04/22/231

IB PHYSICS Topic 3: Thermodynamics.Thermodynamics: Study of conversion of heat to other forms of energy (mechanical, light, sound, chemical, electromagnetic, nuclear, and atomic). Ex. Mechanical to Heat: 4.186 J = 1 cal. 1st Law: Energy is conserved. ΔU = Q - W > 02nd Law: Disorder (change in entropy, ΔU) tends to increase. Entropy is unavailable energy (waste heat).

Thermodynamics is based on Kinetic Theory:1. All matter is composed of tiny particles (atoms and molecules).2. These particles are in constant motion.

04/22/232

Thermal Physics Applications:

fabrication of materials

chemical reactions

biological processes

phase transitions

04/22/233

The Four States of Matter

1. Gases - easy to compress, particles far apart, expand to fill any container, and repel each other.

2. Liquids - no definite shape, hard to compress, particles close together, and attract each other.

3. Solids - definite shape, much harder to compress, closer spacing than liquids.

4. Plasma – electrically charged particles in chaotic motion.

04/22/234

THE GAS LAWS1. Boyle’s Law: states that the product of pressure and volume is constant. PV = k or P1V1 = P2V2

2. Charles’ Law – states that volume and temperature are directly proportional. V1 / T1 = V2 / T2

3. Combined Law – a combination of Boyle’s and Charles’ Laws. P1V1 / T1 = P2V2 / T2

4. Ideal Gas Law – relates volume, temperature, pressure, and number of particles (n). PV = nRT where R = 8.315 J/mol∙K , Universal Gas Constant.

04/22/235

3 temperature scales: Fahrenheit TF, Celsius TC, Kelvin TK.

Metric unit for temperature is the Kelvin.a. TK = TC + 273 , ex. (10oC = 283K)b. TC = TK – 273 , ex. (10K = -263oC)c. TC = 5/9(TF – 32) , ex. (32oF = 0oC)d. TF = 9/5TC + 32 , ex. (100oC = 212oF)Thermal Energy – total of all the kinetic and potential energy of all the particles in a substance. Proportional to temperature.

04/22/236

1. Solids: L = • L • T = coefficient of linear expansion

L L2. Liquids: V = • V • T

= coefficient of volume expansion

V V

First Law Equation: ΔU = (Uf -Ui) = Q-W

Types of Thermal Processes)A thermal process is considered quasi-static when it occurs slowly enough that a uniform pressure and temperature exist throughout the system at all times. Process Occurs at or with•Isobaric - constant pressure.•Isochoric - constant volume.•Isothermal - constant temperature.•Adiabatic - takes place without the transfer of heat.

Heat Engine (schematic)

04/22/239

Heat Transfer MechanismsHeat is the Thermal Energy transferred from an object

to its surroundings due to a difference in temperature.

There are now four ways of moving heat:• Convection (moving heat with a material)• Conduction (moving heat through a material)• Radiation (moving heat away from a source)• Evaporation (using latent, hidden, heat)Temperature determines the direction of heat transfer. Heat ALWAYS moves from a hot to a cold object.

04/22/2310

How to calculate changes in thermal energy

Q = m • c • TQ = change in thermal energy, Jm = mass of substance, kgc = specific heat capacity of substance (ex. Water, 4186 J/kg °C)T = change in temperature, C

04/22/2311

Law of Heat Exchange, Q = 0 QG + QL = 0 QG = -QL

QL = heat lost by substance at high temperature

QG = heat gained by substance at low temperatureT = change in temperature (Tf – Ti) So now we have, when mixing 2 substances

m1•c1•(Tf – Ti) = -[m2 •c2 •(Tf – Ti)]m1•c1•(Tf – Ti) = m2 •c2 •(Ti – Tf)

04/22/2312

Specific heat - amount of heat needed to raise the temperature of 1 kg of substance by 1°C or 1 K). 1) Cwater = 4186 J / kg oC 2) Csand = 664 J / kg oC

Why the beach (sand) heats up quickly during the day and cools quickly at night, but water takes

longer to do both.

Beware of Phase Changes. Watch out for Latent (hidden) Heat.

