phy 113 c general physics i 11 am – 12:15 p m mwf olin 101 plan for lecture 23:

PHY 113 C Fall 2013 -- Lecture 23 111/19/2013

PHY 113 C General Physics I11 AM – 12:15 PM MWF Olin 101

Plan for Lecture 23:Chapter 22: Heat engines

1. Thermodynamic cycles; work and heat efficiency

2. Carnot cycle3. Otto cycle; diesel cycle4. Brief comments on entropy


Comment about Exam 3:

• Part I – take home portion (1 problem): available Thursday 11/21/2013 after class; must be turned in before Part II – in-class portion (3 problems): Tuesday 11/25/2013

• Some special arrangements for early exams have been (or will be) arranged by prior agreement

• Of course, all sections of the exam are to be taken under the guidelines of the honor code


Important equations for macroscopic and microscopic descriptions of thermodynamic properties of matter

1 :/ with moleculesFor

31

21

32

21

32

) massmolar of moles or mass of molecules (assume :molecules gas of analysis cMicroscopi

:Law Gas Ideal

: WorkmicThermodyna

:micsThermodyna of LawFirst

int

2

220

0

int

nRTECC

RTMv

nRTMvnvmNPV

MnmN

nRTPV

PdVW

WQΔE

VP

rms

rmsrms

V

V

f

i


Webassign – Assignment 20

The rms speed of an oxygen molecule (O2) in a container of oxygen gas is 563 m/s. What is the temperature of the gas?

RTMv

nRTMvnvmNPV

MnmN

rms

rmsrms

2

220

0

31

21

32

21

32

) massmolar of moles or mass of molecules (assume

:molecules gas of analysis kinetic theFrom



In a constant-volume process, 213 J of energy is transferred by heat to 0.99 mol of an ideal monatomic gas initially at 299 K. (a) Find the work done on the gas.

(b) Find the increase in internal energy of the gas.

(c) Find its final temperature.

For constant volume process, W=0.

DEint = Q + 0 = 213J + 0 = 213 J

ifV TTnCQ



A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.06 atm and a volume of 12.2 L to a final volume of 29.6 L. (a) What is the final pressure of the gas?(b) What are the initial and final temperatures?(c) Find Q for the gas during this process.(d) Find ΔEint for the gas during this process.(e) Find W for the gas during this process.


Digression: Adiabatic process (Q=0)

γγγ

γ

lnln

γ

1γ

ffiii

f

i

f VPVPPP

VV

PP

VV

VPPVVP-TnR

DD

DDDD

TnRVPPVnRTPV

VPTR-n

WE

DDD

DD

D

1γ

int



A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.06 atm and a volume of 12.2 L to a final volume of 29.6 L.

(a) What is the final pressure of the gas?

b) What are the initial and final temperatures?PV=nRT

c) Find Q for the gas during this process. Q=0d) Find ΔEint for the gas during this process. ΔEint=We) Find W for the gas during this process.

For diatomic ideal gas: 1.4

4.1

γγ

12.2/29.6atm06.5/

fiif

ffii

VVPP

VPVP



(a) How much work is required to compress 4.95 mol of air at 19.6°C and 1.00 atm to one-tenth of the original volume by an isothermal process?

(b) How much work is required to produce the same compression in an adiabatic process?

(c) What is the final pressure in part (a)?

(d) What is the final pressure in part (b)?



(a) How much work is required to compress 4.95 mol of air at 19.6°C and 1.00 atm to one-tenth of the original volume by an isothermal process?

101ln75.292314.895.4

ln

:process isothermalan For

W

VV

nRTdVV

nRTW

VnRTP

PdVW

i

fV

V

V

V

f

i

f

i



(b) How much work is required to compress 4.95 mol of air at 19.6°C and 1.00 atm to one-tenth of the original volume by an adiabatic process? Note: assume 1.4

RRC

VVTT

VTVT

TTnCWE

V

f

iif

iiff

ifV

5.21

11074.292

:process adiabatican For

:process adiabatican For

4.01

11

int

D


Thermodynamic cycles for designing ideal engines and heat pumps

P (1

.013

x 1

05 ) Pa

Vi Vf

Pi

Pf

A

B C

Din

eng

outin

eng

QW

QQQ

WW

:Efficiency

:system input toHeat

:engine ofWork

Engine process:http://auto.howstuffworks.com/engine1.htm

http://auto.howstuffworks.com/engine1.htm


P (1

.013

x 1

05 ) P

a

Vi Vf

Pi

Pf

A

B C

D

Examples process by an ideal gas:

