2. THERMODYNAMICS OF LIVING SYSTEMS
29
which it is impossible to restore all systems involved to their exact
original states without adding energy from the outside. It is apparent,
therefore, that all real processes are irreversible. However, one can
imagine systems in which all restraints such as friction, for example,
are infinitely small, and which permit with appropriate ingenuity a
restoration of the systems concerned to the exact initial states. Such a
hypothetical process is termed reversible and represents the limit of
actual processes.
Inherent in the comparison of irreversible processes with reversible
ones is the idea that systems may differ in degree of reversibility. One
of the most fruitful contributions to modern science was the establishment of a quantitative measure of this difference. The measure of irreversibility is called the increase in entropy for a given process and is
defined as
S B - S A = Q/T
(26)
where S B is the entropy of the final state, S A the entropy of the initial
state, and Q is the amount of heat reversibly exchanged from one part
of the universe to another part at temperature T.
Equation 26 implies that entropy is a state function since it depends
only on the final and initial states. Thus, we speak of it as a property.
In common with energy and heat capacity, we shall be mostly concerned with the difference between two states rather than with absolute
values of the individual states.
As an example of the calculation of entropy change, consider the
case of a perfect gas. The gas is introduced into a container separated
from another identical one with a stopcock. The second container is
evacuated. Let the volume of the container holding the gas be V A and
let the total volume of the containers after the stopcock is opened be
V B . Upon opening the stopcock the gas expands into the evacuated
cylinder. We assume the containers to be an isolated system so that
there is no change in energy and thus the temperature remains constant. Under such conditions if we compress the gas back into the
original container by means of a frictionless piston, work is required
with a concomitant surrender of an equivalent amount of heat to the
environment. Assuming the compression to take place very slowly so
that the internal pressure is kept equal to the external pressure, the
amount of work done is
W = Q
or, for the case above,
W = Q = f^PdV
(27)
29
which it is impossible to restore all systems involved to their exact
original states without adding energy from the outside. It is apparent,
therefore, that all real processes are irreversible. However, one can
imagine systems in which all restraints such as friction, for example,
are infinitely small, and which permit with appropriate ingenuity a
restoration of the systems concerned to the exact initial states. Such a
hypothetical process is termed reversible and represents the limit of
actual processes.
Inherent in the comparison of irreversible processes with reversible
ones is the idea that systems may differ in degree of reversibility. One
of the most fruitful contributions to modern science was the establishment of a quantitative measure of this difference. The measure of irreversibility is called the increase in entropy for a given process and is
defined as
S B - S A = Q/T
(26)
where S B is the entropy of the final state, S A the entropy of the initial
state, and Q is the amount of heat reversibly exchanged from one part
of the universe to another part at temperature T.
Equation 26 implies that entropy is a state function since it depends
only on the final and initial states. Thus, we speak of it as a property.
In common with energy and heat capacity, we shall be mostly concerned with the difference between two states rather than with absolute
values of the individual states.
As an example of the calculation of entropy change, consider the
case of a perfect gas. The gas is introduced into a container separated
from another identical one with a stopcock. The second container is
evacuated. Let the volume of the container holding the gas be V A and
let the total volume of the containers after the stopcock is opened be
V B . Upon opening the stopcock the gas expands into the evacuated
cylinder. We assume the containers to be an isolated system so that
there is no change in energy and thus the temperature remains constant. Under such conditions if we compress the gas back into the
original container by means of a frictionless piston, work is required
with a concomitant surrender of an equivalent amount of heat to the
environment. Assuming the compression to take place very slowly so
that the internal pressure is kept equal to the external pressure, the
amount of work done is
W = Q
or, for the case above,
W = Q = f^PdV
(27)