Basic Physics (Thermodynamics) - Pt. 12

Having examined how heat and mechanics are related, and specifically how Newton’s laws give rise to the basic kinetic theory for ideal gases, we now enter the realm of thermodynamics proper. We begin by further inquiring into the link between kinetic theory and temperature, and that we already saw:


PV = 2/3 N(½mv^2)

Which can be compared to what is called the “empirical equation of state for an ideal gas”:

PV = nkT, where k is the Boltzmann constant.

Equating the two:

2/3 N(½mv^2) = N kT

And solving for T, temperature:

T = 2/3k [(½mv^2)]

Which discloses the direct link between temperature and the microscopic behavior of a gas. Thus, temperature T is indeed a direct measure of the average molecular kinetic energy of a gas. We can also write this:

3k T/ 2 = (½mv^2)

Now, the total translational kinetic energy (for all N molecules of a gas) is just:

E = N((½mv^2) = N (3kT/2) = 3 nRT/2

Where we have replaced k using k = R/N_A

Where R is the molar gas constant and N_A is the “Avogradro number”

R = 8.3 J/ mole-K

Now, with these preliminaries out of the way, we can explore further the First Law of Thermodynamics (introduced in the two earlier blogs) but now in terms of the experimental set up shown. Here we have an apparatus consisting of a gas confined by a movable piston such that when heat (Q) is applied (added) using the Bunsen burner, external work W (= P(V2 – V1) ) is done in expanding the contained gas and hence pushing the piston upward. From the First Law:

+Q = +U + delta W or

delta Q = delta U + p(V2 – V1) = p(delta V)

Note again that (delta U) includes translational, rotational and vibrational kinetic molecular energies. The pressure itself P = F(a)/ A where F(a) > mg and A is the area of the piston.

Now, consider the experiment in the context of keeping the pressure P constant, then we say the process is isobaric. We also allow that it is reversible, in other words just as I can increase Q to do work to expand the gas, so also I can reduce Q (by lowering the heat of the burner) to decrease the gas.

Given n moles of an ideal gas (taking n = const.) then we can write:

delta Q = n Cp,m (delta T)

where: C p,m = delta Q/ n (delta T)

is the molar heat capacity at constant pressure

Then for an ideal gas, taking only V and T changing:

PV = nR T -> P(delta V) = nR(delta T)

Then:

delta Q = delta U + delta W becomes

n Cp,m (delta T) = n Cv,m (delta T) + nR (delta T)

Since:

n Cv,m (delta T) = delta U

Using some algebra on the earlier equation, and canceling out delta T’s:

C p,m = C v,m + R

Or R = C p,m - C v,m

In other words, the molar gas constant R is the difference between the molar specific heat capacity at constant pressure and the molar specific heat capacity at constant volume.

Sample Problem:

One mole of a gas has a volume of 0.0223 cubic meters at a pressure P = 1.01 x 10^5 N/m^2 at 0 degrees Celsius. If the molar heat capacity at constant pressure is 28.5 J/mol-K find the molar heat capacity at constant volume, C v,m.

Solution:

We have: PV = nRT and

R = PV/T = [(1.01 x 10^5 Pa) (0.0223 m^3)]/ 273 K

Note: that 0C = 273 Kelvin (K) and for pressure, 1 Pa (Pascal) = 1 N/m^2

Then R = 8.3 J/ mol K

So:

C v,m = C p,m – R = (28.5 – 8.3) J/mol K = 20.2 J /mol K

Problem for ambitious readers:

20 g of a gas initially at 27 C is heated at a constant pressure of 101 kPa (kiloPascals), so its volume increases from 0.250 m^3 to 0.375 m^3. Find:

a) the external work done in the expansion

b) the increase in the internal energy U

c) the quantity of heat supplied (Q) to achieve the expansion.

Michelle Malkin: Is She A Heartless Nincompoop?

Normally, I try to avoid reading anything put out by the loathsome Michelle Malkin, but yesterday's screed was just too much. I also tried to see it through the prism of the typical Right wing looney tune and how s/he would parse it. The results weren't pretty or comforting!

