Physics 231 introductory physics i
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PHYSICS 231 INTRODUCTORY PHYSICS I. Lecture 18. Chapter 12. The Laws of Thermodynamics. Principles of Thermodynamics. Energy is conserved FIRST LAW OF THERMODYNAMICS Examples: Engines (Heat -> Mechanical Energy) Friction (Mechanical Energy -> Heat) All processes must increase entropy

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PHYSICS 231 INTRODUCTORY PHYSICS I

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Physics 231 introductory physics i

PHYSICS 231INTRODUCTORY PHYSICS I

Lecture 18


Chapter 12

Chapter 12

The Laws of Thermodynamics


Principles of thermodynamics

Principles of Thermodynamics

  • Energy is conserved

    • FIRST LAW OF THERMODYNAMICS

    • Examples:

      • Engines (Heat -> Mechanical Energy)

      • Friction (Mechanical Energy -> Heat)

  • All processes must increase entropy

    • SECOND LAW OF THERMODYNAMICS

    • Entropy is measure of disorder

    • Engines can not be 100% efficient


Work done on a gas

Work done on a gas

  • Adding heat Q can:

    • Change temperature

    • Change state of matter

  • Can also change U by doing work on the gas

Change of

Internal Energy U

Work done on the gas


First law of thermodynamics

  • Conservation of Energy

  • Can change internal energy U by

    • Adding heat to gas: Q

    • Doing work on gas:

First Law of Thermodynamics

Note:

(Work done by the gas) = - (Work done on the gas)

Add heat => Increase Int. Energy & Gas does work


Example 12 1

Example 12.1

A cylinder of radius 5 cm is kept at pressure with a piston of mass 75 kg.

a) What is the pressure inside the cylinder?

b) If the gas expands such that the cylinder rises 12.0 cm, what work was done by the gas?

c) What amount of the work went into changing the gravitational PE of the piston?

d) Where did the rest of the work go?

1.950x105 Pa

183.8 J

88.3 J

Compressing the outside air


Example 12 2a

Example 12.2a

A massive copper piston traps an ideal gas as shown to the right. The piston is allowed to freely slide up and down and equilibrate with the outside air.

The pressure inside thecylinder is _________ thepressure outside.

a) Greater than

b) Less than

c) Equal to


Example 12 2b

Example 12.2b

A massive copper piston traps an ideal gas as shown to the right. The piston is allowed to freely slide up and down and equilibrate with the outside air.

The temperature inside the cylinder is __________ the temperatureoutside.

a) Greater than

b) Less than

c) Equal to


Example 12 2c

Example 12.2c

A massive copper piston traps an ideal gas as shown to the right. The piston is allowed to freely slide up and down and equilibrate with the outside air.

If the gas is heated by a steady

flame, and the piston rises to a new equilibrium position, the new pressure will be _________ than

the previous pressure.

a) Greater than

b) Less than

c) Equal to


Some vocabulary

V

V

V

V

Some Vocabulary

P

  • Isobaric

    • P = constant

  • Isovolumetric

    • V = constant

    • W = 0

  • Isothermal

    • T = constant

    • U = 0 (ideal gas)

  • Adiabatic

    • Q = 0

P

P

P


Example 12 3a

Example 12.3a

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

Weight is slowly added to the piston, isothermally compressing the gas to

half its original volume (b)

Pb is _______ Pa

a) Greater than

b) Less than

c) Equal to


Example 12 3b

Example 12.3b

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

Weight is slowly added to the piston, isothermally compressing the gas to

half its original volume (b)

Tb is ________ Ta

a) Greater than

b) Less than

c) Equal to


Example 12 3c

Example 12.3c

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

Weight is slowly added to the piston, isothermally compressing the gas to

half its original volume (b)

Wab is ________ 0

a) Greater than

b) Less than

c) Equal to

Vocabulary: Wab is work done by gas between a and b


Example 12 3d

Example 12.3d

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

Weight is slowly added to the piston, isothermally compressing the gas to

half its original volume (b)

Ub is ________ Ua

a) Greater than

b) Less than

c) Equal to


Example 12 3e

Example 12.3e

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

Weight is slowly added to the piston, isothermally compressing the gas to

half its original volume (b)

Qab is ________ 0

a) Greater than

b) Less than

c) Equal to

Vocabulary: Qab is heat added to gas between a and b


Example 12 4a

Example 12.4a

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

Weight is slowly added to the piston, adiabatically compressing the gas to

half its original volume (b)

Pb is _______ Pa

a) Greater than

b) Less than

c) Equal to


Example 12 4b

Example 12.4b

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

Weight is slowly added to the piston, adiabatically compressing the gas to

half its original volume (b)

