+ All Categories
Home > Documents > Thermal Physics IB Physics

Thermal Physics IB Physics

Date post: 04-Jan-2016
Category:
Upload: priscilla-copeland
View: 275 times
Download: 19 times
Share this document with a friend
Description:
Thermal Physics IB Physics. Topic 3: Ideal gases. Ideal Gases. Understand and Apply the following. Pressure. Gas Laws (by name) PV = nRT Kinetic Molecular Theory Explain Pressure. WilliamThompson (Lord Kelvin). Pressure. Click on Me. Pressure is defined as force per unit area - PowerPoint PPT Presentation
Popular Tags:
28
Thermal Physics Thermal Physics IB Physics IB Physics Topic 3: Ideal gases Topic 3: Ideal gases
Transcript
Page 1: Thermal Physics IB Physics

Thermal PhysicsThermal PhysicsIB Physics IB Physics

Topic 3: Ideal gasesTopic 3: Ideal gases

Page 2: Thermal Physics IB Physics

Ideal GasesIdeal Gases

Understand and Understand and Apply the following.Apply the following. Pressure. Pressure. Gas Laws (by name)Gas Laws (by name) PV = nRTPV = nRT Kinetic Molecular Kinetic Molecular

TheoryTheory Explain PressureExplain Pressure

WilliamThompson (Lord Kelvin)

Page 3: Thermal Physics IB Physics

PressurePressure Pressure is defined as Pressure is defined as

force per unit areaforce per unit area Newtons per square metre Newtons per square metre

or N/m or N/m22

1 Nm1 Nm-2-2 = 1 Pa (pascal) = 1 Pa (pascal) The weight of the person The weight of the person

is the force applied to is the force applied to the bed and the small the bed and the small area of each nail tip area of each nail tip combines to make an combines to make an overall large area.overall large area.

The result is a small The result is a small enough pressure which enough pressure which does not puncture the does not puncture the person.person.

A

FP

Click on Me

Page 4: Thermal Physics IB Physics

Atmospheric PressureAtmospheric Pressure

Basically weight of atmosphere!Basically weight of atmosphere! Air molecules are colliding with you Air molecules are colliding with you

right now!right now! Pressure = 1.013 x10Pressure = 1.013 x1055 N/m N/m22 = 14.7 = 14.7

lbs/inlbs/in22!! Example: Sphere w/ r = 0.1 mExample: Sphere w/ r = 0.1 m

DemoDemo

A = 4 A = 4 r r22 = .125 m = .125 m22

F = 12,000 Newtons (over 2,500 lbs)!F = 12,000 Newtons (over 2,500 lbs)!

21

Page 5: Thermal Physics IB Physics

Qualitative Demonstration Qualitative Demonstration of Pressureof Pressure

y

t

ymv

typ

yf

force verticalaverage

16

Force due to molecules of fluid colliding with Force due to molecules of fluid colliding with container.container. Force Force αα Impulse = Impulse = pp

Average Pressure = F / AAverage Pressure = F / A

Page 6: Thermal Physics IB Physics

PressurePressure Pressure is defined as force per unit areaPressure is defined as force per unit area

Newtons per square metre N/mNewtons per square metre N/m22

The pressure exerted by a gas results from the The pressure exerted by a gas results from the atoms/ molecules “bumping” into the atoms/ molecules “bumping” into the container wallscontainer walls More atoms gives more bumps per second and More atoms gives more bumps per second and

higher pressurehigher pressure Higher temperature means faster atoms and gives Higher temperature means faster atoms and gives

more bumps per second and higher pressuremore bumps per second and higher pressure At sea level and 20°C, normal atmospheric At sea level and 20°C, normal atmospheric

pressure ispressure is 1atm ≈ 1 x 101atm ≈ 1 x 1055 N/m N/m22

Page 7: Thermal Physics IB Physics

GasesGases Gases (as we will see) can Gases (as we will see) can

behave near perfectly.behave near perfectly. NNAA= 6.02 x 10= 6.02 x 102323 molecules mol molecules mol-1-1

Molecules size ~ 10Molecules size ~ 10-8-8 m to 10 m to 10-10-10 mm

Example: How molecules are there in 6 Example: How molecules are there in 6 grams of hydrogen gas?grams of hydrogen gas?

We have 3 moles, HWe have 3 moles, H22 has 2 grams mol has 2 grams mol-1-1

3 x 6.02 x 103 x 6.02 x 102323 = 1.81 x 10 = 1.81 x 102424 molecules.molecules.

Page 8: Thermal Physics IB Physics

ExampleExampleMake a rough estimate of the number of water Make a rough estimate of the number of water

molecules in an ordinary glass of water.molecules in an ordinary glass of water.

A glass contains about 0.3 L of water, which has A glass contains about 0.3 L of water, which has a mass of about 300 g. Since the molar mass of a mass of about 300 g. Since the molar mass of water (Hwater (H22O) is 18 g molO) is 18 g mol-1-1

Hence, 300g/18g molHence, 300g/18g mol-1-1 ~ 17 mol ~ 10 ~ 17 mol ~ 102525 molecules molecules

Page 9: Thermal Physics IB Physics

The Boyle-Mariotte Law The Boyle-Mariotte Law Gases (at Gases (at constant constant

temperaturetemperature) decrease in ) decrease in volume with increasing volume with increasing pressure.pressure.