The title of Malkin's latest effort was: Adult Baby Syndrome: It's the New American Waaaahh, in which she tries to link the outrageous behavior of a couple of extreme cases to the behavior of all those receiving Social Security disability - and thereby concludes we're a nation of needy infants! (At least all those who have to depend on SS disability or food stamps). Thus, they are all emblematic of the far excesses of the "Nanny state".

The screed hit home at several levels, not least of which because I have two brothers who receive Social Security disability and another who ought to be getting it, all for legitimate disabilities! However, the way Malkin portrays all the recipients (via tarring with wide brush), they are all the next thing to dependent parasites! This sort of thing makes my blood boil, not least because I behold the same despicable tactics used on atheists, liberals, Planned Parenthood and many others. Thus, atheists are depicted as pillagers of civilization simply because they base their morality on a pragmatic objective thesis. Meanwhile, Planned Parenthood is depicted as the repository of mass-murdering thugs (via abortions), never mind that more than 95% of all their services are basic health treatments and preventive visits for low-income women, such as for mammograms, pap smears or to receive birth control pills, or condoms. But hey! The trick works! Trot out the most extreme behavior and tie it to the target, then pillory the target like some hapless pinata!

In her assault on Social Security disability, Malkin trots out one lamentable sufferer of infantilism. The sad and sorry case of a 30-year old man confined to his home and who wears diapers and lives on baby bottles of milk supplied by a nurse (who also received S.S. disability). Malkin openly uses the example of a "baby bottle guzzling 350 pound man" and why he "qualified for federal disability benefits". She then continues to throttle his life style and adult infant ways while lacerating the S.S. Administration for treating him as an incurable dependent. But hey, maybe he is! Did Malkin ever take the time to consult the bible of psychiatry, the Diagnostic and Statistic Manual?

If instead of mocking this poor case, she actually consulted the text, she would find listed under its compendium of paraphilias:

"Paraphilic infantilism, a paraphilia involving the desire to wear diapers and/or fantasies of a return to infancy." It appears to be common to a certain subset of Caucasian males, and the theory of at least one contributor is that either the victim was never properly breast fed to begin with, or it was prematurely terminated. And, oh....by the way, before Malkin or any other mean-spirited Right wing twit howls in derision, please consult the latest issue of WIRED (June, 2011) and the article by Judy Dutton (Liquid Gold: Inside the Booming Market for Breast Milk(p. 144), in which these miscreants and Nanny-state attackers will find mention of how many breast feeding women are selling their (extra) milk to males who demand it, for whatever reason. From the scale of the market, and sales, it seems clear that "infantilism" (if that's what it really is) is more widespread than we have been led to believe.

I would also argue, and this is not being a "liberal", that neither Michelle Malkin, assorted right wing preachers, myself or anyone else is qualified to judge these people! Hell, there are lots worse things that "perverts" (to use Malkin's turn of phrase) do than simply deck themselves out in diapers, or buy breast milk and drink it! (Think of the behavior of John Wayne Gacy, Jeffrey Dahmer -who kept severed heads in his fridge- or Ted Bundy, who kept preserved heads and other body parts of his female victims in his rooms- oh, and became a "born again" Christian just before being led to Florida's 'Old Sparky' for his execution. Anyone out there really want to spend eternity in the company of this sadistic kook- or hectoring pastors that needle us about 'accepting this free gift of salvation' like Bundy? Not me! Pardon me while I head for the eternal microwave first! It may be hotter but at least I know the company will be tolerable!)

Malkin's other idiotic ploy was to try to conflate 'Junior' (the adult baby suffering from infantilism) with Hugh Hefner, the Founder of Playboy, who she describes as "perpetually stunted" with a "fetish for velvet robes and self-indulgent decadence." Well, I'm sure Hef can easily defend himself, but let me just say he's done more to advance Americans out of their hyper-anal Puritan mores via his Playboy Philosophy, than any other ten contemporaries put together -including Susan Jacoby and Camille Paglia. Also, Hef via his hard work earned the right to those "velvet robes" and at least they are appropriate for the (female) company he keeps at his Mansion, and he doesn't have to resort to raping maids like a certain recently apprehended rich pig banker! Who, I am almost sure, is one of Malkin's idols, like the rich pig bankers that nearly brought this nation to perdition three years ago!

