Page 241 - Standard Handbook Of Petroleum & Natural Gas Engineering

214 General Engineering and Science

system for doing work. All natural systems proceed towards a state of equilibrium
and, during any change process, useful work can be extracted from the system. The
property called entropy, and given the symbol S or s, serves as a quantitative measure
of the extent to which the energy of a system is “degraded” or rendered unavailable
for doing useful work.
For any reversible process, the sum of the changes in entropy for the system and
its surroundings is zero. All natural or real processes are irreversible and are
accompanied by a net increase in entropy.
Several useful statements have been formulated concerning the second law that
are helpful in analyzing thermodynamic systems, such as:
No thermodynamic cycle can be more efficient than a reversible cycle operating
between the same temperature limits.
The efficiency of all reversible cycles absorbing heat from a single-constant higher
temperature and rejecting heat at a single-constant lower temperature must be
the same.
Every real system tends naturally towards a state of maximum probability.
For any actual process, it is impossible to devise a means of restoring to its
original state every system participating in the process.
For any reversible process, the increase in entropy of any participating system is
equal to the heat absorbed by that system divided by the absolute temperature
at which the transfer occurred. That is, for a system, i,

SQi
dSi =- T~ (reversible processes) (2-111)

Alternatively, for an ideal reversible process, the sum of all the changes in entropy
must be zero or

SQ
xdSi=x-=O ( reversible processes)
Ti (2-112)
Because all real processes are irreversible as a result of friction, electrical resistance,
etc., any processes involving real systems experience an increase in entropy. For
such systems

x dS, > 0 (irreversible processes) (2-113)

The entropy change of a system during any process depends only upon its initial
and final states and not upon the path of the process by which it proceeds from its
initial to its final state. Thus one can devise a reversible idealized process to restore a
system to its initial state following a change and thereby determine AS = Sfin=, - Sinitia,.
This is one of the most useful aspects of the concepts of a reversible process.

Entropy Production: Flow Systems
In general, for all real processes, there is a net production of entropy and Equation
2-1 13 applies. Since many practical engineering processes involve open systems, it is
useful to develop a generalized expression of the second law applied to such systems.