P =F/AP =F/A V = V = ππrr22 h h

Page 10: Thermal Physics IB Physics

Figure 17-3Figure 17-3Increasing Pressure by Decreasing VolumeIncreasing Pressure by Decreasing Volume

Page 11: Thermal Physics IB Physics

The Boyle-Mariotte Law The Boyle-Mariotte Law Gases (at constant Gases (at constant

temperature) temperature) decrease in volume decrease in volume with increasing with increasing pressure.pressure.

IsothermalIsothermal ProcessProcess

PV = constantPV = constant

PP11VV11 = P = P22VV22

Page 12: Thermal Physics IB Physics

ExampleExample

The pressure of gas is 2 atm and its The pressure of gas is 2 atm and its volume 0.9 L if the pressure is increased volume 0.9 L if the pressure is increased to 6 atm at constant temperature, what is to 6 atm at constant temperature, what is the new volume?the new volume?

Answer:Answer:PP11VV11 = P = P22VV22

2 x 0.9 = 6 x V; hence V = 0.3 L2 x 0.9 = 6 x V; hence V = 0.3 L

Page 13: Thermal Physics IB Physics

The volume-temperature The volume-temperature law law

Charles & Gay-LussacCharles & Gay-Lussac

IsobaricIsobaric Process Process

V/T = constantV/T = constant

VV1 1 // TT11 = V = V2 2 // TT22

At absolute zero a gas would At absolute zero a gas would take up zero volume. In reality take up zero volume. In reality they liquefy when they get really they liquefy when they get really cold!cold!

Page 14: Thermal Physics IB Physics

The pressure-The pressure-temperature Law temperature Law

Gases (at constant Gases (at constant volume) increase volume) increase in temperature in temperature with increasing with increasing pressure.pressure.

Isochoric ProcessIsochoric Process

P/T= constantP/T= constant

PP11/T/T11 = P = P22/T/T22

0 100 200-200 -100

temp. °C

pres

sure

Page 15: Thermal Physics IB Physics

ExampleExample

A bottle of hair A bottle of hair spray is filled to a spray is filled to a pressure of pressure of 1 atm at 20°C1 atm at 20°C

What is the canister What is the canister pressure if it is pressure if it is placed into boiling placed into boiling water, and allowed water, and allowed to reach thermal to reach thermal equilibrium?equilibrium?

P1/ T1 = P2/ T2

orp1 T2 = p2 T1

1 / 293 = p2 / 373 p2 = 373/293p2 = 1.27 atm

Page 16: Thermal Physics IB Physics

Absolute zeroAbsolute zero

Ideal gas has zero Ideal gas has zero volumevolume

Resistance of metal Resistance of metal drops to zero (actually drops to zero (actually superconductivity cuts in superconductivity cuts in above 0K)above 0K)

Brownian motion ceases!Brownian motion ceases!(kinetic energy = 3/2 kT)(kinetic energy = 3/2 kT)

But lowest temperature But lowest temperature attained is ≈ 10attained is ≈ 10-9-9KK

0-273 °C temp. °C

pres

sure

Page 17: Thermal Physics IB Physics

Equations of stateEquations of state

State, identifies whether solid liquid State, identifies whether solid liquid or gasor gas

Key parameters or state variablesKey parameters or state variables Volume, V (mVolume, V (m33)) Pressure, p (N/mPressure, p (N/m22)) Temperature, T (K)Temperature, T (K) Mass, M (kg) or number of moles, Mass, M (kg) or number of moles, nn

Equation of state relates V, p , T, m Equation of state relates V, p , T, m or or nn

Page 18: Thermal Physics IB Physics

Bulk vs moleculesBulk vs molecules

Consider force Consider force between two between two molecules molecules

At absolute zeroAt absolute zero No thermal energyNo thermal energy Molecules sit at rMolecules sit at r00

Above absolute zeroAbove absolute zero Some thermal energySome thermal energy Molecules are at r> rMolecules are at r> r0 0

(thermal expansion)(thermal expansion) At high temperatureAt high temperature

Thermal energy > Thermal energy > binding energybinding energy

Molecules form a gasMolecules form a gas

r

forceenergy

r0repulsion

attractionbindingenergy

thermal energy

Page 19: Thermal Physics IB Physics

Equation of state for a Equation of state for a gasgas

All gases behave nearly the sameAll gases behave nearly the same pV = pV = nnRTRT

R = 8.3 J/(mol K) for R = 8.3 J/(mol K) for allall gases (as long as gases (as long as they remain a gas)they remain a gas)

T is in K!!!!!!T is in K!!!!!!