Yes, Time to Take Down TABOR in Colorado!

After moving to Colorado ten years ago, my wife and I have beheld an increasing and appalling deterioration of conditions. It's not just an increase of potholes in the roads (belying the image shown of a road not far from where we live), but also the fact many parks and outdoor areas are being left to the weeds, as paths for hiking become overgrown and fit only for the rattlers that frequenly cross them - while restrooms remain shuttered, and swimming pools for kids are closed during the summer. What happened? Some deadly virus? No, something worse! TABOR: The misnamed "Taxpayers' Bill of Rights" that passed in 1992.

As with many ill-conceived referenda, people-citizens of the state didn't study its long term consequences enough. All they saw was the savings they'd get on property taxes (like the California voters that passed Proposition 13 way back when, and now whine because their schools are falling apart and they have to let good teachers go!) - but not how the benefits would cost them their quality of life, surroundings, schools, highways etc. Now, nearly twenty years later, many citizens groups have seen what it's brought and are coming together to try to get it repealed. That is, both Republicans AND Democrats are coming together.

Why is this misbegotten law so bad? Well, because TABOR inherently limits state spending (even during large population growth-influx) based on an insane formula that - if more citizens had math backgrounds - would never have seen the light of day. TABOR dictated spending limits are fixed by the general condition that the rate of increase in state budget spending cannot exceed the rate of population growth (dp/dt) and the rate of inflation (di/dt) for any given year. Thus, in general:


dS/dt < dp/dt + di/dt

In addition, TABOR fixes a "baseline" for spending growth each succeeding year by tailoring it to the rate of growth in the prior year. Thus, say if the rate of growth dG/dt was -2% (as it was in 2001-2002) with the recession following 9-11, then the total rate of spending growth for the next fiscal year cannot exceed:

dG/dt + dp/dt + di/dt

To give an example, say the state spending budget was $800 million in 2002-03. And the prior fiscal year (2001-02) it was $700 million. The real rate of increase in spending was therefore:

(100/ 700) x 100% = 14%

Now, the TABOR baseline for that particular fiscal (net) population growth (those entering the state - those exiting) was 3%. Then:

(dG/dt + dp/dt + di/dt) = [-2% + 3% + 3%] = 4%


This means that a difference of: 14% - 4% = 10% of the state budget spending increase must be returned as refund to the taxpayers. In other words, six-tenths or 60% of the 14% by which the state "over-spent" must be returned. That is

0.6 x ($100 million) = $60 million

is refunded as TABOR refunds. (E.g. the state loses that amount, and must allocate the NEXT year's budget spending total minus that decrement).

The inherent problem as to why refunds are usually generated and not avoided is simply that state budgets must be planned and spending allocated in advance of the new fiscal year, while TABOR's oversight on them only occurs ex post facto (e.g. when the spending year has already passed). Thus, the inevitable delay means that taxpayers will always collect since the state will always typically tend to spend MORE (based on increasing cost of basic needs- health care, construction materials etc.) than not. The obvious problem is that a losing wicket (as we call it in Barbados) is continuously dug out, and the people of the state must see their schools, roads, parks etc. deteriorate because the money simply isn't there even for the most menial upkeep.

Even college bound students suffer, as part of the funds normally allocated for universities (to keep in-state tution down) are now no longer available, forcing the state's universities to increase tuition, room and board etc. Those increases have now been so high the past ten years (more than 40%) that most prospective students can't afford them without taking out ruinous loans. As we see, the cost of getting what you wish for may not always provide all the benefits you think you had coming. This is a lesson one hopes other states learn, before they also implement TABOR-style fooolishness!

Is "MHD" a Short Cut for Solar Physicists?

