2. THERMODYNAMICS OF LIVING SYSTEMS
23
E. WORK
Several different kinds of work may be distinguished. Ordinary
mechanical work is equal to the product of the distance some mass is
moved in the direction of the applied force and the force necessary to
bring about the movement. If the force is expressed in dynes and the
distance in centimeters, the work done will be in ergs.
The calculation of electrical work is somewhat more complicated.
The maximum possible electrical work (at constant pressure and temperature ) which can be obtained from an electrical cell operating under
reversible conditions is given by the following equation:
W = nFE
(14)
where W is the work in joules, n is the valence change involved in the
reaction of the particular electrical cell, F is the Faraday constant of
electricity, and E is the voltage of the cell. It should be pointed out
that pressure-volume work is involved in certain electrical cells in addition to electrical work, e.g., when the cell produces a gas during
operation.
For the calculation of pressure-volume work, consider a system in
which a perfect gas is allowed to expand against a pressure essentially
equal to the pressure of the gas itself. The maximum possible work
produced in such a system is given by the equations:
rv,
rv*
dV
W = / PdV = / nRT %JVi
JVi
V
= nRT In ^ = nRT In J
(15)
where V x and P x represent the initial volume and pressure, V 2 and P 2
represent the final volume and pressure, and n, R, and T have the same
meanings as in the perfect gas equation.
In living organisms energy can be used to "pump" material through
membranes against concentration gradients. This type of work is usually termed osmotic work and is equal to the difference in the chemical
potential of the compound or ion under consideration on the two sides
of the membrane. The chemical potential represents a type of energy
associated with each component of a solution or gas mixture. This energy can be thought of as representing the tendency of a component
to "escape" from one phase to another. Gibbs pointed out an interesting
analogy between chemical potential and potential functions of mechanics. In mechanics, potentials depend solely on the position of one
23
E. WORK
Several different kinds of work may be distinguished. Ordinary
mechanical work is equal to the product of the distance some mass is
moved in the direction of the applied force and the force necessary to
bring about the movement. If the force is expressed in dynes and the
distance in centimeters, the work done will be in ergs.
The calculation of electrical work is somewhat more complicated.
The maximum possible electrical work (at constant pressure and temperature ) which can be obtained from an electrical cell operating under
reversible conditions is given by the following equation:
W = nFE
(14)
where W is the work in joules, n is the valence change involved in the
reaction of the particular electrical cell, F is the Faraday constant of
electricity, and E is the voltage of the cell. It should be pointed out
that pressure-volume work is involved in certain electrical cells in addition to electrical work, e.g., when the cell produces a gas during
operation.
For the calculation of pressure-volume work, consider a system in
which a perfect gas is allowed to expand against a pressure essentially
equal to the pressure of the gas itself. The maximum possible work
produced in such a system is given by the equations:
rv,
rv*
dV
W = / PdV = / nRT %JVi
JVi
V
= nRT In ^ = nRT In J
(15)
where V x and P x represent the initial volume and pressure, V 2 and P 2
represent the final volume and pressure, and n, R, and T have the same
meanings as in the perfect gas equation.
In living organisms energy can be used to "pump" material through
membranes against concentration gradients. This type of work is usually termed osmotic work and is equal to the difference in the chemical
potential of the compound or ion under consideration on the two sides
of the membrane. The chemical potential represents a type of energy
associated with each component of a solution or gas mixture. This energy can be thought of as representing the tendency of a component
to "escape" from one phase to another. Gibbs pointed out an interesting
analogy between chemical potential and potential functions of mechanics. In mechanics, potentials depend solely on the position of one