Some may have wondered why me (a creationist) has taken the side of the ID-haters with regards to the 2nd law. It is because I am concerned for the ability of college science students in the disciplines of physics, chemistry and engineering understanding the 2nd law. The calculations I’ve provided are textbook calculations as would be expected of these students.
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The fundamental problem is 2LOT is concerned with energy (or position\/momentum) microstates, whereas IDists are concerened with “design space” microstates. The number of microstates can both be expressed in information bits, but it does not mean we are dealing with the same microstates. I’m providing sample calculations to prove the point that it is disastrous for IDists to invoke textbook 2LOT for the simple reason 2LOT is concerened with energy (or position\/momentum) microstates which has little or nothing to do with “design space” microstates of interest to ID.<\/p>\n
I’m going through textbook thermodynamics here. If we have 500 fair copper pennies, how many “design space” microstates are there? Standard ID answer:<\/p>\n
2^500<\/p>\n
since there are 500 coins and each coin has 2 states, a system of 500 coins then has 2^500 possible symbolic configurational states or microstates. This can also be expressed in bits:<\/p>\n
I_design_space = – log2( 1\/ (2^500) ) = 500 bits<\/p>\n
What is the design space entropy?<\/p>\n
I_design_space = S_design_space = 500 bits<\/p>\n
IN CONTRAST, how many thermodynamic energy microstates are there in this system of 500 pure copper pennies at standard “room” temperature (298 Kelvin). The textbook style calculation is as follows:<\/p>\n
Mass of a copper penny 3.11 grams.
\nMolar weight of copper 65.546.
\nStandard molar entropy of copper 33.2 J\/K\/mol. <\/p>\n
Thermodynamic entropy of 500 copper pennies is therefore:<\/p>\n
S_thermodynamic = 500 * 33.2 Jolues\/Kelvin\/Mol * 3.11 grams 65.546 grams\/ mol = 826.68 J\/K<\/p>\n
The thermodynamic entropy in J\/K can be converted to bits by simply dividing by Boltzman’s constant and then converting the natural log measure to log-base-2 measure. <\/p>\n
Boltzmann’s constant is 1.381x 10-23 J\/K).
\nThe natural log to log-base-2 conversion is ln(2) = .693147.<\/p>\n
Thermodyamic entropy in bits is computed as follows:<\/p>\n
S_thermodynamic = I_thermodynmic =826.86 J\/K = 826.68 J\/K \/ (1.381x 10^-23 J\/K) \/ .693147 = 8.636 x 10^25 bits<\/p>\n
The number of thermodynamic microstates is simply taking 2 raised to the power of I_thermodynmic<\/p>\n
2^(8.636 x 10^25) <\/p>\n
which is a GIGANTIC number.<\/p>\n
Clearly the design space entropy is not the same as the thermodynamic entropy because the design space microstate is not the same as the thermodynamic microstate.<\/p>\n
Now let us heat the coins from room temperature to near boiling of water (373 Kelvin). What is the change in entropy or the number of microstates?<\/p>\n
At 373 Kelvin the “design space” entropy is still 500 bits since the possible number heads tails microstates does not change with this increase in temperature.<\/p>\n
However the thermodynamic entropy and thermodynamic microstates change. What is the change in entropy? Again using standard textbook thermodynamics.<\/p>\n
Specific heat of copper 0.39 J\/gram
\nHeat capcity C of 500 copper pennies:<\/p>\n
C = 0.39 J\/gram\/K * 500 pennies * 3.11 grams\/penny\/K = 606 J\/K<\/p>\n
T_initial = 298 K
\nT_final = 373 K<\/p>\n
To calculate the change in entropy I used the formulas from:
\nhttp:\/\/web.mit.edu\/16.unified\/www\/FALL\/thermodynamics\/notes\/node41.html<\/p>\n
delta-S_thermodynamic = C ln ( T_final\/T_initial) = 606 J\/K ln (373\/298) = 136.13 J\/K<\/p>\n
Total thermodynamic entropy is calculated as follows:<\/p>\n
S_thermodynamic_initial = 826.86 J\/K<\/p>\n
S_thermodyanmic_final = S_thermodyanmic_initial + delta-S_thermodynamic = 826.86 J\/K + 136.13 J\/K = 963.0 J\/K<\/p>\n
Again we can convert this to bits using procedures similar to the above conversions:<\/p>\n
S_thermodyanmic_final = 963.0 J\/K = 963.0 J\/K \/ (1.381x 10-23 J\/K) \/ .693147 = 1.01 x 10^26 bits<\/p>\n
The ADDED number of microstates due to the increase in temperature is calculated as follows:<\/p>\n
delta-S_thermodynamic = 136.13 J\/K = 136.13 J\/K \/ (1.381x 10^-23 J\/K) \/ .693147 = 1.42 x 10^25 bits<\/p>\n
Thus the number of thermodynamic microstates added by heating is simply found by rasing 2 to the power of delta-S_thermodynamic<\/p>\n
2^delta-S_thermodyanmic = 2^(1.42 x 10^25)<\/p>\n
Adding heat can be said to make the copper molecules bounce around more chaotically (disorderly if you will), and hence increase the thermodynamic entropy and microstates, but it says nothing of the change in design space entropy or microstates.<\/p>\n
BOTTOM LINE:<\/p>\n
Increasing heat increases the thermodynamic entropy and the individual copper molecules look more chaotic (disorderly if you will) because they are vibrating faster from the added heat, but it does nothing to change the design space entropy. <\/p>\n
At 298 Kelvin<\/b>:<\/p>\n
Design Space Entropy: 500 bits
\nnumber of Design Space microstates: 2^500<\/p>\n
Thermodyamic Entropy: 8.636 x 10^25 bits
\nnumber Thermodynamic microstates: 2^(8.636 x 10^25)<\/p>\n
At 373 Kelvin by adding heat<\/b> :
\nDesign Space Entropy: 500 bits
\nnumber of Design Space microstates: 2^500
\nchange in Design Space entropy due to heat change : 0 bits
\nchange in number of Design Space microstate due to heat change: 0 microstates<\/p>\n
Thermodyamic Entropy: 1.01 x 10^26 bits
\nnumber Thermodynamic microstates: 2^(1.01 x 10^26)
\nchange in thermodynamic entropy due to heat change : 1.42 x 10^25 bits
\nchange in number of thermodynamic microstates due to heat change: 2^(1.42 x 10^25) microstates<\/p>\n
Moral of the story: don’t use 2lot to argue for design space entropy change. Besides, as pointed out earlier, increasing design complexity usually entails increase of both design and thermodynamic entropy. <\/p>\n
Why all this obsession with reducing entropy to increase design complexity? I hope one can see it can be desirable to INCREASE entropy (both design and thermodynamic) in order to increase design complexity. A warm living complex human has more thermodynamic and design space entropy than a dead lifeless ice cube.<\/p>\n","protected":false},"excerpt":{"rendered":"
Some may have wondered why me (a creationist) has taken the side of the ID-haters with regards to the 2nd law. It is because I am concerned for the ability of college science students in the disciplines of physics, chemistry … Continue reading