Latent Heat (H) – The amount of heat per kilogram that must be added or removed to change the phase of a particular substance

Q = m·Hf Hf = Latent Heat of Fusion (freezing or melting)

Q = m·Hv

Hv = Latent Heat of Vaporization (evaporating or condensing)

We can calculate the amount of heat that passes through a conductor……

A

L

Q = (k·A·ΔT·t)/Lk = thermal conductivity

The radiant energy emitted by an object……

Temp T

Q = energy emittedDepends on:A = surface area of objectt = timee = emissivity (depends on surface

and type of radiation), 0<e<1

Q = e T4 A t, Stefan-Boltzmann Law,

with = 5.67 x 10-8 J/sm2K4 , Stefan-Boltzmann Constant

Net Power Emitted by Object = e A (T4 – T0

4)

Recall: Power EnergyTim e

This applies to radiant energy also: Radiant Pow er Q

t e T4 A

Environment at temp T0

Object at temp T

04/22/2317

• Laws of Thermodynamics - First LawEquivalence of different forms of energy

ΔU = Q - W - Second Law

Only fraction of thermal energy can be used to do mechanical work

Eff = 1 – (Tcold / Thot) - Zeroth Law

Temperature is ONLY measure of thermodynamic equilibrium

04/22/2318

Heat Engine (schematic)

For the Heat engine, Change in energy = heat added minus work doneΔU = Q – W

For the Colder region, Entropy = heat added divided by the temperature ΔS = Q/T

Movable piston

Fixed base and walls.

GAS

2 kg

3 m3

GAS2 kg1 m3

Work Done By a Gas: W = P·ΔV , Work = Pressure x change in Volume.

04/22/2320

Carnot Efficiency“To find the Efficiency of a Heat

Engine, take its temperature.”Sadi Carnot (1796-1832) Paris. In his paper, “Reflections on the

Motive Power of Heat”, we find the Carnot efficiency:

Efficiency = (Thot - Tcold) / Thot = 1 – (Tcold / Thot) .

Temperatures in Kelvin. Thot = internal temperature of the engine, and Tcold is temperature of exhaust gases. Typical efficiency today is about 30%.

04/22/2321

1. Hero’s Engine: 100 BC, Greek

inventor, Hero of Alexandria.

Mechanical interaction of heat and water.

HISTORY OF HEAT ENGINES:

04/22/2322

2. Thomas Savery (1650-1715) English military engineer and inventor who in 1698, patented the first crude steam engine, based on a pressure cooker invented in 1679. 

04/22/2323

3. Thomas Newcomen (1663-1729) British blacksmith, invented the

atmospheric steam engine.Improvement over Savery's design.

04/22/2324

• In the 1800’s, US, Fulton and Watt perfected the steam engine. Eff increased from 2% to 20%

• Reasons: 1. Larger engines, 2. Higher pressure and temperature, 3. Special metals

• Steam engine replaced by steam turbine and gasoline engine.

• 2 types of heat engines: 1. Internal combustion, 2. External combustion.

Number of moles n in a sample equals the number of particles N (atoms or molecules) in the sample divided by the number of particles per mole NA. Or n = N/NA NA = 6.022x1023 particles per mole(Avogadro’s Number)

Amedeo Avogadro (1776-1856), Turin, Italy.

Number of moles also equals mass m of the sample (in grams) divided by the mass per mole (in grams per mole ). n = m/(mass per mole). Mass of a particle (in grams) can also be obtained by dividing mass per mole (in g/mol) by Avogadro's number. mparticle = mass per mole/NA.

Temperature is a quantity proportional to the average kinetic energy of the particles. KEavg = ½ mv2

rms where vrms is the root-mean-square speed of the particles, derived statistically by Boltzmann. The internal energy U of n moles of a monatomic ideal gas is U = 3/2 nRT.

Ludwig Boltzmann (1844-1906), Austria, Developed the branch of Physics known as Statistical Mechanics.

Fick’s Law, named after Adolf Eugen Fick (1829-1901), Germany.The mass of a solute that diffuses in time through a channel of known length, L, and cross-sectional area, A, is given by m = (D·A·ΔC)t/L .

ΔC is the solute concentration difference between the ends of the channelD is the diffusion constant.

Zeroth Law of Thermodynamics: “Two systems are in thermal equilibrium if there is no net heat flow between them when they are brought into thermal contact.” First Law of Thermodynamics: “The total increase in thermal energy of a system is equal to the sum of the heat added to it and the work done on it.” ΔU = (Uf -Ui) = Q-W The second law also states that natural processes always go in a direction that increases the entropy, S, unavailable energy, or disorder, of a system. ΔS = Q – W.

