9M305.18.pptq4tr c qt t vwertg wegr werg ywerg ert

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1. 1
Recap
In the previous period you learnt about
•Constant temperature process
•Work done for isothermal process
•Heat transfer for isothermal process

2. 2
Objectives
On the completion of this
period, you would be able to
•Know Adiabatic or Isentropic
process
•Derive an expression for work done
during Adiabatic process
2

3. 3
•A process in which neither heat is supplied
nor removed from the system is called
adiabatic process.
•The gas contained in piston – cylinder
arrangement and completely covered by
insulating material from all sides and is free
from friction is an example for this process
3
Adiabatic process

4. 4
gas
Insulating wall
Fig 1
Adiabatic process (Contd.,)

5. 5
During frictionless adiabatic process heat
transfer across the boundary is zero, i.e,
Q = 0.
Therefore the change in entropy is zero
The frictionless adiabatic process is
known as isentropic process
It can be represented by the equation ,
PV

= constant

Where  = adiabatic index
= C
p/C
v
Adiabatic process (Contd.,)

6. 6
From NFEE, Q
1-2
= U
2
– U
1
+ W
1-2
For adiabatic process, Q=0
0 = U
2 – U
1 + W
1-2
or W
1-2
= - ( U
2
– U
1
)
= U
1 – U
2
Therefore work done by or on the system
during adiabatic expansion or compression
is only at the expense of internal energy.
Adiabatic process (Contd.,)

7. 7
Derivation of adiabatic process (PV

= constant)
From NFEE , Q
1-2
= U
2
– U
1
+ W
1-2
or dQ = dU + dW
For adiabatic process , dQ = 0
0 = dU + dW
= mC
v
dT + p dV
Dividing throughout by m, C
v and T
Adiabatic process (Contd.,)

8. 8
0 = mC
v
dT + PdV
mC
v
T mC
v
T
= dT + PdV
T mC
v
T
But PV = mRT or P = mR and C
v = R
T V  -1
Substituting these values
Adiabatic process (Contd.,)

9. 9
0 = dT + mR . dV
T V m R /  -1
0 = dT + ( -1) dV
T V
On integration,
Constant = log
eT + ( -1 )log
eV

Adiabatic process (Contd.,)

10. 10


Adiabatic process (Contd.,)

or log
e
T + ( -1 )log
e
V = Constant
log
e
( PV )+ ( -1 )log
e
V = Constant
( mR)
log
e
( PV )+ log
e
V
( 

-1)
= Constant
mR
log
e( PV .V


-1
= Constant
mR
log
e( P V

) = Constant
mR
or PV

= Constant

11. 11

Expression for Work done :

Consider m kg of gas
being heated
adiabatically from state
1 to state 2.
The adiabatic expansion
process is shown on p-
V diagram.
Adiabatic process (Contd.,)
2
2
1-2
( pV

= constant )
1
Fig.2 P – V diagram

12. 12

v2
We know that the work done , W
1-2 =  pdV

v
1
Since adiabatic process follows, PV

= C or P = C
V



v2

v2
W
1-2

=  C dV = C  V
-
dV

v
1 V


v
1

v2

= C V
- +1
- +1
v
1
Adiabatic process

13. 13
W
1-2 = C[ V
2
- +1
- V
1
- +1
]
- +1

= [ C V
2
- +1
- C V
1
- +1
]
- +1

But PV

=C = P
1V
1

= P
2V
2


= [P
2V
2

V
2
- +1
- P
1V
1

V
1
- +1
]
- +1


=

P
2
V
2
- P
1
V
1
= P
1
V
1
- P
2
V
2
- +1  -1
Adiabatic process (Contd.,)

14. 14
W
1-2
= P
1
V
1
- P
2
V
2
 -1
= mRT
1 – mRT
2
 -1
= mR ( T
1
– T
2
)
 -1
Adiabatic process (Contd.,)

15. 15
Similarly for adiabatic compression,
W
1-2
= P
2
V
2
- P
1
V
1
 -1

= mR ( T
2
– T
1
)
 -1
Adiabatic process (Contd.,)

16. 16
For adiabatic process,
W
1-2
= - ( U
2
– U
1
)

= U
1
– U
2

=mR ( T
1
– T
2
) = mC
v
( T
1
– T
2
)
 -1
Expression for Adiabatic index :
Adiabatic process (Contd.,)
1
v
R
C



1
p v
v
C C
C





17. 17
C
p
- C
v
= C
v
(  -1)
Dividing throughout by C
v ,
C
p
- 1 = (  -1)
C
v
C
p
= 
C
v
Thus the ratio of specific heats is called adiabatic index.

Adiabatic process (Contd.,)

18. 18
We have discussed about
•Adiabatic or isentropic process: In this process heat
transfer is zero
• Work done for adiabatic process
W
1-2
= P
1
V
1
– P
2
V
2
 -1

= mR ( T
1
– T
2
)
 -1
18
Summary

19. 19
QUIZ
19

20. 20
1). An adiabatic process is one in which

c) heat enters or leaves the gas
b) no heat enters or leaves the gas

a) there is no change in internal energy

d) none of the above

21. 21

2). The change in internal energy is equal to the
work done in
a) Isothermal process
c) Isobaric process
d) Adiabatic process
b) Isochoric process

22. 22
3)The adiabatic index is equal to
a) C
v / C
p
b) C
p
/ C
v
c) C
p
- C
v
d) C
v - C
p