PHYSICS 231 INTRODUCTORY PHYSICS I · INTRODUCTORY PHYSICS I Lecture 18. The Laws of Thermodynamics...

PHYSICS 231

INTRODUCTORY PHYSICS I

Lecture 18

The Laws of ThermodynamicsThe Laws of Thermodynamics

Chapter 12

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

• Adding heat Q can:

• Change temperature

• Change state of matter

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

Work done on a gas

Change ofInternal Energy !U

Work done on the gas

!

W =r F " #

r x = F($#y) = (PA)($#y)

!

W = "P#V

First Law of Thermodynamics

!

"U =Q+W

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

•Conservation of Energy•Can change internal energy !U by

• Adding heat to gas: Q• Doing work on gas:

!

W = "P#V

!

Q = "U +Wby the gas

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

Wby the gas = +P"V

Example 12.1

A cylinder of radius 5 cm is kept at pressure with apiston 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

A massive copper piston traps an idealgas as shown to the right. The piston isallowed to freely slide up and down andequilibrate with the outside air.

The pressure inside thecylinder is _________ thepressure outside.

a) Greater thanb) Less thanc) Equal to

Example 12.2b

A massive copper piston traps an idealgas as shown to the right. The piston isallowed to freely slide up and down andequilibrate with the outside air.

The temperature inside the cylinderis __________ the temperatureoutside.


Example 12.2c

A massive copper piston traps an idealgas as shown to the right. The pistonis allowed to freely slide up and downand equilibrate with the outside air.

If the gas is heated by a steadyflame, and the piston rises to a newequilibrium position, the new pressurewill be _________ thanthe previous pressure.


Some Vocabulary

• Isobaric• P = constant

• Isovolumetric• V = constant• W = 0

• Isothermal• T = constant• !U = 0 (ideal gas)

• Adiabatic• Q = 0

V

V

V

V

P

P

P

P

A massive piston traps an amount ofHelium gas as shown. The piston freelyslides up and down.The system initially equilibrates atroom temperature (a)Weight is slowly added to the piston,isothermally compressing the gas tohalf its original volume (b)

Pb is _______ Pa

Outside Air: Room T, Atm. PExample 12.3a


!

"U =Q# P"V

Wby the gas = P"V


Tb is ________ Ta

Outside Air: Room T, Atm. PExample 12.3b


!

"U =Q# P"V

Wby the gas = P"V


Wab is ________ 0

Outside Air: Room T, Atm. P

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

Example 12.3c


!

"U =Q# P"V

Wby the gas = P"V


Ub is ________ Ua

Outside Air: Room T, Atm. PExample 12.3d


!

"U =Q# P"V

Wby the gas = P"V


Qab is ________ 0

Outside Air: Room T, Atm. P

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

Example 12.3e


!

"U =Q# P"V

Wby the gas = P"V

A massive piston traps an amount ofHelium gas as shown. The piston freelyslides up and down.The system initially equilibrates atroom temperature (a)Weight is slowly added to the piston,adiabatically compressing the gas tohalf its original volume (b)

Pb is _______ Pa



!

"U =Q# P"V

Wby the gas = P"V


Wab is ______ 0



!

"U =Q# P"V

Wby the gas = P"V


Qab is _______ 0

Outside Air: Room T, Atm. PExample 12.4c


!

"U =Q# P"V

Wby the gas = P"V


Ub is _______ Ua



!

"U =Q# P"V

Wby the gas = P"V


Tb is _______ Ta

Outside Air: Room T, Atm. PExample 12.4e


!

"U =Q# P"V

Wby the gas = P"V

A massive piston traps an amount ofHelium gas as shown. The piston freelyslides up and down.The system initially equilibrates atroom temperature (a)The gas is cooled, isobaricallycompressing the gas to half itsoriginal volume (b)

Pb is _______ Pa



PV = nRT

!

"U =Q# P"V

Wby the gas = P"V


Wab is _______ 0



PV = nRT

!

"U =Q# P"V

Wby the gas = P"V


Tb is _______ Ta

Outside Air: Room T, Atm. PExample 12.5c


PV = nRT

!

"U =Q# P"V

Wby the gas = P"V


Ub is _______ Ua



PV = nRT

!

"U =Q# P"V

Wby the gas = P"V


Qab is _______ 0

Outside Air: Room T, Atm. PExample 12.5e


PV = nRT

!

"U =Q# P"V

Wby the gas = P"V

P-V DiagramsP

V

Path moves to right:

Wby the gas = Area under curve

P

V

Path moves to left:

Wby the gas = - Area under curve

(Won the gas = - Wby the gas)

Work from closed cycles

Consider cycle A -> B -> A

WA->B = Area

WB->A = - Area

(work done by gas)


Consider cycle A -> B -> A

WA->B->A= Area

(work done by gas)


Reverse the cycle, make it counter clockwise

WB->A = - Area

WA->B = Area

(work done by gas)


WA->B->A= - Area

Reverse the cycle, make it counter clockwise

(work done by gas)

Internal Energy in closed cycles

in closed cycles

!

"U = 0

Example 12.6 a) What amount of work isperformed by the gas in thecycle IAFI?

b) How much heat wasinserted into the gas in thecycle IAFI?

c) What amount of work isperformed by the gas in thecycle IBFI?

W=3.04x105 J

W = -3.04x105 J

Q = 3.04x105 J

V (m3)

Example 12.7Consider a monotonic ideal gas.

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

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

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

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

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

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

V (m3)

P (kPa)

25

50

75

0.2 0.4 0.6

A

B

C

20,000 J

20,000

-10,000 J

-25,000 J

0

15,000 J

Example Continued

Take solutions from last problem and find:

a) Net work done by gas in the cycleb) Amount of heat added to gas

WAB + WBC + WCA = 10,000 JQAB + QBC + QCA = 10,000 J

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

Example 12.8a

Consider an ideal gasundergoing the trajectorythrough the PV diagram.In going from A to B toC, the work done BY thegas is _______ 0.

P

V

AB

a) >

b) <

c) =

C

Example 12.8b

In going from A to B toC, the change of theinternal energy of thegas is _______ 0.

P

V

AB

a) >

b) <

c) =

C

Example 12.8c

In going from A to B toC, the amount of heatadded to the gas is_______ 0.

P

V

AB

a) >

b) <

c) =

CD

Example 12.8d

In going from A to B toC to D to A, the workdone BY the gas is_______ 0.

P

V

AB

a) >

b) <

c) =

CD

Example 12.8e

In going from A to B toC to D to A, the changeof the internal energy ofthe gas is _______ 0.

P

V

AB

a) >

b) <

c) =

CD

Example 12.8f

In going from A to B toC to D to A, the heatadded to the gas is_______ 0.

P

V

AB

a) >

b) <

c) =

CD

PHYSICS 231 INTRODUCTORY PHYSICS I · INTRODUCTORY PHYSICS I Lecture 18. The Laws of Thermodynamics...

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