The Ideal Gas Ideal Gas Law Van der Waals Equation Distribution of Molecular Speeds

The Ideal GasThe Ideal Gas

Ideal Gas LawIdeal Gas Law

Van der Waals EquationVan der Waals Equation

Distribution of Molecular SpeedsDistribution of Molecular Speeds

Reading QuestionReading QuestionWhat is the SI unit of pressure?

1. The Nm2 (Newton-meter-squared)2. The atmosphere3. The p.s.i. 4. The Pascal5. The Archimedes

Reading QuestionReading QuestionWhat is the SI unit of pressure?

1. The Nm2 (Newton-meter-squared)2. The atmosphere3. The p.s.i. 4. The Pascal5. The Archimedes

Reading QuestionReading Question

The ideal gas model is valid if

1. the gas density is low. 2. the gas density is high. 3. the temperature is low.4. the gas pressure is large.5. none of the above

Reading QuestionReading Question

The ideal gas model is valid if

1. the gas density is low. 2. the gas density is high. 3. the temperature is low.4. the gas pressure is large.5. none of the above

Reading QuestionReading Question

An ideal-gas process in which the volume doesn’t change is called

1. isobaric.2. isothermal.3. isochoric.4. isentropic.

Reading QuestionReading Question

An ideal-gas process in which the volume doesn’t change is called

1. isobaric.2. isothermal.3. isochoric.4. isentropic.

The Ideal GasThe Ideal GasHeat of Transformation• Heat of fusion – the heat to transform a gram of substance from solid to liquid.

• Heat of vaporization – the heat to transform a gram of substance from liquid to gas.

• Sublimation – solid to gas

Slope heat capacity

Q time

Qf = mLf

Qv = mLv

The Ideal GasThe Ideal Gas

SubstanceSubstance Melting Melting point, Kpoint, K

Lf, kJ/kgLf, kJ/kg Boiling Boiling point, Kpoint, K

Lv, kJ/kgLv, kJ/kg

AlcoholAlcohol 159159 109109 351351 879879

CopperCopper 13571357 205205 28402840 47264726

MercuryMercury

OxygenOxygen 54.854.8 13.813.8 90.290.2 213213

SulfurSulfur

WaterWater 273273 334334 373373 22572257

Heat of TransformationHeat of Transformation

The Ideal GasThe Ideal Gas

Sublimation

Boiling

Phase DiagramPhase Diagram

The Ideal GasThe Ideal Gas• Phase Diagram for Water

The Ideal GasThe Ideal Gas

Student WorkbookStudent Workbook

freezing point at temperature T

triple point

boiling point at pressure p

critical pointsublimation at pressure p

Student WorkbookStudent Workbook

boiling point temperature decreases

Class QuestionClass QuestionWhen you warm up CO2 or dry ice it goes directly from a solid to a gas. This processes is called

1. critical point2. sublimation3. isochoric processes4. isentropic processes5. None of the above.

Class QuestionClass QuestionWhen you warm up CO2 or dry ice it goes directly from a solid to a gas. This processes is called

1. critical point2. sublimation3. isochoric processes4. isentropic processes5. None of the above.

The Ideal GasThe Ideal GasThe Ideal Gas LawThe Ideal Gas Law

NkTPV • P pressure exerted by the gas (Pa)• V volume of the gas• N number of molecules in the gas (m3)• T temperature of the gas (K)• k = 1.38X10-23 J/K Boltzmann’s constant

Most real gases obey this law with very slight deviations

A mole is 6.022X1023 molecules. nRTPV • R = NAk = 8.314 J/Kmole universal gas constant

The Ideal GasThe Ideal Gas Quasi-static and Irreversible ProcessesQuasi-static and Irreversible Processes

The Ideal GasThe Ideal Gas Isochoric ProcessesIsochoric Processes

The Ideal GasThe Ideal Gas Isobaric ProcessesIsobaric Processes

The Ideal GasThe Ideal Gas Isothermal ProcessesIsothermal Processes

The Ideal GasThe Ideal Gas Isothermal ProcessesIsothermal Processes

Student WorkbookStudent Workbook

w

atmF

0netF

because the liquid is not accelerating

the pressure is less.

Student WorkbookStudent Workbook

NkTPV pVT

Nk

22

2

11

1

VpT

VpT

11

2

11

1

23 VpT

VpT

12 6TT

Student WorkbookStudent Workbook

NkTpV VTp

Nk

22

2

11

1

VpT

VpT

12

1

11

1

32

VpT

VpT

12 32

pp

Student WorkbookStudent Workbook

Student WorkbookStudent Workbook

isochoric isothermal isobaric

00

011

Student WorkbookStudent Workbook

NkTpV

Class QuestionClass Question

1. Thelium < Tnitrogen

2. Thelium = Tnitrogen

3. Thelium > Tnitrogen

4. There is not enough information

You have two containers of equal volume. One is full of helium gas. The other holds an equal mass of nitrogen gas. Both gases have the same pressure. How does the temperature of the helium compare to the temperature of the nitrogen?

Class QuestionClass Question

1. Thelium < Tnitrogen

2. Thelium = Tnitrogen

3. Thelium > Tnitrogen

4. There is not enough information

You have two containers of equal volume. One is full of helium gas. The other holds an equal mass of nitrogen gas. Both gases have the same pressure. How does the temperature of the helium compare to the temperature of the nitrogen?

Class QuestionClass Question

What is the ratio Tf /Ti for this process?

1. 42. 23. 1 (no change)

4.

5.

Class QuestionClass Question

What is the ratio Tf /Ti for this process?

1. 42. 23. 1 (no change)

4.

5.

The Ideal GasThe Ideal GasKinetic Theory of the Ideal GasKinetic Theory of the Ideal Gas

The Ideal GasThe Ideal GasKinetic Theory of the Ideal GasKinetic Theory of the Ideal Gas

KvmkT

2

21

23

mkT

vthermal

3

vevkT

mNvvN kT

vm

2

21

2

23

24)(

The Ideal GasThe Ideal GasReal GasesReal Gases

Van der Waals Equation

kTnbVV

anP

2

2

Takes into account1. Size of the molecules2. Interaction between the molecules