Most solar physicists work in what's called the "MHD" or magneto-hydrodynamic regime, which numerous plasma physicists have criticized as "taking the easy way out". But is it really? For example, treatments based on the analysis of the indigenous magnetic fields currently occupy a predominant role in analysis of energy stored in sunspot regions. The majority of these are based on MHD (magneto-hydrodynamic) theory wherein low frequency, long scale length and quasi-neutral (electric charge) assumptions are introduced into the plasma physics. Such assumptions lead to a basic set of what we call "MHD" equations, which include:

i) @rho/@t + DIV*(rho v)= 0

ii) rho @V/ @t + rho (v*grad)v = -grad p + 1/c J X B

iii) E + v X B = 0


In truth, MHD does represent the end product of successive information loss in the transition from Vlasov theory to two-fluid theory to one-fluid theory and thence MHD. But is the criticism that MHD is "oversimplified" valid in the solar case? Let's first look a bit at the key condition: whether a magnetic field is frozen in or not. Whether a given field is "frozen in" will depend on the magnitude of what is called the “magnetic Reynolds number” (R_m) If R_m >> 1 then diffusion can be ignored, and we have the frozen –field condition and MHD.

The magnetic Reynolds number is commonly expressed:

R_m = L V_A / q(m)


where L is a typical length scale for the particular solar environment, V_A is the Alfven velocity and q(m) is the magnetic diffusivity or:

q(m) = (5.2 x 10^7 ln K T^3/2) m2 /s

where the Coulomb logarithm is:

ln K = 9.00 + 3.45 log (T) - 1.15 log (n_e)

For a solar active region of T = 10^4 K, one has log (T) = 4.00

For an associated (electron) particle density of n_e = 10^10 /m^3 one has: log (n_e) = 10.00

Then:

ln K = 9.00 + 3.45 (4.00) - 1.15 (10.00)


ln K = 17.8 – 11.5 = 6.3

Then the magnetic diffusivity is:

q(m) = 327.6 m^2 /s


Now, let L = 10^7 m and V_A = 10^3 m /s, then

R_m = [10^10 m^2 /s] / 327.6 m^2 /s = 3.00 x 10^7

which is a typical value for the conditions referenced, and shows the magnetic field to be frozen into the plasma. Hence, MHD is a valid approach!

Apart from this, the most conspicuous agent of solar plasma containment and topological change is the coronal loop – which is fully consistent with a low beta-plasma regime- since otherwise gas kinetic pressure would predominate and the configuration would be ‘open’(Note: beta = (½ rho v^2)/ B^2/2u where rho is the fluid density, v the fluid velocity, B the magnetic induction and u the magnetic permeability of free space.)

With this little exercise, we see that the solar physicist is more than amply justified in employing the MHD approach. Indeed, for most applications for assessing sunspot regions, say, two fluid theory would be far too complicated while achieving little additional insight.

If one is determined to go the 2-fluid route the approach is straightforward: simply take the original MHD equations and treat them as if for two separate fluids (ions and electrons) instead of one. Then the first, or charge conservation equation would become, for example:

@ rho_e,i/ @t + DIV*(rho_e,i v_e,i) = 0

where the subscripts (e,i) alert the user to process the equations separately for electrons (e) and ions (i). Is all the extra work worth the information or information quality gleaned? The user would have to determine that for himself in the context of his problem, analysis!

NO! There will NEVER be a "Last Judgment!"

First, let me make it clear there WILL definitely be an end of the world! But this is apart from an end of humankind which could come as early as the next fifty years, from either being wiped out in a Torino Scale 10 asteroid strike, or from the runaway greenhouse effect (in which life will be unsustainable because of the super hot temperatures, averaging 144 F even on a "cool" day!) No, the actual, absolute end of the world - as in PLANET- will come in approximately 4.5 billion years after the last of the Sun's hydrogen stores have been converted to helium. At this point, to compensate for the much lower nuclear efficiency, the Sun will expand into a Red Giant and actually engulf the Earth, incinerating it.

Second, let me also make it clear that neither the aforementioned planetary end, nor any earlier one for humanity, will be part of any "judgment" or other nonsense. This is all an amusing offshoot of the Harold Camping fiasco two days ago, which actually saw some fundies asserting a Judgmental END still is coming, it's just that Camping didn't get it right! They then proceed to cite chapter and verse of their bibles to try to prove all the predictions are factual, and especially cite from the famous verses of Matthew 25:31-46, which as Oxford Biblical Scholar Geza Vermes has noted (The Authentic Gospel of Jesus, pp. 149-150) is a PARABLE only and not to be taken literally. Thus it is referred to as "the parable of the last judgment". As Vermes describes it (p. 150):

"The composite apocalytpic picture here is akin to the judgment scene presided over by the Son of man in the Similitudes of Enoch, a book probably dating to the last decades of the first century A.D., and thus roughly contemporaneous with and possibly affecting the redaction of the gospel of Matthew."

