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6
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
Specific heats
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay3
Lect-6
• It takes different amounts of energy to raise the temperature of identical masses of different substances by one degree.
• Therefore, it is desirable to have a property that will enable us to compare the energy storage capabilities of various substances.
• This property is the specific heat.
Specific heats
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay4
Lect-6
• Specific heat is defined as the energy required to raise the temperature of a unit mass of a substance by one degree.
• In general, this energy depends on how the process is executed.
• There are two kinds of specific heats: specific heat at constant volume, cv and specific heat at constant pressure, cp.
Specific heats
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay5
Lect-6
m = 1 kgΔT = 1oC
Specific heat = 5 kJ/kgoC
5 kJ
Specific heat is the energy required to raise the temperature of a unit mass of a substance by one degree in a specified way.
Specific heat at constant volume
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay6
Lect-6
• Consider a fixed mass in a stationary closed system undergoing a constant-volume process
• The conservation of energy principle for this process can be expressed in the differential form as
duee outin =−δδ
Specific heat at constant volume
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay7
Lect-6
• The left-hand side of this equation represents the net amount of energy transferred to the system.
• Thus,
vv
v
Tuc
dudTc
∂∂
=
=
or,
olumeconstant vat
Specific heat at constant pressure
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay8
Lect-6
• Similarly, an expression for the specific heat at constant pressure, cp can be obtained by considering a constant-pressure expansion or compression process.
• It yields,
pp
p
Thc
dhdTc
∂∂
=
=
or,
pressureconstant at
Specific heats
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay9
Lect-6
• cp and cv are properties of a system.• Are valid for any processes• cp is always > cv
• Because at constant pressure the system is allowed to expand and the energy for the expansion must also be supplied
• Specific heat of a substance change with temperature.
Specific heats
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay10
Lect-6
(2)
V = constantm = 1 kgΔT = 1o C
cv = 3.12 kJ/kgoC
P = constantm = 1 kgΔT = 1o C
cp = 5.19 kJ/kgoC
3.12 kJ 5.19 kJ
(1)
cp is always > cv
Specific heats
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay11
Lect-6
Airm = 1 kg
300 301 K
Airm = 1 kg
1000 1001 K
0.718 kJ 0.855 kJ
The specific heat of a substance changes with temperature.
Energy transfer mechanisms
Energy can cross the system boundaries of a closed system: heat and work
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay12
Lect-6
Closed system(m = constant)
Heat
Work
System boundary
Energy transfer by heat
• Heat: the form of energy that is transferred between two systems (or a system 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 system boundary.
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay13
Lect-6
Energy transfer by heat
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay14
Lect-6
25oC 15oC 5oC
No heat transfer 8 J/s 18 J/s
Heat HeatRoom air: 25oC
Temperature difference is the driving force for heat transfer. The larger the temperature difference, the higher is the rate of heat transfer.
Energy transfer by heat
• In thermodynamics, heat refers to heat transfer.
• A process during which there is no heat transfer is called Adiabatic process.
• Heat transfer mechanisms: – Conduction– Convection – Radiation
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay15
Lect-6
Energy transfer by heat
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay16
Lect-6
System boundary
Surrounding air
5 kJ thermal energy
5 kJ Heat
5 kJ thermal energy
Heat
Energy is recognized as heat transferonly as it crosses the system boundary.
Energy transfer by heat
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay17
Lect-6
System boundary
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
Energy transfer by work
• Any energy interaction of a closed system other than heat is work.
• An energy interaction that is not caused by a temperature difference between a system and its surroundings is work.
• Work is the energy transfer associated with a force acting through a distance.
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay18
Lect-6
Sign conventions
• Heat transfer to a system and work done by a system are positive; heat transfer from a system and work done on a system are negative.
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay19
Lect-6
System
Surroundings
QoutQin
WoutWin
Energy transfer by heat and work• Both heat and work are boundary
phenomena.• Systems possess energy, but not heat or
work.• Both are associated with a process, not a
state. Unlike properties, heat or work has no meaning at a state.
• Both are path functions (i.e., their magnitudes depend on the path followed during a process as well as the end states).
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay20
Lect-6
Path and Point functions• Path functions
– Have inexact differentials, sometimes designated by symbol, δ or đ
– Eg. δQ or đQ and δW or đW instead of dQ and dW
• Point functions– Have exact differentials, designated by
symbol, d– Eg. dP, dV, dT
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay21
Lect-6
Path and Point functions
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay22
Lect-6
1
2
1m3 5m3 V
p ΔV=4m3; WA=10 kJ
ΔV=4m3; WB=15 kJ
Process A
Process B
Properties are point functions; but heat and work are path functions.
∫
∫∫ −≠−=
zero isproperty a of
but, 1
2
121
2
12 WWWVVdV δ
Work
• Work done by a system on its surroundings during a process is defined as that interaction whose sole effect external to the system could be viewed as the raising of a mass through a distance against gravity.
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay23
Lect-6
Work
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay24
Lect-6
Battery
MotorFan
Surroundings
System boundary
W+ _
Work
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay25
Lect-6
Battery
Motor
Surroundings
System boundary Pulley
+ _
Weight
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
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay26
Lect-6
Work
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay27
Lect-6
Shaft work: rotation of a shaft Spring work
Stretching of a liquid film Electrical work: heating of a resistor
Displacement work
• Moving boundary or displacement work is of significant interest to engineers.
• Many engineering systems generate useful work output by this mode.
• Examples: automobile engines, steam engines, pumps etc.
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay28
Lect-6
Displacement work
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay29
Lect-6
A gas does a differential amount of work δWb as it forces the piston to move by a differential amount ds
A ds
P
F
∫=
===2
1
)(kJPdVW
dVPdsPAdsFW
b
bδ
Displacement work
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay30
Lect-6
The area under the process curve on a P-V diagram is equal, in magnitude, to the work done during a quasi-equilibrium expansion or compression process of a closed system.
dV
P
∫ ∫===2
1
2
1
PdVdAAArea
V2 VV1
P 1
2
dA=P dV
Process path
Displacement work
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay31
Lect-6
V2 VV1
P
1
2
WA = 12 kJWB = 10 kJ
WC = 7 kJ
A
B
C
The boundary work done during a process depends on the path followed as well as the end states.
Displacement work
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay32
Lect-6
V2 VV1
P
1
2
A
B
Wnet
The net work done during a cycle is the difference between the work done by the system and the work done on the system.
Displacement work
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay33
Lect-6
• Displacement work during Various processes:
Constant pressure processConstant volume processPV= contantPolytropic process, PVn = constant
Constant pressure process
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay34
Lect-6
V2 VV1
P
1 2
W1-2
)( 1221
2
1
VVppdVWV
V
−== ∫−
Constant volume process
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay35
Lect-6
V
P1
P
1
2
0)( 1221
2
1
=−== ∫− VVppdVWV
VP2
PVn = constant (Polytropic processes)
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay36
Lect-6
nVPVP
nVVCW
CVPVP
CPV
dVCVPdVW
nn
nn
n
n
−−
=+−−
=
==
=
==
+−+−
−
−− ∫∫
11
Now,
)(
11221
11
221
2211
2
1
2
121
V
P1 2n=0
n=∞
PVn =constant
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
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay37
Lect-6
In the next lecture ...
• Solve problems related to calculation of– Work done (displacement work)
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay38
Lect-6
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