Thermodynamics in Materials Engineering

1
Thermodynamics in Materials Engineering Mat E
212 R. E. Napolitano Department of Materials
Science Engineering Iowa State
University Irreversible processes
2
Reversible Processes
We consider a slow expansion followed by a slow
compression within an infinite constant-T heat
reservoir.
P1
PintPext
P1
P2
V1
P1
V2
Suppose we vary the external pressure very slowly
from P1 to P2, so that the internal pressure is
always equal to the external pressure. (i.e. an
infinitely slow process)
T
3
Reversible Processes
We consider a slow expansion followed by a slow
compression within an infinite constant-T heat
reservoir.
Pext
P1
PintPext
P2
Pint
V1
V2
Suppose we vary the external pressure very slowly
from P1 to P2, so that the internal pressure is
always equal to the external pressure. (i.e. an
infinitely slow process)
T
4
Reversible Processes
We consider a slow expansion followed by a slow
compression within an infinite constant-T heat
reservoir.
Pext
P1
PintPext
P2
Pint
V1
V2
Suppose we vary the external pressure very slowly
from P1 to P2, so that the internal pressure is
always equal to the external pressure. (i.e. an
infinitely slow process)
T
5
Reversible Processes
We consider a slow expansion followed by a slow
compression within an infinite constant-T heat
reservoir.
Pext
P1
PintPext
P2
Pint
V1
V2
Suppose we vary the external pressure very slowly
from P1 to P2, so that the internal pressure is
always equal to the external pressure. (i.e. an
infinitely slow process)
T
6
Reversible Processes
We consider a slow expansion followed by a slow
compression within an infinite constant-T heat
reservoir.
Pext
P1
PintPext
P2
Pint
V1
V2
Suppose we vary the external pressure very slowly
from P1 to P2, so that the internal pressure is
always equal to the external pressure. (i.e. an
infinitely slow process)
T
7
Reversible Processes
We consider a slow expansion followed by a slow
compression within an infinite constant-T heat
reservoir.
P2
P1
w
P2
V1
P2
V2
The work done by the gas on the surroundings is
given by the area under the P-V curve.
T
8
Reversible Processes
We consider a slow expansion followed by a slow
compression within an infinite constant-T heat
reservoir.
Because the process is isothermal, internal
energy is constant and the heat flow into the
cylinder is equal to the work done by the
internal gas.
P2
w
q
P2
T
TDS
9
Reversible Processes
We can easily imagine following the expansion
with a slow compression within the same
constant-T heat reservoir.
P2
w
q
P2
T
The corresponding values of heat and work are
changed only in sign.
10
Reversible Processes
The work performed by the system during the
expansion is equal to the work performed on the
system during the compression.
P1
P2
V1
V2
The work is equal to the area inside the closed
loop, which is zero.
11
Irreversible Processes
We consider an expansion caused by a sudden
change in the external pressure.
We begin with a piston and cylinder in a
constant-T reservoir.
PextP1
-?P
We decrease the external pressure by a small
increment ?P.
The piston accelerates upward.
PintP1
Tres
12
Irreversible Processes
We consider an expansion caused by a sudden
change in the external pressure.
We begin with a piston and cylinder in a
constant-T reservoir.
PextP1
-?P
We decrease the external pressure by a small
increment ?P.
The piston accelerates upward.
The gas cools upon the rapid expansion.
DV
Heat flows into the cylinder from the surrounding
reservoir.
TintltTres
After a very short time, PintPext, and the
piston stops.
Tres
The work done on the surroundings is given by
(P1-DP)?V.
13
Irreversible Processes
We now consider an compression caused by a sudden
change in the external pressure.
We now increase the external pressure by ?P, thus
returning it to P1.
PextP1
-?P
The piston accelerates downward.
The gas heats upon the rapid compression, and
heat flows from the cylinder into the heat
reservoir.
After a very short time, PintPext and the piston
stops.
PintP1-DP
The work done by the surroundings on the gas is
given by P1 ?V.
Tres
14
Irreversible Processes
?V
T
Where does this work go?
15
Equilibrium Process
A reversible process is not spontaneous because
it involves a vanishing (zero) driving force and
proceeds at an infinitely low (zero) rate.
16
Spontaneous Process
Any real process that proceeds at a nonzero rate
requires a nonzero driving force. Such a process
is said to be spontaneous or irreversible.
17
Acceleration is the key
Any acceleration indicates that there is an
imbalance of forces and, therefore, a nonzero net
force.
where
and
The work for acceleration causes a change in
kinetic energy (i.e. a degradation to heat).
18
Degree of Irreversibility
P1
P
V1
V
Less work is done on the surroundings.
T
Some of the work done by the gas is degraded to
heat.
19
Degree of Irreversibility
P1
P
V1
V
For a reversible process, no work is degraded to
heat.
T
20
Degree of Irreversibility
P1
P
V1
V
T
21
Degree of Irreversibility
P1
P
V1
V
T
22
Degree of Irreversibility
P1
P
V1
V
T
23
The Second Law
Entropy is a function of state. The entropy of a
system will be increased by heat flowing into the
system due to (a) the thermal
equilibration of the system with its surroundings
(b) the dissipation of work into heat
during an irreversible process dq
TdS The entropy of a system in an adiabatic
enclosure cannot decrease. dS 0
24
The Combined 1st and 2nd Law
Just as work is the mechanical equivalent of
heat, it is reasonable to consider the entropy to
be the thermal analog to volume.
25
The Combined 1st and 2nd Law
We consider the combined 1st and 2nd laws
graphically by examining a differential element
of the internal energy surface, UU(S,V).
26
The Combined 1st and 2nd Law
We consider the combined 1st and 2nd laws
graphically by examining a differential element
of the internal energy surface, UU(S,V).
U
S
V
27
The Combined 1st and 2nd Law
A simple analysis shows the relationship between
(T,P) and (S,V), respectively.