A thermal process is considered quasi-static when it occurs slowly enough that a uniform pressure and temperature exist throughout the system at all times.

1. An isobaric process is one that occurs at constant pressure. W = P·ΔV = P(Vf -Vi). 2. An isochoric process is done at constant volume and no work is done. W = 03. An isothermal process is done at constant temperature. W = 04. An adiabatic process takes place without the transfer of heat. W = 3/2 nR(Ti -Tf)

The work done in any kind of quasi-static process is given by the area under the pressure versus volume graph. W = nRT·ln(Vf /Vi).

For an Adiabatic Process, ideal gas obeys:

1. Ideal Gas Law, PV = NRT

2. PiViγ = PfVf

γ, where γ = cp/cv, ratio of specific heat capacities at constant pressure and constant volume.

The molar specific heat capacity of a substance determines how much heat is added or removed when the temperature of n moles of the substance changes.

This is given by the equation Q = C·n·ΔT.

For a monatomic ideal gas, the molar specific heat capacities at constant pressure and constant volume are, respectively,

CP = 5/2 R and CV = 3/2 R, where R = 8.31 J/(mol·K)

the Ideal Gas Constant.

For any ideal gas, the difference between CP and CV is R, or

CP - CV = R.

A heat engine continuously converts thermal energy to mechanical energy and does work.The efficiency, e, of a heat engine is expressed by the equation e = (Work done)/(Input heat) = W/QH. Conservation of energy requires that QH = W + QC . Combining the equations we get, e = 1 – (QC / QH ).

From Carnot, we have QC/QH = TC/TH. This gives an equation for the maximum efficiency that an engine can have operating between two fixed temperatures. e Carnot = 1 - TC/TH.

A heat pump, air conditioner, or refrigerator uses mechanical energy to transfer heat from an area of lower to higher temperature. These are governed by the Law of Conservation of Energy with QH = W + QC.

The coefficient of performance of a refrigerator or air conditioner is given by the equation Coefficient of performance = QC / W.

For the heat pump which also moves heat from a cold area, we have a similar relationship, Coefficient of performance = QH / W.

04/22/2333

Famous Early Automobile Makers 1. Nicolaus August Otto invented the gas motor engine in 1876. 2. In 1885, Gottlieb Daimler invented a gas engine that allowed for a revolution in car design. 3. Karl Benz was the German mechanical engineer who designed and in 1885 built the world's first practical automobile to be powered by an internal-combustion engine. Named it Mercedes, after his daughter.

04/22/2334

Principle of an Internal Combustion Engine

04/22/2335

4 Cycles:1.Induction2.Compression3.Power4.Exhaust

The Internal Combustion Engine

04/22/2336

That Thing Got A Hemi?Sweeeeeeeeeeeeet.

1900’s: Jet engines were developed.Rely on Newton’s 3rd Law (action/reaction) to produce motion.1.RamJet - simple, no moving parts, must be moving to operate, propelled by a rocket. Supersonic? Scramjet.

04/22/2338

2. Turbo-JetTurbine (fan blades) force air into combustion chamber. Thrust produced by escaping hot gases. Auxiliary power must start engine. Ex. Today’s jet engines.

04/22/2339

3. Rocket – reaction force (thrust) produces motion. Carries fuel and oxygen needed for combustion. Travels beyond atmosphere.Specific Impulse of the fuel, S.I. = (Thrust / Weight) x Time                         

SPECIFIC IMPULSE

04/22/2340

Fuel is compressed to ignition temperature. Low power to weight ratio. Cheaper fuel (at one time).

                                   

      

4. DIESEL ENGINE –developed by Rudolf Diesel (1858-1913), Germany.

04/22/2341

5. Gas turbine – continuously drawn-in air. Fan blades. Fuel burns with steady flame. Gases pass through exhaust nozzle at high speed. Runs its own turbine. Used in aircraft.

04/22/2342

Fossil-fuel electric plant: thermodynamics

04/22/2343Phys Hon Subatomic Physics (Ch.25) Page 28(A Nuclear Reactor Used to Boil Water for a Steam TurbineNUCLEAR REACTOR

04/22/2344

Efficiencies of Power Plants

Power plants these days (almost all of which are heat-engines) typically get no better than 33% overall efficiency.

The End.