intro-propulsion-lect-6.pdf

7/29/2019 Intro-Propulsion-Lect-6.pdf

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In this lecture ...

Specific heat At constant pressure and constant

volume

Heat transfer Meaning of heat transfer

Types of heat transfer

Work Thermodynamic meaning of work

Different types of work

Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay2

Lect-6


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Specific heats


Lect-6

It takes different amounts of energy toraise the temperature of identical massesof different substances by one degree.

Therefore, it is desirable to have aproperty that will enable us to comparethe energy storage capabilities of varioussubstances.

This property is the specific heat.


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Specific heats


Lect-6

Specific heat is defined as the energyrequired to raise the temperature of aunit mass of a substance by one degree.

In general, this energy depends on howthe process is executed.

There are two kinds of specific heats:specific heat at constant volume, cvand

specific heat at constant pressure, cp.


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Specific heats


Lect-6

m = 1 kgT = 1oC

Specific heat = 5 kJ/kgoC

5 kJ

Specific heat is the energy required to raise thetemperature of a unit mass of a substance byone degree in a specified way.


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Specific heat at constant volume


Lect-6

Consider a fixed mass in a stationaryclosed system undergoing a constant-volume process

The conservation of energy principle forthis process can be expressed in thedifferential form as

duee outin =


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Specific heat at constant volume


Lect-6

The left-hand side of this equationrepresents the net amount of energytransferred to the system.

Thus,

v

v

v

T

uc

dudTc

=

=

or,

olumeconstant vat


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Specific heat at constant pressure


Lect-6

Similarly, an expression for the specific heatat constant pressure, cp can be obtained byconsidering a constant-pressure expansionor compression process.

It yields,

p

p

p

Thc

dhdTc

=

=

or,

pressureconstantat


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Specific heats


Lect-6

cp and cv are properties of a system.

Are valid for any processes

cp

is always > cv

Because at constant pressure the systemis allowed to expand and the energy forthe expansion must also be supplied

Specific heat of a substance change withtemperature.


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Specific heats


Lect-6

(2)

V = constantm = 1 kg

T = 1o C

cv = 3.12 kJ/kgoC

P = constantm = 1 kg

T = 1o C

cp = 5.19 kJ/kgoC

3.12 kJ 5.19 kJ

(1)

cp is always > cv


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Specific heats


Lect-6

Air

m = 1 kg

300 301 K

Air

m = 1 kg

1000 1001 K

0.718 kJ 0.855 kJ

The specific heat of a substancechanges with temperature.


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Energy transfer mechanisms

Energy can cross the system boundariesof a closed system: heat and work


Lect-6

Closed system(m = constant)

Heat

Work

System boundary


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Energy transfer by heat

Heat: the form of energy that istransferred between two systems (or asystem and its surroundings) by virtue of

a temperature difference. Energy interaction is heat only if it takes

place by virtue of temperature difference.

Heat is energy in transition; it is

recognised only as it crosses the systemboundary.


Lect-6


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Lect-6

25oC 15oC 5oC

No heat transfer 8 J/s 18 J/s

Heat Heat

Room air: 25oC

Temperature difference is the driving force forheat transfer. The larger the temperaturedifference, the higher is the rate of heat transfer.


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In thermodynamics, heat refers to heattransfer.

A process during which there is no heat

transfer is called Adiabatic process. Heat transfer mechanisms:

Conduction

Convection Radiation


Lect-6


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Lect-6

Systemboundary

Surrounding air

5 kJthermalenergy

5 kJHeat

5 kJthermalenergy

Heat

Energy is recognized as heat transferonly as it crosses the system boundary.


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Lect-6

Systemboundary

Qn. Is there is any heat transfer during this burning process?Qn. Is there is any change in the internal energy of the system?

Insulation


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Energy transfer by work

Any energy interaction of a closedsystem other than heat is work.

An energy interaction that is not caused

by a temperature difference between asystem and its surroundings is work.

Work is the energy transfer associatedwith a force acting through a distance.


