•Temperature

•Thermal Expansion

•Ideal Gas Law

•Kinetic Theory

•Heat

•Heat Transfer

•Phase Changes

•Specific Heat

•Calorimetry

Zeroeth Law

• Two systems individually in thermal

equilibrium with a third system (such as a

thermometer) are in thermal equilibrium

with each other.

• That is, there is no flow of heat within a

system in thermal equilibrium

1st Law of Thermo

• The change of internal energy of a system

due to a temperature or phase change is

given by (next chapter):

Temperature Change: Q = mcT

Phase Change: Q = mL

• Q is positive when the system GAINS heat

and negative when it LOSES heat.

2nd Law of Thermo

• Heat flows spontaneously from a substance

at a higher temperature to a substance at a

lower temperature and does not flow

spontaneously in the reverse direction.

• Heat flows from hot to cold.

• Alternative: Irreversible processes must

have an increase in Entropy; Reversible

processes have no change in Entropy.

• Entropy is a measure of disorder in a system

3rd Law of Thermo

It is not possible to

lower the

temperature of any

system to absolute

zero.

9( ) ( ) 32

5T F T C

5( ) ( ) 32

9T C T F

( ) ( ) 273.15T K T C

Temperature is measured by a thermometer.

Kelvin is the Absolute Scale.

What is "room temperature" (68 degrees F) in Celsius and Kelvin?

5( ) ( ) 32

9T C T F

( ) ( ) 273.15T K T C

568 32

9 20 C

293.15K

Do book quiz 2!

30 is HOT.

20 is NICE.

10 is CHILLY.

Zero is ICE!

Thermal Expansion of Solids: Linear

0L L T

Coefficients determined experimentally!

Thermal Expansion: Volume

0V V T

~ 3

Thermal Expansion: Linear

Thermal Expansion: Linear

The coefficient of linear expansion of steel is 12 x 10-6/°C.

A railroad track is made of individual rails of steel 1.0 km in length.

By what length would these rails change between

a cold day when the temperature is -10 °C and a hot day at 30 °C?

6 3(12 10 / )(10 )(30 ( 10 ))L x C m C C

.48L m

0L L T

What change in temperature is needed to fill the gap, 1.3 x 10 -3 m?

6 0 1 6 0 119 10 23 10 brass ALx C x C

0L L T

31.3 10brass AlL L x m

31.3 1011

brass brass Al Al

x mT C

L L

21

Thermal Expansion

When the temperature of a metal ring increases,

does the hole become larger?

Smaller? Or stay same?

Circle Expansion

The coefficient of linear

expansion of aluminum is

23 x 10-6/C°. A circular

hole in an aluminum plate is

2.725 cm in diameter at 0°C.

What is the diameter of the

hole if the temperature of

the plate is raised to 100°C?

0L L T 6(23 10 / )(2.725 )100x C cm C

2.731d cm36.3 10x cm

Fluids: Liquids & Gases

•Fluids are substances that are free to flow.

•Atoms and molecules are free to move.

•They take the shape of their containers.

•Cannot withstand or exert shearing forces.

Liquids: Incompressible (density constant)

Gases: Compressible (density depends on pressure)

Parameters to describe Fluids:

Density: = mass/volume

Pressure: P = Force/Area

[P] = N/m2 = 1 Pascal (Pa)

Liquid Units

There are 1000 liters in 1 cubic meter!

1 liter = 10-3 m3 = 103 cm3

1 liter of water has a mass of 1 kg and a weight of 9.8N.

2 0 3

1 1000H

kg kg

liter m

Density • Density of water @4°C:

water = 1g/cm3 = 1000 kg/m3 = 1kg/liter

• Density of air @ 0°C:

Air = 1.29x10-3 g/cm3 = 1.29 kg/m3

Density depends on temperature! Most substances EXPAND upon heating.

m

V

How does that change their densities?

REDUCES DENSITY! m

V

m V

Water: The Exception

• Water @4°C: water =1000 kg/m3

• Ice @ 0°C: ice = 917 kg/m3

Increasing the Pressure

Does increasing the external pressure increase

or decrease the boiling temperature of water?

