Download The Second Law of Thermodynamics

Chapter 6
The Second Law of
Thermodynamics
6.1 Introduction
The first law of thermodynamics is simple,
general, but does not constitute a complete
theory because certain processes it permits do
not occur in nature!
The problems arise from:
1.Classical thermodynamics is connected with
states of equilibrium and various processes
connecting them.
2.The exact process by which a system reaches
the final state from its initial state is
immaterial. i.e. the transition is independent
of the particular path taken
3. The theory emphasizes reversible processes!
Yet, real processes are irreversible!
Examples of processes which are not prohibited
by the first law, but cannot happen in a real
world.
• Perfect machine
• Transfer heat from cold to hot subject
• Gas expansion
6.2 The mathematical concept of entropy
The reciprocal of the absolute temperature is an
integrating factor that permits the
replacement of the inexact differential
by
the exact differential .
The above equation is the Clausius definition of
the entropy S.
The first law of thermodynamics can be now
expressed as
for a reversible process
Pressure P can also act as an integration factor to let
the inexact differential
be replaced by the exact differential dv
i.e.
6.3 Irreversible Processes
1.
A battery discharges through a resistor, releasing energy.
The reverse process will not occur.
2.
Two gases, initially in separated adjoining chambers, will
mix uniformly.
3. A free expansion of gas (in Gay-Lussar-Joule
experiment)
4.
Heat flows from a high temperature body to a low
temperature reservoir in the absence of other effect
Two statements of the second law of
thermodynamics:
Clausius Statement: It is impossible to construct a
device that operates in a cycle and whose sole effect
is to transfer heat from a cooler body to a hotter
body.
Kevin-Planck Statement: It is impossible to construct a
device that operates in a cycle and produces no
other effects than the performance of work and the
exchange of heat with a single reservoir.
6.4 Carnot’s Theorem
When assuming
should be smaller then
If
then
since
As a result, the device does no work, but
extracts heat
from the cold
reservoir and delivers it to the hot reservoir.
Such a conclusion is again Clausius statement.
6.5 The Clausius Inequality & the Second Law
Clausius Inequality
For an irreversible process connecting states 1
and 2
Thus
or
The entropy of an isolated system increases in
any irreversible process and is unaltered in
any reversible process. This is the principle of
increasing entropy.
The fact that the entropy of an isolated system
can never decrease in a process provides a
direction for the sequence of natural events.
6.6 Entropy and Available Energy
It is impossible to utilize all the internal energy
of a body for the production of mechanical
work.
There exists no process that can increase the
available energy in the universe.
6.7 Absolute Temperature
6.8 Combined First & Second Laws
For a reversible process
The second law states that
Thus
Comparing with the general expression
One gets