Lect-6


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Sign conventions

Heat transfer to a system and work doneby a system are positive; heat transferfrom a system and work done on a systemare negative.


Lect-6

System

Surroundings

QoutQin

WoutWin


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Energy transfer by heat and work

Both heat and work are boundaryphenomena.

Systems possess energy, but not heat orwork.

Both are associated with a process, not astate. Unlike properties, heat or work hasno meaning at a state.

Both are path functions (i.e., theirmagnitudes depend on the path followedduring a process as well as the end states).


Lect-6


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Path and Point functions

Path functions Have inexact differentials, sometimes

designated by symbol, or

Eg. Q or Q and Wor Winstead ofdQ and dW

Point functions

Have exact differentials, designated bysymbol, d

Eg. dP, dV, dT


Lect-6


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Path and Point functions


Lect-6

1

2

1m3

5m3

V

pV=4m3; WA=10 kJ

V=4m3; WB=15 kJ

Process A

Process B

Properties are point functions; butheat and work are path functions.

=

zeroispropertyaof

but, 1

2

1

21

2

1

2 WWWVVdV


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Work

Work done by a system on its surroundingsduring a process is defined as thatinteraction whose sole effect external to

the system could be viewed as the raisingof a mass through a distance againstgravity.


Lect-6


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Work


Lect-6

Battery

MotorFan

Surroundings

Systemboundary

W+

_


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Work


Lect-6

Battery

Motor

Surroundings

Systemboundary Pulley

+_

Weight


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Work

Examples: PdV: displacement work

Electrical work: heating of a resistor

Shaft work: rotation of a shaft Paddle wheel work

Spring work

Stretching of a liquid film


Lect-6


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Work


Lect-6

Shaft work: rotation of a shaft Spring work

Stretching of a liquid filmElectrical work: heating of a resistor


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Displacement work

Moving boundary or displacement workis of significant interest to engineers.

Many engineering systems generate

useful work output by this mode. Examples: automobile engines, steam

engines, pumps etc.


Lect-6


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Displacement work


Lect-6

A gas does a differential amountof work Wb as it forces thepiston to move by a differential

amount ds

A ds

P

F

=

===2

1)(kJPdVW

dVPdsPAdsFW

b

b


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Displacement work


Lect-6

The area under theprocess curve on a P-Vdiagram is equal, inmagnitude, to the work

done during a quasi-equilibrium expansion orcompression process ofa closed system.

dV

P

===2

1

2

1

PdVdAAArea

V2 VV1

P 1

2

dA=P dV

Process path


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Displacement work


Lect-6

V2 VV1

P

1

2

WA = 12 kJWB = 10 kJ

WC = 7 kJ

A

BC

The boundary work done during a processdepends on the path followed as well as theend states.


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Displacement work


Lect-6

V2 VV1

P1

2

A

B

Wnet

The net work done during a cycle is thedifference between the work done by thesystem and the work done on the system.


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Displacement work


Lect-6

Displacement work during Variousprocesses:

Constant pressure processConstant volume processPV= contantPolytropic process, PVn = constant

6


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Constant pressure process


Lect-6

V2 VV1

P

1 2

W1-2)( 1221

2

1

VVppdVW

V

V

==

L 6


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Constant volume process


Lect-6

V

P1

P

1

2

0)( 1221

2

1

=== VVppdVWV

VP2

L t 6


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PVn = constant (Polytropic processes)


Lect-6

n

VPVP

n

VVCW

CVPVPCPV

dVCVPdVW

nn

nn

n

n

=

+

=

===

==

++

11

Now,)(

1122

1

1

1

221

2211

2

1

2

1

21

V

P1 2n=0

n=

PVn =constant

L t 6


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Recap of this lecture

Specific heat At constant pressure and constant

volume

Heat transfer Meaning of heat transfer

Types of heat transfer

Work

Thermodynamic meaning of work

Different types of work


Lect-6

L t 6


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In the next lecture ...

Solve problems related to calculation of

Work done (displacement work)

38

Lect-6

intro-propulsion-lect-6.pdf

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