Here, by 'redaction', we mean an annotation of the content of one work within the body of the other (Matthew) and Vermes then shows a number of instances from the Similitudes of Enoch that were transferred to Matthew and set up in a kind of parlance of judgment. In other words, the words of one book were essentially transferred to another to form the parable. Vermes adds that in Matthew's rendering the parable structure incorporates the metaphor of the shepherd dividing the sheep from the goats. More importantly, according to Vermes (p. 151):

"In its final form the parable is set in the context of the event of the Parousia and as such belongs to the ideology of the early church, with the son of Man ...empowered to be a final judge."

But again, as I noted in a previous blog, the Parousia was all about a generic, benign return of Christ. The insertion (by later copyists) of all manner of distracting rhetoric concerning terrible -terrifying future events (e.g. in Matt. 24:5-8) concerning "wars and rumors or wars"..."famines, pestilences and earthquakes" as "birth pangs" and forerunners of a judgmental termination is really a parlor trick well known to early rhetoreticians (as well as modern politicians)! That is, take events that will 100% occur in any interval of time T, and then embellish them into future forecasts to make a point!

Thus, earthquakes and volcanoes erupting and wreaking havoc is a given in any given year. Also in any given year (such as currently) there are at least 1-2 major volcanoes that have been building up pressure for decades or centuries and hence ready to erupt! Similarly, The earth averages two to three Richter scale 6.5-7.0 quakes each month, albeit most in relatively poorly occupied regions. The planet also averages 1-2 major volcanic eruptions a year, and that has also been on schedule. There is nothing amiss, or extraordinary going on, in other words, and certainly nothing on which to base any 'end of the world scenario'. As for "wars and rumors of wars", give me an effing break already! Humans have been waging wars (and hence hatched rumors of such) since the year dot! The more serious end time prediction would therefore have been all wars and rumors of wars had ceased! Trouble is, no one considers these aspects in parsing the copyist text!

In connection with all this baloney, 'Revelation" is always referenced. The problem is that Revelation can't be taken seriously other than by a druggie in a drug-induced bender. Much of this derives from the work's bastardization by having originally been authored by Gnostics then re-formulated and redacted into a supposed orthodox Christian text. In other words, a mutant hybrid of two polar opposite traditions! The problem is the concatenation of mixed metaphors, juxtaposed symbols, and stripped similes doesn't work! It ends up being mostly the blatherings of a madman and reads like such! Former science writer Isaac Asimov, also a Judaic Biblical expert in his own right, in his superb Asimov's Guide to the Bible, also correctly notes that the idioms and ancillary language used in Revelation trace the author to be an inhabitant of Patmos. Other specific references are directed to people living in the western third of the peninsula of Asia Minor.

Asimov also correctly notes that just as the tales in Genesis were borrowed and adapted (some might less generously say, stolen) from ancient Babylonian creation fables, so also is most of Revelation taken or adapted from earlier eschatological material in the Jewish Old Testament, especially Daniel. So on top of Gnostic borrowings, there are OT overtones mixed in, which all contribute to leading so many astray.

Worse, Asimov notes the copyist errors - for example in listing the 12 tribes (Judah, Reuben, Gad, Asher etc.)in the wrong order and misspelling several (e.g. Man written for Dan). This section is also important because it's where fundies dredge up their horse pockey that "only 144,000 Jews will be saved at the end" (12,000 from each of the 12 tribes). But as Asimov notes, the number "144,000" was never meant to be taken literally, it simply represented an emphatic way of saying "All the righteous!"

Something along the lines of someone saying today, "It's raining cats and dogs", but no one familiar with the colloquial speech would take it literally!