Wab is ______ 0

a) Greater than

b) Less than

c) Equal to


Example 12 4c

Example 12.4c

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

Weight is slowly added to the piston, adiabatically compressing the gas to

half its original volume (b)

Qab is _______ 0

a) Greater than

b) Less than

c) Equal to


Example 12 4d

Example 12.4d

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

Weight is slowly added to the piston, adiabatically compressing the gas to

half its original volume (b)

Ub is _______ Ua

a) Greater than

b) Less than

c) Equal to


Example 12 4e

Example 12.4e

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

Weight is slowly added to the piston, adiabatically compressing the gas to

half its original volume (b)

Tb is _______ Ta

a) Greater than

b) Less than

c) Equal to


Example 12 5a

Example 12.5a

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

The gas is cooled, isobarically compressing the gas to half its original volume (b)

Pb is _______ Pa

a) Greater than

b) Less than

c) Equal to


Example 12 5b

Example 12.5b

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

The gas is cooled, isobarically compressing the gas to half its original volume (b)

Wab is _______ 0

a) Greater than

b) Less than

c) Equal to


Example 12 5c

Example 12.5c

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

The gas is cooled, isobarically compressing the gas to half its original volume (b)

Tb is _______ Ta

a) Greater than

b) Less than

c) Equal to


Example 12 5d

Example 12.5d

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

The gas is cooled, isobarically compressing the gas to half its original volume (b)

Ub is _______ Ua

a) Greater than

b) Less than

c) Equal to


Example 12 5e

Example 12.5e

Outside Air: Room T, Atm. P

A massive piston traps an amount of

Helium gas as shown. The piston freely slides up and down.

The system initially equilibrates at

room temperature (a)

The gas is cooled, isobarically compressing the gas to half its original volume (b)

Qab is _______ 0

a) Greater than

b) Less than

c) Equal to


P v diagrams

P-V Diagrams

P

Path moves to right:

Wby the gas = Area under curve

P

V

Path moves to left:

Wby the gas = - Area under curve

V

(Won the gas = - Wby the gas)


Work from closed cycles

WA->B = Area

WB->A = - Area

Work from closed cycles

Consider cycle A -> B -> A

(work done by gas)


Work from closed cycles1

Work from closed cycles

Consider cycle A -> B -> A

WA->B->A= Area

(work done by gas)


Work from closed cycles2

WB->A = - Area

WA->B = Area

Work from closed cycles

Reverse the cycle, make it counter clockwise

(work done by gas)


Work from closed cycles3

Work from closed cycles

Reverse the cycle, make it counter clockwise

WA->B->A= - Area

(work done by gas)


Internal energy in closed cycles

Internal Energy in closed cycles

in closed cycles


Example 12 6

Example 12.6

a) What amount of work is performed by the gas in the cycle IAFI?

b) How much heat was inserted into the gas in the cycle IAFI?

c) What amount of work is performed by the gas in the cycle IBFI?

W=3.04x105 J

Q = 3.04x105 J

V (m3)

W = -3.04x105 J


Example 12 7

Example 12.7

Consider a monotonic ideal gas.

a) What work was done by the gas from A to B?

b) What heat was added to the gas between A and B?

c) What work was done by the gas from B to C?

d) What heat was added to the gas beween B and C?

e) What work was done by the gas from C to A?

f) What heat was added to the gas from C to A?

P (kPa)

A

75

20,000 J

50

20,000

B

25

-10,000 J

C

V (m3)

-25,000 J

0.2

0.4

0.6

0

15,000 J


Example continued

Example Continued

Take solutions from last problem and find:

a) Net work done by gas in the cycle

b) Amount of heat added to gas

WAB + WBC + WCA = 10,000 J

QAB + QBC + QCA = 10,000 J

This does NOT mean that the engine is 100% efficient!


Example 12 8a

Example 12.8a

C

P

Consider an ideal gas undergoing the trajectory through the PV diagram.

In going from A to B to C, the work done BY the gas is _______ 0.

B

A

V

>

<

=


Example 12 8b

Example 12.8b

C

P

In going from A to B to C, the change of the internal energy of the gas is _______ 0.

B

A

V

>

<

=


Example 12 8c

Example 12.8c

C

D

P

In going from A to B to C, the amount of heat added to the gas is _______ 0.

B

A

V

>

<

=


Example 12 8d

Example 12.8d

C

D

P

In going from A to B to C to D to A, the work done BY the gas is _______ 0.

B

A

V

>

<

=


Example 12 8e

Example 12.8e

C

D

P

In going from A to B to C to D to A, the change of the internal energy of the gas is _______ 0.

B

A

V

>

<

=


Example 12 8f

Example 12.8f

C

D

P

In going from A to B to C to D to A, the heat added to the gas is _______ 0.

B

A

V

>

<

=


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