Physics 20 Thermal Physics Notes 1

Physics 20 Thermal Physics Notes

1

•Temperature•Thermal Expansion•Ideal Gas Law•Kinetic Theory•Heat•Heat Transfer•Phase Changes•Specific Heat•Calorimetry•Kinetic theory•Engines

• 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

• Any two systems placed in thermal contact will have an exchange of heat energy until they reach the same temperature.

• If the systems are in thermal equilibrium then no changes take place.

• The change of internal energy of a system due to a temperature or phase change is given by:

Temperature Change: Q = mcT

Phase Change: Q = mL

• Q is positive when the system GAINS heat and negative when it LOSES heat.

•Heat Energy is a flow of energy from hotter to colder because of a difference in temperature. Objects do not have heat. [Heat] = Joule

•Heat Energy entering or leaving a system will cause either a Temperature Change: Q = mcT or a Phase Change: Q = mL

• 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.

It is not possible to lower the

temperature of any system to absolute zero.

Zero Temperature means zero volume (PV=nRT) and that is not possible since atoms take up space.


2

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.

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 Density 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.

m

V

• 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.How does that change their densities?

REDUCES DENSITY!m

V

• 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

P V = nRTn = # moles

R = 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!

•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

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


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• Particles have different speeds• Gas Particles are in RANDOM motion• Pressure is due to momentum transfer•Average translational KE of each particle is: 3/2 kT

Speed ‘Distribution’ at CONSTANT Temperature is given by the Maxwell Speed Distribution

The Kinetic Theory: A Molecular Interpretation of Temperature

• The Kelvin temperature is a direct measure of average translational kinetic energy per particle:

• Average KE per molecule:

• Average KE per N molecules:

• Root Mean Square Speed:

𝑃𝑉 𝑁 KE =nRT=NkT

KE12𝑚𝑣

32𝑘𝑇

KE 𝑁12𝑚𝑣

32𝑁𝑘𝑇

2 3rms

kTv v

m

Specific Heat: Thermal InertiaThe Specific Heat of a substance is the amount of Energy it requires to raise the temperature of 1 kg, 1 degree Celsius.

Q mc T 0

Q Jc

m T kg C

•The higher the specific heat, the more energy it takes and the longer it takes to heat up and to cool off.

•The lower the specific heat, the less energy it takes and the quicker it takes to heat up and cool off.

•Substances with HIGH specific heat STORE heat energy and make good thermal moderators. (Ex: Water, Oceans)

Equipartition of Energy

• Each translational degree of freedom contributes an equal amount to the energy of the gas

– In general, a degree of freedom refers to an independent means by which a molecule can possess energy

• Only Translational KE contributes to TEMPERATURE. Energy flowing into a substance goes into different MODES of motion. Monatomic gases heat up fast because they can only translate. Water takes longer to heat up because it can translate, rotate and vibrate and the heat flow goes into exciting all these modes equally – so it takes longer to heat up.

• Equipartition Theory overturned by QUANTUM PHYSICS

Phase Change Q mL•A change from one phase to another•A phase change always occurs with an exchange of energy!•A phase change always occurs at constant temperature!

Thermal Expansion: Linear


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•Heat flows from HOT to COLD•Conduction (solids)•Convection (liquids & gases)•Radiation (solids, gases, plasma)

Hot Air rises, expands and cools, and then sinks back downcausing convection currents that transport heat energy.

Hot air rises because fast moving molecules tend to migrate towardregions of least obstruction - UP - into regions of lesser density!

Rising air cools because a decrease in densityreduces number of collisions & speeds decrease.

As the air cools, it becomes denser, sinking down,producing a convection current.

•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.

kA TtQ

L

The heat Q conducted during a

time t through a material witha thermal conductivity k.

h cdT T T

dx L

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

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Stefan’s Law: 1879

Rate of radiation of a Black Body• 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– With his law Stefan determined the temperature of the

Sun’s surface and he calculated a value of 5430C. This was the first sensible value for the temperature of the Sun.

– Boltzmann was his student and derived Stefan’s Law from Thermodynamics in 1884 and extended it to grey bodies.

Jožef Stefan (1835–1893)

A good absorber reflects little and appears BlackA good absorber is also a good emitter.

4P e T A

The net heat transfer by radiation is: 4 4

2 1( )P e A T T


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Intensity: The Radiation Power, P, passing through an area, A.

2 2

W

4 m

PI

r

Work in Thermodynamics• A force is applied to slowly compress the

gas. In general, the work done on a gas is given by pressure times change in volume. For an isobaric process:

VPAsPFsW

For an isochoric process: W =0

Thermo Processes• Adiabatic

– No heat exchanged– Q = 0 and Eint = W

• Isobaric– Constant pressure– W = P (Vf – Vi) and Eint = Q + W

• Isochoric– Constant Volume– W = 0 and Eint = Q

• Isothermal– Constant temperatureEint = 0 and Q = -W

intE Q W

ln i

f

VW nRT

V

int 0E Q W

First Law for Gases:

• Cyclic Processes

PV Diagrams

Fig. 20-9, p. 569


6

Molar Specific HeatsIsobaric requires MORE HEAT than Isochoric for the

same change in Temperature!!!!

The total change in thermal energy for ANY PROCESS, due to work and heat, is:

This applies to all ideal gases, not just monatomic ones! WOW!

Monatomic and Diatomic GasesThe thermal energy of a monatomic gas of N atoms is

A diatomic gas has more thermal energy than a monatomic gas at the same temperature because the molecules have rotational as well as translational kinetic energy.

15.8 Heat Engines

A heat engine is any device that uses heat to perform work. It has three essential features.

1. Heat is supplied to the engine at a relatively high temperature from a place called the hot reservoir.

2. Part of the input heat is used to perform work by the working substance of the engine.

3. The remainder of the input heat is rejected to a place called the cold reservoir.

heatinput of magnitude HQ

heat rejected of magnitude CQ

done work theof magnitude W

HQ

We

H

C

Q

Qe 1

The efficiency of a heat engine is defined as the ratio of the work done to the input heat:

CH QWQ

15.9 Carnot’s Principle and the Carnot Engine

The Carnot engine is useful as an idealizedModel made of two adiabats and two isotherms. It is the most efficient engine possible.

All of the heat input originates from a singletemperature, and all the rejected heat goesinto a cold reservoir at a single temperature.

Since the efficiency can only depend onthe reservoir temperatures, the ratio of heats can only depend on those temperatures:

H

C

H

C

T

T

Q

Qe 11

H

C

H

C

T

T

Q

Q

1796 – 1832French engineer

Heat Pumps and Refrigerators

• Heat engines can run in reverse

– This is not a natural direction of energy transfer

– Must put some energy into a device to do this

– Devices that do this are called heat pumps or refrigerators

energy transferred at high tempCOP =

work done by heat pumph

heating

Q

W

energy transferred at low tempCOP =

work done by heat pumpC

cooling

Q

W

2nd Law: Perfect Heat EngineCan NOT exist!

• It takes in some amount of energy and does an equal amount of work

• e can never be100%• No Free Lunch!• Limit of efficiency is a Carnot Engine

Physics 20 Thermal Physics Notes 1

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