Lastly, Asimov correctly observes (as my first Theology prof at Loyola did, in Theology 200) that the horrific events referred to could have transpired at any future age and would have been believed to fit by the people alive then. For example, as Asimov notes:

"Never did the four horsemen ride with such effect as in the days of World War I. Not only was there the bloodiest and most stupidly savage slaughter ever seen, on both western and eastern fronts, but there was a revolution in Russia that affects us even today, a famine in both Germany and Russia immediately after the war, and a world wide influenza pandemic in 1918 that killed many more than the war did".


What to make of Revelation then? As the same Theology Prof observed: "Take it as a rather florid and fulsome poem, perhaps written right after a dream...or more likely a nightmare after consuming too much liquor of the day"

Meanwhile, the inherent problem is that statistics and facts don't matter to religious zealots and whackos. In order to keep all their sheep in the fold, paying attention to their screeds, they must use scare tactics and that means holding the scythe of "end times" perdition over the heads of the gullible and weak-minded. They refer to citations in their good books (based on late copyist insertions, or misread parables about "signs" such as famines), but are too dishonest to indicate these have always been with us, and often emerged in combinations of the worst! So why didn't "the end" follow some of those terrible "signs" much earlier? Think back merely 40- odd years: the world came this close (--) to real Armageddon during the Cuban Missile crisis, and millions were dying in Africa (Biafra) from an ongoing famine, even as earthquakes and massive volcanic activity erupted. So, why wasn't the "end" upon us then? Rather than hitting the brakes and saying, okay....here's the end ...with these signs NOW. ...the end of the world miscreants allow the unfolding events to expire as they move on to the next events of a future time, including the Mt. Pinatubo eruption in 1992, the first Gulf War, and other famines....but still refuse to hit the brakes and assert, "okay, this is it my friendlies!" With this type of game (which any casino in Vegas would take) they can't lose a freakin' bet!

In one of the most memorable exchanges ever, ca. 1991, Magician James Randi squared off against a Christian Bible bigot who kept yammering about being in the "last days" (based on the Gulf War) and "we can tell they are here - what with wars, all the horrid crimes, and monumental disasters". To hear the Christian yap, you would believe have believed Armageddon was five years away.

Randi, not one to punt, kept pressing the fool to say exactly when. He reminded the bible puncher that "last days" invocations have been going on and off for the past 100 years or more. And still, none of the forecasters warning us have gotten any closer, despite volcnaoes blowing their lids, massive earthquakes and new diseases and famines appearing all the while. Of course, the guy escaped by saying that "It is not ours to know the day, nor the hour. Only the Lord's!"

And as Randi replied: "Convenient!"

The problem with all such attempts (by Randi's opponent) to use modern events in the service of ancient "prophecies" is that they're like tea leaves or Rorshach blots: anyone can read anything into any statement or claim. At the time of Randi's face off, the worst thing that had been going on was the Gulf War. Everyone, including the pretend preacher, insisted it was the war to lead into Armageddon - since Israel was so near to Iraq. Today, only the nations have been changed, so now it's Iran that may lead us into it. And so it goes, and goes...over and over and over....with no end in sight.

Then there are the prophecies about the "Antichrist". But who or what is it, or he? Numerous excellent religious scholars, including past Jesuit professors I had at Loyola, have made it clear that the Antichrist is not a person at all. It rather represents a metaphor for that nascent, atavistic spirit of aggression and hate within humanity. In other words, the Antichrist is within us all, as a regressive nature or force emanating from our ape-linked genes that still have much further to evolve.

Now, to answer the $64 question: Will Jesus be returning?

No, because Jesus was a MAN, M-A-N, not a divinity. He died, and was buried and while his disciples used some trickery to make people think he had risen again, it was all a ruse. (See Prof. Hugh Schonfeld's: 'The Passover Plot'). This was also why the followers grew so hacked off and impatient after one hundred or more years awaiting the Parousia that they replaced the benevolent returning Christ with a vengeful judge and then altered the scriptures to reflect that - by inserting words into Yeshua's mouth that he would be this very vengeful judge!

Whether or not one accepts Schonfeld's thesis of an actual Passover conspiracy, the myth of a God-Man returning for a "Second coming" is not new, but existed for thousands of years in earlier pagan sources, including for their god-men Horus, and Mithra (The ancient Persian version, not the Roman one). It therefore is quite reasonable to conjecture that later Christian authors, in their yen for "savior"-ship, copied-plagiarized the same legends and superposed them onto Yeshua.

