Kelvin scales: (a) the boiling point of liquid hydrogen, –252.87°C; (b) the temperature of a room at 20°C.

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 10Problem 14

A cube of solid aluminum has a volume of 1.00 m3 at 20°C. What temperature change is required to produce a 100-cm3 increase in the volume of the cube?

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

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

Chapter 10Problem 30

A tank having a volume of 0.100 m3 contains helium gas at 150 atm. How many balloons can the tank blow up if each filled balloon is a sphere 0.300 m in diameter at an absolute pressure of 1.20 atm?

James Clerk Maxwell(1831-1879)

Distribution of molecular speeds

• Not all the molecules have the same speed

• Maxwell’s speed distribution law:

NvΔv – fraction of molecules with speeds in the range

from v to v + Δv

Tk

vm

Bv

BevTk

mNN 22

2/3

0

20

24

Distribution of molecular speeds

• Average speed:

• RMS speed:

• Most probable speed:

M

RTvavg

8

M

RTvrms

3

M

RTvmp

2

Questions?

Answers to the even-numbered problems

Chapter 10

Problem 28

(a) 3.0 mol(b) 1.80 × 1024 molecules

Answers to the even-numbered problems

Chapter 10

Problem 42

3.34 × 105 Pa