From: skroger@zeus.calpoly.edu (Seth L. Kroger)
Newsgroups: talk.origins
Subject: Re: Thermodynamics FAQ
Date: 30 Jul 92 21:16:13 GMT
Organization: California Polytechnic State University, San Luis Obispo

henley@eng.auburn.edu (James Paul Henley) writes:
>In article <1992Jul30.042012.8151@murdoch.acc.Virginia.EDU> lfoard@Turing.ORG (Lawrence C. Foard) writes:
>>
>>The claim that creationists have made is that a system such as
>>the earth must have increasing entropy. However a simple experment
>>can demonstrate that a system which has no exchange of matter
>>but does have an exchange of energy can lower its entropy. If you
>
>With no exchange of matter, what is required is a net heat loss.  When you
>put your water in the freezer, it has a net heat loss.  Can you prove that
>the earth has a net heat loss?

No net heat loss is required.

>
>The sign on dS indicates whether entropy is increasing or decreasing
>The sign on dQ indicates whether net heat is transfer in or out
>T is absolute temperature   >= 0
>
>The sign on dS is always the same as the sign on dQ

The following is part of an essay I wrote recently on the 2nd Law of
Thermodymanics called "Random Musing on the 2nd Law."  This will
hopefully answer the question.

"Random Musing on the 2nd Law" is Copyright (c) 1992 Seth L. Kroger.
All rights reserved.

=====================================================================

The entropy of the Earth need not increase, as I will show in the
example below.

A thermodynamic equation for entropy is dS = dQ/T + dP_s where dS is
the change in entropy, dQ is heat transfer, T is temperature, and dP_s
is the entropy production.  By the 2nd Law, dP_s >= 0[1, p.  206].

Figure~1 is a diagram of the Sun and Earth.

                                                   dQ_2  dQ_3
                                                    ^     ^
                                                    |     |
                                                    |     |
       /--------\                                   |     |
      /          \                                   /---\
     /            \                                 /  |  \
     |            |                   dQ_1          |  |  |
     |            |               ----------->      |  |  |
     \            /                                 \  |  /
      \          /                            T_d--> \---/ <--T_n
       \--------/


         Sun                                         Earth


               Figure 1:  A simplified Sun-Earth system


We receive heat from the sun (dQ_1) on our daylight side and radiate
heat back out into space on both our day and night sides (dQ_2, dQ_3).
Overall the Earth's energy stays constant, so dQ_1 = dQ_2 + dQ_3.  T_d
and T_n are the average temperatures of the day and night sides,
respectively.  It should be obvious that T_d is greater than T_n.

Neglecting entropy production for the moment, the change of entropy
for the Earth is:
                             dQ_1   dQ_2   dQ_3
                      dS =   ---- - ---- - ----
                             T_d    T_d    T_n

Substituting dQ_2 + dQ_3 for dQ_1 (since they're equal):

                         dQ_2 + dQ_3   dQ_2   dQ_3
                    dS = ----------- - ---- - ----
                             T_d       T_d    T_n

                         dQ_2   dQ_3   dQ_2   dQ_3
                    dS = ---- + ---- - ---- - ----
                         T_d    T_d    T_d    T_n

                                dQ_3   dQ_3
                           dS = ---- - ----
                                T_d    T_n

Since T_n is smaller than T_d, dQ_3/T_n > dQ_3/T_d (like 1/2 is more
than 1/3), therefore:

                                dS < 0

The entropy of the Earth can actually decrease!  How is this possible?
dQ_2 and dQ_3 are essentially transferring entropy away from the Earth
to the universe at large.  The dS_universe is still positive, even
though the entropy of a small part of the (Earth) has been reduced.

[1] Reynolds, William C., and Perkins, Henry C., _Engineering_
    _Thermodynamics_, 2nd ed., McGraw-Hill, Inc., 1977.

=====================================================================
>Interpretation:  To decrease system entropy, you have to have a *net* heat
>loss.

Sorry James, but no net heat loss is required if you get rid of heat at a
lower temperature than you recieved it at.

>James P. Henley Jr.

|======================================================================|
| Seth Kroger                       "If God made us in His image we    |
| skroger@pan.calpoly.edu               have certianly returned the    |
| Cal Poly, San Luis Obispo             compliment."  -Voltaire        |
                                             ^---spelling error corrected
Newsgroups: talk.origins