Indeed, as Oxford scholar Geza Vermes notes (op. cit., p. 402, Epilog) Jesus “never chose to call himself ‘Messiah’ or ‘son of God’ even when others questioned him about his alleged Messiahship he usually declined to give a straight answer”. Vermes adds that as for the epithet ‘Son of God’- disallowing the combined expression “Messiah, the Son of God” in Matt. 26:63 (where the two are obviously used as synonyms) it is NEVER spoken by Jesus himself. Vermes adds: “One has to be foolish to believe the mockery of the chief priests and scribes, taunting Jesus to get down from the cross because he claimed to be the ‘Son of God’ (Matt.27:43) . Indeed, “only demons or people possessed by demons addressed Jesus with this title” (Matt. 4:3, Luke 4:3, Matt. 3:11, Luke 4:41 etc).

Will any of this alter the perspective of the End of worlders? Hardly! When one is committed to a hobby horse and is 110% invested in it, it becomes difficult if not impossible to change. They will continue to read into their good books exactly what they want and nothing else. All other explanations dismissed as "Satanic" or "lies" or whatnot. Denial and rationalization triumph in the end over reason. But that is the genesis of faith anyway, isn't it?

Solutions of 'Mechanics to Heat' Problems

In the last Basic Physics instalment we left off with a series of problems:


1) Work is done on water by a rotating paddle wheel driven by two weights of 1 kg mass each, falling at constant speed. Water is then stirred by the paddles increasing its temperature. Assuming that the loss in potential (mechanical) energy = work done by the paddle wheel on water, where the latter is defined according to:

m(H2O) c(H2O) (T2 - T1), and T2 = 15.5 C, T1 = 14.5 C,

find the height needed for the weights to drop to obtain 4.18J. (take the specific heat of water, c(H2O) = 4200 J/Kg K, and g = 9.8 m/sec/sec and the mass of the water = 10 kg.

2) A 200 pound weight falls 40 feet. How much heat was developed? (Take g = 32 ft/sec/sec and 1 Btu = 778 ft-lbs.)

3) A lead bullet (mass m) traels at velocity v = 300 m/s, and is fired into a wood target. Assuming that half the heat developed goes into the target and the rest into the bullet, how much will the temperature of the bullet be raised?

4)A 2 kg object has a speed of 2.5 m/s. Find: (a) its kinetic energy in joules, and b) the equivalent energy in calories.

time
The solutions are as follows:

(1) Find work done by paddle wheel on water:

m(H2O) c(H2O) (T2 - T1) = (100 kg)(4,200 J/kg K) (1 K) = 4.2 x 10^5 J

But we need to find the height dropped (h) to obtain nearly 100,000 time less (e.g. 4.18J). So: Loss in potential energy of falling weights = energy gained = 4.18J, or 2 mgh = 4.18 J = 2 (1 kg) (9.8 m/sec/sec) h, so that:

h = (4.18J)/ (19.6 kg m/sec^2)= 0.21 m.

(2) We let Q (amt. of heat) = mgh = (200 lb.) (40 ft.) = 8,000 ft-lb. (N.B. The value of g isn't needed, since lbs is already = mg (weight) so is already incorporated).

The amount of this Q in Btu = (8,000 ft-lbs)/ 778 ft-lb/Btu) = 10.3 Btu

(3)The kinetic energy of the bullet = E_k = ½ mv^2 = ½(m)(300m/s)^2

E_k = 45 000m (J) and this is equal to:

4.5m x 10^4 J

Let t be amount the temperature is raised and the specific heat of lead = 128 J/kgK

Then: (128 J/kg K)(m) t = ½( 4.5m x 10^4 J) = 2.25 x 10^4 J

Canceling 'm' from both sides and equating:

128 J/kg K(t) = 2.25 x 10^4 J or t = (2.25 x 10^4 J)/ (128 J/kg/K) = 175 K or 175C (Since the Kelvin temperature difference is equivalent to the Centigrade one)

(4)(a) KE in Joules = ½ m v^2 = ½ (2 kg)(2.5 m/s)^2 = 6.25 J

(b) the equivalent energy in calories:

Since by Joule's law (J = W/H)so 1 cal = 4.18 J, then

6.25 J = (6.25J)/(4.18 J/cal) = 1.5 cal

So What Happened with the 'End of the World?'