Page 20: Thermal Physics IB Physics

ExampleExample

What is the mass What is the mass of a cubic metre of of a cubic metre of air?air? Molecular weigh of Molecular weigh of

air ≈ 32gair ≈ 32g

pV = nRT

Atmospheric pressure = 105 N/m2

Atmospheric temp. = 300K

For a volume of 1 m3

n = pV/RT = 105 / (8.3 x 300) = 40 moles

M = 40 x 0.032 = 1.3kg

Page 21: Thermal Physics IB Physics

Constant mass of gasConstant mass of gas

For a fixed amount of gas, its mass or For a fixed amount of gas, its mass or number of moles remains the samenumber of moles remains the same pV/T = pV/T = nnR = constantR = constant

Comparing the same gas under different Comparing the same gas under different conditionsconditions pp11VV11/T/T11 = p = p22VV22/T/T22

Hence can use pressure of a constant volume of gas Hence can use pressure of a constant volume of gas to define temperature (works even if gas is impure - to define temperature (works even if gas is impure - since all gases the same)since all gases the same)

Must use T in K!!!!!!Must use T in K!!!!!!

Page 22: Thermal Physics IB Physics

ExampleExample

A hot air balloon A hot air balloon has a volume of has a volume of 150m150m33

If heated from If heated from 20°C to 60°C how 20°C to 60°C how much lighter does much lighter does it get?it get? Molecular weight of Molecular weight of

air ≈32gair ≈32g

pV/T = nRn = pV/RT

Balloon has constant volume and constant pressure

ncool =105x150 / (8.3 x293) = 61680

nhot =105x150 / (8.3 x333) = 54271 n = 7409 moles

M = 7409 x 0.032 = 237kg

Page 23: Thermal Physics IB Physics

Molecules have finite Molecules have finite sizesize

Cannot reduce volume of gas to zero!Cannot reduce volume of gas to zero! When you try, it becomes a liquidWhen you try, it becomes a liquid Slightly increases the measured volumeSlightly increases the measured volume

Atoms/ molecules always attract each Atoms/ molecules always attract each otherother Slightly reduces the measured pressureSlightly reduces the measured pressure Van de Waals forcesVan de Waals forces

Page 24: Thermal Physics IB Physics

p-V diagrams (for gases)p-V diagrams (for gases) Useful to Useful to

consider the consider the pressure/volume pressure/volume changes at changes at constant constant temperaturetemperature Isotherms are p-V Isotherms are p-V

values for a fixed values for a fixed amount of gas at amount of gas at constant volumeconstant volume

p p 1/V 1/Vvolume

Pre

ssur

e

Increasing temperature

Page 25: Thermal Physics IB Physics

Kinetic theory of Kinetic theory of gasesgases

A gas consists of a large number A gas consists of a large number of molecules.of molecules.

Molecules move randomly with a range Molecules move randomly with a range of speeds. (Maxwell's Distribution)of speeds. (Maxwell's Distribution)

The Volume of the molecule is negligible The Volume of the molecule is negligible compared with the volume of the gas compared with the volume of the gas itself.itself.

Collisions are elastic (KE conserved)Collisions are elastic (KE conserved) No inter-molecular forces.No inter-molecular forces. Collision time with walls are very smal.Collision time with walls are very smal. Molecules obey Newton’s Laws of Molecules obey Newton’s Laws of

Mechanics Mechanics

Page 26: Thermal Physics IB Physics

Molecules in a gasMolecules in a gas Gas atoms/molecules move Gas atoms/molecules move

in a straight linein a straight line velocity due to thermal energyvelocity due to thermal energy

KE = 1/2 m vKE = 1/2 m vxx22 ≈ 3/2 kT ≈ 3/2 kT

KEKEavgavg α absolute temp absolute temp RMS – (Root mean squared)RMS – (Root mean squared)

Pressure results from Pressure results from collisions with the walls of collisions with the walls of the container. the container. (NOT collisions between (NOT collisions between moleculesmolecules FFimpactimpact = = ΔΔp/t = p/t = (2m v(2m vxx)/t)/t

Page 27: Thermal Physics IB Physics

ExampleExample

How fast does a typical gas molecule How fast does a typical gas molecule (travel at room temperature? Lets take (travel at room temperature? Lets take Nitrogen-14!Nitrogen-14!(k = 1.38x10(k = 1.38x10-23-23J/K) J/K) KE = 1/2 mv2 = 3/2 kT

v = (3kT/m)1/2

v = [(3)(1.38x10-23 x 293/(4.65x10-26)]1/2

v = 511 m/sec

Page 28: Thermal Physics IB Physics

ExampleExample If it takes 2 mins If it takes 2 mins

for your kettle to for your kettle to begin boiling how begin boiling how much longer does much longer does it take to boil dry?it take to boil dry? Assume kettle is Assume kettle is

3kW3kW Starting temp of Starting temp of

water 20°Cwater 20°C

Work done by kettle = power x time = 2 x 60 x 3000 = 360 000J

= Work to boil water of mass M = T x M x cwater 360 000J = 80 x M x 4190

Mass of water = 1.07kg

Energy to boil water = M x Lv (water)

= 1.07 x 2256 x103 = 2420 000J

Time required = Energy /power = 2420 000/3000 = 808 s ≈ 13mins


Recommended