A®B B®C C®D D®A

Q

W 0 -Pf(Vf-Vi) 0 Pi(Vf-Vi)

DEint

1-γ)( ifi PPV

1-γ)(γ iff VVP

1-γ)( iff PPV

1-γ)(γ ifi VVP-

1-γ)( ifi PPV

1-γ)( iff PPV

1-γ)( iff VVP

1-γ)( ifi VV-P

BCAB

ifif

in

eng

QQVVPP

QW

:Efficiency


Example from homework

BCAB

ifif

in

eng

QQVVPP

QW

:Efficiency

BCAB

DACD

in

out

in

outin

outineng

QQQQ

QQ

QQQ

QQQWW

1

1

:Also


Most efficient thermodynamic cycle -- Carnot

Sadi Carnot 1796-1832


Carnot cycle:AB Isothermal at Th

BC AdiabaticCD Isothermal at Tc

DA Adiabatic

h

c

in

out

in

outin

TTε

QQ

QQQ

1

1

cycleCarnot of Efficiency


iclicker exercise:We discussed the efficiency of an engine as

Is this resultA. Special to the Carnot cycleB. General to all ideal thermodynamic cycles

iclicker exercise:We discussed the efficiency of an engine running with hot and cold reservoirs as

Is this resultA. Special to the Carnot cycleB. General to all ideal thermodynamic cycles

in

out

in

outin

QQ

QQQ

1

h

c

TT

1


h

c

in

out

ABDC

DcAh

CcBh

ABh

DCc

CD

AB

in

out

TT

QQ

VVVVVTVT

VTVT

VVnRTVVnRT

WW

QQ

//

process adiabaticFor

)/ln()/ln(

:cycleCarnot afor that Note

11

11

h

c

TT

1 For Carnot cycle:


iclicker exercise:Why should we care about the Carnot cycle?

A. We shouldn’tB. It approximately models some

heating and cooling technologiesC. It provides insight into another

thermodynamic variable -- entropy


Webassign Assignment 21

A heat engine operates between a reservoir at 28°C and one at 362°C. What is the maximum efficiency possible for this engine?

36215.2732815.27311

:res temperatucold andhot between operating processefficient most theis cycleCarnot The

h

c

TT


Webassign Assignment 21

An ideal gas is taken through a Carnot cycle. The isothermal expansion occurs at 260°C, and the isothermal compression takes place at 50.0°C. The gas takes in 1.28 x103 J of energy from the hot reservoir during the isothermal expansion.

(a) Find the energy expelled to the cold reservoir in each cycle.

(b) (b) Find the net work done by the gas in each cycle.h

c

h

c

QQ

TT

126015.2735015.27311


The Otto cycle

1

1

21

:efficiency lTheoretica

VV

V1/V2 is the “compression ratio” -- typically V1/V2 = 8 =0.56


The Diesel cycle

BC

AD

TTTT

11

:efficiency lTheoretica

In principle, higher efficiency than comparable Otto cycle.


Engine vs heating/cooling designs

(Carnot)

: mode heating pump;Heat

ch

hh

TTT

WQ

(Carnot)

: mode cooling pump;Heat

ch

cc

TTT

WQ


Brief comments about entropy – macroscopic picture

Carnot cycle

h

h

c

c

h

c

h

c

ABDC

DcAh

CcBh

ABh

DCc

CD

AB

h

c

TQ

TQ

TT

QQ

VVVVVTVT

VTVT

VVnRTVVnRT

WW

QQ

//

process adiabaticFor

)/ln()/ln(

:cycleCarnot afor that Note

11

11


Brief comments about entropy – continued

) (like variable"state"

0 cycleCarnot aFor

:Define

:cycleCarnot aFor

intESTQ

TQ

S

TdQdS

TQ

TQ

c

c

h

hcycle

h

h

c

c

D

KJJS

TmL

TdQS

f

i

Q

Q melting

fusion

/1219K 15.273

333000 K) (273.15 C 0at water kg 1 meltingFor

:melting ileentropy wh of Change

:entropy of examplesOther

ooo D

D

phy 113 c general physics i 11 am – 12:15 p m mwf olin 101 plan for lecture 23:

Documents

c fall

final volume

constantvolume process

constant volume process

diatomic ideal gas

isothermal process

final pressure

webassign assignment