•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 = mcΔTPhase 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.

Absolute Zero

• In a constant volume thermometer, readings are virtually independent of the gas used

• If the lines for various gases are extended, the pressure is always zero when the temperature is –273.15o C

• This temperature is called absolute zero

Absolute Temperature Scale

• Absolute zero is used as the basis of the absolute temperature scale

• The size of the degree on the absolute scale is the same as the size of the degree on the Celsius scale

• To convert:TC = T – 273.15

• The absolute temperature scale is based on two fixed points– Adopted by in 1954 by the International

Committee on Weights and Measures– One point is absolute zero– The other point is the triple point of water

• This is the combination of temperature and pressure where ice, water, and steam can all coexist

Absolute Temperature Scale, K

Phase Change: Triple PointA temperature and pressure at which all three phases

exist in equilibrium.

Freezing-Melting Evaporation-Condensation

Sublimation

Lines ofequilibrium

9( ) ( ) 325

T F T C= +o o

5( ) ( ) 329

T C T F⎡ ⎤= −⎣ ⎦o o

( ) ( ) 273.15T K T C= +o

Temperature is measured by a thermometer.Kelvin is the Absolute Scale.

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

5( ) ( ) 329

T C T F⎡ ⎤= −⎣ ⎦o o

( ) ( ) 273.15T K T C= +o

5 68 329⎡ ⎤= −⎣ ⎦

o 20 C= o

293.15K=

Do book quiz 2!

30 is HOT.20 is NICE.10 is CHILLY.Zero is ICE!

http://hyperphysics.phy-astr.gsu.edu/Hbase/kinetic/pcokem.html#c1

Thermal Expansion: Linear

0L L TαΔ = ΔCoefficients determined experimentally!

Thermal Expansion: Volume

0V V TβΔ = Δβ ~ 3α

Thermal Expansion: Linear

Thermal Expansion: LinearThe 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−Δ = − −o o o

.48L mΔ =

0L L TαΔ = Δ

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 Cα α

− − − −= =

Thermal Expansion: Linear0L L TαΔ = Δ

31.3 10brass AlL L x m−Δ + Δ =

31.3 10 11brass brass Al Al

x mT CL Lα α

−

Δ = =+

o21

Thermal Expansion

When the temperature of a metal ring increases, does the hole become larger?

Smaller? Or stay same?

Circle ExpansionThe 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 TαΔ = Δ6(23 10 / )(2.725 )100x C cm C−= o o

2.731d cm=36.3 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: ρ = mass/volumePressure: P = Force/Area

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

Liquid UnitsThere 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 kgliter m

ρ = =

Density• Density of water @4°C:

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

• Density of air @ 0°C: ρAir = 1.29x10-3 g/cm3 = 1.29 kg/m3

Density depends on temperature!Most substances EXPAND upon heating.

mV

ρ =

How does that change their densities?REDUCES DENSITY!m

Vρ =

m Vρ=

Water: The Exception• Water @4°C: ρwater =1000 kg/m3

• Ice @ 0°C: ρice = 917 kg/m3

Note: The graph is for ice water only.Ice is not on the graph!

Thermal Expansion: WaterWater Expands when it cools below 4 °C !Thus, the solid state is less dense than the liquid state:

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

Pressure in a fluid is due to the weight of a fluid.

ForcePArea

=

mgA

=

Pressure depends on Depth!

( )V gA

ρ=

( )Ah gA

ρ=

P ghρ=

Pressure Acts ONLY Perpendicularly to the Surface

Pressure depends on depth.

Pressure IN a Fluid

•Is due to the weight of the fluid above you•Depends on Depth and Density Only•Does NOT depend on how much water is present•Acts perpendicular to surfaces (no shearing)•Pressure’s add•At a particular depth, pressure is exerted equally in ALL directions including sideways (empirical fact)

The Atmosphere

At sea level,the atmosphere has a density of about 1.29 kg/m3.The average density up to120 km is about8.59 x10-2 kg/m3.

The AtmosphereA square meterextending up throughthe atmosphere has a mass of about 10,000 kg and a weightof about 100,000 N.1 N/m2 is a Pascal.

51 1.013 10 14.7atm x Pa psi= =

Measuring Pressure 51 1.013 10atm x Pa=

760h mm=

13.6mercury waterρ ρ=

mercuryP ghρ=

mercury

Phgρ

=

2

3 2

101,300 /13,600 / 9.8 /

N mhkg m x m s

=

P ghρ=

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 mρ =

Measuring PressureCan a barometer be made with Water instead of Mercury?

waterP ghρ=

water

Phgρ

=

2

3 2

101,300 /1000 / 9.8 /

N mhkg m x m s

=

10.3h m=

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

13.6mercury waterρ ρ=

31000 /water kg mρ =

10.3m

Mercury Barometer Water Barometer

Not to Scale!!!

51 1.013 10atm x Pa= 760mm=

BarometersMeasuring Air Pressure

Fluid in the tube adjusts until the weight of the fluid column balances the atmospheric force exerted on the reservoir.

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 ghρ=0Absolute Pressure: P P ghρ= +

Why does the water stop whenthe top is closed?

Pressure is greater in the fluid at the spout due to weight of water so water flows. Hand covers top and water keeps flowing until

the pressure is reduced to 1 atm by increasing volume of air above the fluid just like with a closed barometer!

n = # molesR = 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 ofthe gas and inversely proportional to the volume V of the gas:

P V = nRT

n = # molesR = 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 UnitsThe 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 NumberNA= 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 / molmass/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 massNa: 22.9898 g / moln = 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 = # molesR = 8.31 J/(mol-K) Universal Gas Constant

PV = NktN= # 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 ProblemAn 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 TV T

= =

22 1

1

TV VT

= 3 33481.5 1.72303

Km mK

= =

Hot QuestionSuppose you apply a flame to 1 liter of water for a certain time and its temperature rises by 10 degrees C. If you apply the same flame for the same time to 2 liters of water, by how much will its temperature rise?

a) 1 degree b) 5 degrees c) 10 degrees d) zero degrees

Zeroeth Law 1st Law of Thermo 2nd Law of Thermo 3rd Law of Thermo Absolute ZeroAbsolute Temperature ScaleAbsolute Temperature Scale, KPhase Change: Triple PointThermal Expansion: LinearThermal Expansion: VolumeThermal Expansion: LinearThermal Expansion: LinearThermal Expansion: LinearCircle ExpansionFluids: Liquids & GasesLiquid UnitsDensityWater: The ExceptionThermal Expansion: WaterThermometer, Liquid in GlassPressure in a fluid is due to the weight of a fluid.Pressure Acts ONLY Perpendicularly to the SurfacePressure IN a FluidThe AtmosphereThe AtmosphereMeasuring PressureMeasuring PressureBarometers�Measuring Air PressureWhy does the water stop when�the top is closed?Moles and Avogadro’s Number�NA= 6.022 x 1023 mol-1More on MolesIdeal Gas ProblemHot Question