Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Maximum reversible work in a steady-state earth/atmosphere system



Dear Colleagues,

I need help with the following problem: Calculate the maximum
reversible work that can be done in a steady-state earth (including its
atmosphere). My degree is in chemical engineering. Although I have studied mathematical physics at the Courant Institute, I am not up on
statistical mechanics or irreversible thermophysics. I have
Sommerfeld's Lectures, Yourgrau et al., and a book on exergy analysis,
but I find them somewhat formidable. I believe I would have to review
optics, electricity and magnetism, and kinetic theory to get started
even. That seems rather excessive in a case where only two or three
pages of the book is at stake. Nevertheless, I would like to have this
development in the book and I would certainly give proper attribution to whoever can show me how to solve the problem. (I am willing to accept
someone else's solution, but I must be made to understand it.)

I am writing a long book *On the Preservation of Species* that
perforce touches upon environmental concerns including the rapid
depletion of our once vast storehouses of high-grade energy or, more
properly, Helmholtz availability. I shall discuss the theory of emergy
(with an m) due to the famous ecologist Howard Odum, but I must base my emergies on availability. Many moons ago I decided to compute the
difference between the rate at which availability reaches the earth from
the sun and the rate at which it radiates to outer space as junk heat. This provides a hard limit on the rate at which we may carry on our
irreversible activities.

If anyone is willing to talk about this problem I would be most
grateful. If necessary, I am willing to send material on the problem
developed by myself or photocopied from standard texts. In an Appendix
to my book I have derived a version of the Combined First and Second Laws which is trimmed of its negligible terms to get a simpler equation
the right-hand side of which is the rate of accumulation of Helmholtz
availability, U - T(surroundings)S, inside the control volume consisting
of the earth and its atmosphere (minus the core) and the left-hand side
of which is the rate at which photons reach the earth from the sun
multiplied by the average Gibbs availability, h-T(surroundings)s, per
photon minus the same term for photons radiating to outer space minus
the rate at which "lost work" happens here on earth and in the earth's
atmosphere. Most of this lost work occurs because of the tremendous
activity we recognize as weather and without which we could not live.

Thus, I am faced with the problem of calculating the enthalpy and
entropy of photons. I realize that photons trapped in a cavity the walls of which are in thermal equilibrium with the photon "cloud" can be
treated as a Bose-Einstein gas. I know how to compute the enthalpy and
entropy for this case, BUT photons streaming toward the earth from the sun are not in equilibrium with anything - as far as I know - and I don't
see how I can apply the formulas I got from Yourgrau et al.

Moreover, I am concerned about the proper temperature to use for
T(surroundings). Should it be the temperature of outer space, 3.7 K
say? Should it be the (average) temperature of heat sinks available
here on earth, 300 K say? Also, I am not clear on just what the solar
constant represents. Must one compute the loss of availability due to
radiant heat transfer between objects of widely different temperatures?

I could send some material by snail mail, however I would welcome the
opportunity merely to discuss the problem with someone over the
telephone (at my expense, of course). Please let me know if anyone can
spare a little time from his or her busy schedule. I would appreciate
any help I can get be it only a literature reference.

Yours truly,
Tom Wayburn, PhD