Increases! Boiling happens when vapor pressure in the

liquid exceeds the external vapor pressure - now greater

due to the increased pressure – so the boiling temperature

increases!

n = # moles

R = 8.31 J/(mol-K) Universal Gas Constant

The absolute Pressure P of an ideal gas is directly proportional to

the absolute (Kelvin) temperature T and the number of moles n of

the gas and inversely proportional to the volume V of the gas:

P V = nRT

Thermometer, Liquid in Glass

• A common type of

thermometer is a

liquid-in-glass

• The material in the

capillary tube

expands as it is

heated

• The liquid is

usually mercury or

alcohol

10.3m

Mercury Barometer Water Barometer

Not to Scale!!!

51 1.013 10atm x Pa 760mm

Barometers

Measuring Air Pressure Fluid in the tube adjusts until the weight of the fluid column

balances the atmospheric force exerted on the reservoir.

The Atmosphere

At sea level,

the atmosphere

has a density of

about 1.29 kg/m3.

The average

density up to

120 km is about

8.59 x10-2 kg/m3.

The Atmosphere

A square meter

extending up through

the atmosphere has a

mass of about

10,000 kg and a weight

of about 100,000 N.

1 N/m2 is a Pascal.

51 1.013 10 14.7atm x Pa psi

Pressure in a fluid is due to the weight

of a fluid. Force

PArea

mg

A

Pressure depends on Depth!

( )V g

A

( )Ah g

A

P gh

Measuring Pressure 51 1.013 10atm x Pa

760h mm

13.6mercury water

mercuryP gh

mercury

Ph

g

2

3 2

101,300 /

13,600 / 9.8 /

N mh

kg m x m s

P gh

Why is the pressure at X equal to atmospheric pressure?

Because if it didn’t, the mercury would

be pushed out of the dish!

31000 /water kg m

Measuring Pressure

Can a barometer be made with Water instead of Mercury?

waterP gh

water

Ph

g

2

3 2

101,300 /

1000 / 9.8 /

N mh

kg m x m s

10.3h m

(Notice: 10.3m is just 13.6 x 760mm!)

13.6mercury water

31000 /water kg m

Absolute vs. Gauge Pressure

• Guage pressure is

what you measure in

your tires

• Absoulte pressure is

the pressure at B and

is what is used in

PV = nRT

0Guage Pressure: P gh

0Absolute Pressure: P P gh

n = # moles

R = 8.31 J/(mol-K) Universal Gas Constant

Note: PV is units of Energy!

P V = nRT

•Atomic Number: # protons

•Atomic Mass: # atomic mass units (u)

•Atomic Mass Unit: 1/12 mass of C-12 atom

• amu = u = 1.66 x 10-27 kg

•Atomic Mass of C = 12.011u (1% is C-13)

•Mass of 1 C = (12.011u) (1.66 x 10-27 kg/u)

Atomic Units

The Basics

•Mole (mol) = # atoms or molecules (particles) as

are in 12 grams of Carbon-12:

1 mole = 6.022 x 1023 particles

• Avogadro’s Number: the number of particles in

one mole: NA= 6.022 x 1023 mol-1

•# moles n contained in a sample of N particles:

n = N/ NA

• # particles in a sample is: N = n NA

Moles and Avogadro’s Number NA= 6.022 x 1023 mol-1

The mass / mol for any substance

has the same numerical value

as its atomic mass:

mass/mol C-12 = 12 g / mol

mass/mol Li = 6.941 g / mol

More on Moles

n = mass / atomic mass

n = mass / (mass/mole) = mass / atomic mass

Q: How many moles are in 1 kg of Sodium?

mass/mole = atomic mass

Na: 22.9898 g / mol

n = mass / (mass/mole)

= 1000 g / (22.9898g/mol)

= 43.5 moles

Q: How many atoms in 1 kg of Sodium?

# particles in a sample is: N = n NA

N = (43.5mol) 6.022 x 1023 mol-1

= 2.62 x 1025 atoms

n = # moles

R = 8.31 J/(mol-K) Universal Gas Constant

PV = Nkt N= # particles

k =1.38 x 10-23 J/K Boltzmann’s Constant

Note: PV is units of Energy!

P V = nRT

• The only interaction between particles are

elastic collisions (no sticky - no loss of KE)

• This requires LOW DENSITY

• Excellent Approximation for O, N, Ar, CO2

@ room temperature and pressures

• “State” is described by the Ideal Gas Law

• Non “Ideal” are Van der Waals gases

Ideal Gas Problem An ideal gas with a fixed number of molecules

is maintained at a constant pressure. At 30.0

°C, the volume of the gas is 1.50 m3. What is

the volume of the gas when the temperature is

increased to 75.0 °C?