We sat around Saturday waiting for the "Judgment" but, alas, it never came. It was to commence at 4 p.m. our local time (6 p.m. Eastern Time) according to Harold Camping and his cult, but all we saw outside were some raindrops, a mild gust of wind and that was about it. So, yet another "end times" prediction, like Camping's previously one in 1994, goes into the crapper. When will the next one come forth? Will these nitwits now hang their heads in shame? I doubt it, as most religionists have no shame!

Now, many (especially fundamentalists) will miss the whole point of this inane non-event and hold Camping up as another "false prophet" or whatever. Of course, we KNOW Harold Camping is a nut, as the octogenarian numerologist wouldn't know a true forecast calculation from a confabulation. But, that doesn't make generic fundies any LESS nuts! Thus, holding Harold Camping out as a whacko or fruitcake, doesn't mean they are any less fruitcakes!

For example, both groups- Camping's screwballs along with the prototypical fundies- accept a non-biblical "Rapture". But as I noted this has no basis in the scriptures and was a confection instigated in 18th century Scotland. A 13-year old girl reported assorted night visions of people being levitated away. She referred these to a Scottish Minister who then expanded on them before going through assorted scriptures and finding as many specious references and citations as he could to retroactively justify the bogus concept. The whole sordid set of bunkum then acquired a life of its own and subsequently became almagamated into the most extreme forms of fundamentalist Protestantism. Today, this codswallop finds outlets in numerous places, conferring a spurious benediction, not least in Tim LaHaye's fantasy "Left Behind" series.

The whole eschatological-end times thingie is also a recent development. As Oxford Bible Scholar Geza Vermes has noted, the 'Parousia' has been around at least from the time of the earliest Christians. But the earliest renditions were not embellished with horror stories of Armageddon and destruction, but rather the simple re-appearance of Christ to support the belief he survived his death. After more than 100 years of no re-emergence, the original Parousia began to undergo re-evaluation, revision and rewriting to become something much more, with malignant overtones.

The way Vermes recounts it, is that having become so impatient with their Master's failure to return to Earth, Christ's followers soon began to see him as a vengeful Messiah not merely a 'returning from the grave' icon. Over the centuries, Christians of every stripe began to become immersed and heavily invested in End time sort of prophecies, especially based on Revelation, though anyone who had done scriptural exegesis and textual analysis knew that that book was originally a Gnostic text that had been re-molded into an orthodox format. Some of the Loyola Theology professors I had estimated as much as 45% of the original Gnostic text was omitted in recasting Revelation, and that meant that many of the symbols and imagery used (without the supporting context) would have little or no meaning. Even the meaning of 'the Beast' would be perverted, if the ancillary text was bowdlerized or removed.

Worse travesties awaited as portions and passages in Revelation were then linked up with the standard Old Testament text of Daniel, thereby marrying a partial Gnostic scripture to an ancient Judaic one, completing the transformation into eschatological scatology. Of course, we know human psychology will play into this, and people tend to see what they want to see if they look long and hard enough. Hence, if they find references to the "Beast" in Revelation, they will also find them in Daniel, as a basis to support what they already believe. Thereby digging the bunkum ever deeper. All such interminglings of valid whole texts, and partial ones that have been re-worked, are largely responsible for the "end times" nuttiness.

Yes, Harold Camping is a purblind, certifiable nut. But no one who thinks the "Judgment" will one day come, "Armageddon" is real, and that the "Rapture" is a precursor escape hatch for the righteous ought to pat himself on the back as being superior to Camping. To me, he or she is just as batshit crazy and clueless as he is! Maybe even moreso, because while they keep harping on the "end of the world"- even writing numerous books and making films about it- they don't even have the courage to give a single prediction! They do it purely out of instilling a constant sense of fear and dread to try to intimidate others into their fold, when if a future date isn't really known they'd do better to shut up until it is. THAT they do not, however, is precisely the sign of real psychotics!