The Second Law of Thermodynamics. Chapter 6. 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:
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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!
3. The theory emphasizes reversible processes! Yet, real processes are irreversible!
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
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.
should be smaller 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
For an irreversible process connecting states 1 and 2
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.
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
Comparing with the general expression