1 1PV nRT

2 2PV nRT

1 1

2 2

V T

V T

22 1

1

TV V

T 3 3348

1.5 1.72303

Km m

K

•Heat flows from HOT to COLD

•Conduction (solids)

•Convection (liquids & gases)

•Radiation (solids, gases, plasma)

Energy transferred via molecular collisions

•Good Conductors: Most Metals (free

electrons!)

•Bad Conductors: Organic & Inert

Materials

•Good Insulators: Air, Water, Wood

•Good Conductors are BAD Insulators

•& Visa Versa

Heat energy is transferred in solids

by collisions between free electrons

and vibrating atoms.

The heat Q conducted during a time t through a material with

a thermal conductivity k. dT/dx is the Temperature Gradient.

dTP kA

dx

Some Thermal Conductivities

Temperature Gradient

h cdT T T

dx L

The quantity |dT / dx| is called the temperature gradient

Q dTkA

t dx

Compound Slab: R values

h c

i i

i

A T T

L k

• For a compound slab containing several

materials of various thicknesses (L1, L2, …) and

various thermal conductivities (k1, k2, …) the

rate of energy transfer depends on the materials

and the temperatures at the outer edges:

• Substances are rated by their R values

– R = L / k and the rate becomes

– For multiple layers, the total R value is the sum of the R values of each layer

• Wind increases the energy loss by conduction in a home

h c

i

i

A T T

R

Conduction Problem

A bar of gold is in thermal contact with a bar of silver of the

same length and area as shown. One end of the compound

bar is maintained at 80.0°C while the opposite end is at

30.0°C. When the energy transfer reaches steady state, what

is the temperature at the junction? Ignore thermal

expansion of the metals.

h cT TkA

L

In the same room, at the same

temperature, the tile floor feels

cooler than wood floor.

How can they be the same

temperature?

Hot Air rises, expands and cools, and then sinks back down

causing convection currents that transport heat energy.

Hot air rises because fast moving molecules tend to migrate toward

regions of least obstruction - UP - into regions of lesser density!

Rising air cools because a decrease in density

reduces number of collisions & speeds decrease.

As the air cools, it becomes denser, sinking down,

producing a convection current.

Uneven heating on the earth and over water cause convection

currents in the atmosphere, resulting in WINDS.

Global wind patterns (Trade Winds, Jet Streams) are due to

convection current from warmer regions (equator) to cooler

regions (poles) plus rotation of Earth.

Convection Currents in the Ocean (Gulf Stream)

transport energy throughout the oceans.

Air & Ocean Convection causes

the WEATHER.

Convection between water and land causes the Winds.

Sea Breeze

High Pressure

Dry Warm Weather

Low Pressure

Stormy Weather

Electromagnetic Radiation is emitted and absorbed via atomic

excitations. All objects absorb and emit EM waves.

Electromagnetic Radiation is emitted and absorbed via atomic

excitations. All objects absorb and emit EM waves.

When an object it heated it will

glow first in the infrared, then the

visible. Most solid materials break

down before they emit UV and

higher frequency EM waves.

Frequency ~ Temperature

Long

Short

Stefan’s Law

• P = σAeT 4

– P is the rate of energy transfer, in Watts

– σ = 5.6696 x 10-8 W/m2 . K4

– A is the surface area of the object

– e is a constant called the emissivity

• e varies from 0 to 1

• The emissivity is also equal to the absorptivity

– T is the temperature in Kelvins

A good absorber reflects little and appears Black

A good absorber is also a good emitter.

4P e T A

Radiant heat makes it impossible to stand close to a hot

lava flow. Calculate the rate of heat loss by radiation

from 1.00 m2 of 1200C fresh lava into 30.0C

surroundings, assuming lava’s emissivity is 1.

The net heat transfer by radiation is: 4 4

2 1( )P e A T T

4 4

2 1( )P e A T T

8 4 2 4 41(5.67 10 / )1 ((303.15 ) (1473.15 ) )x J smK m K K

266P kW

Fur is filled with air. Convection currents are slow

because the convection loops are so small.

How do fur coats keep you warm?