Physics I: Chapter 15

Reference: Beginning Physics I

CHAPTER 15: THERMODYNAMICS I: TEMPERATURE & HEAT

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KEY WORD LIST

Macroscopic Systems, Thermodynamics, Quasistatic Systems, Thermodynamic Variables, Mechanical Equilibrium, Chemical Equilibrium, Thermal Equilibrium, Thermodynamic Equilibrium, Temperature, Zeroth Law of Thermodynamics, Thermometric Property, Celsius Scale, Ice Point, Steam Point, Fahrenheit Scale, Thermometer, Constant Volume Gas Thermometer, Kelvin Temperature Scale, Rankine Temperature Scale, Triple Point, Coefficient of Linear Expansion, Caloric, Thermal Energy, Heat, Internal Energy, Calorie, British Thermal Unit, Specific Heat, Heat Capacity, Calorimetry, Heat of Fusion, Heat of Vaporization, Heat of Sublimation, P-T Diagram, Evaporation

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GLOSSARY

For details on the following concepts, please consult CHAPTER 15.

MACROSCOPIC SYSTEMS
These are large systems that are characterized by their having myriad atoms and/or molecules. They depend on the myriad random motions and interactions of the component atoms and molecules, rather than their lockstep behavior.

THERMODYNAMICS
Thermodynamics deals with macroscopic systems. More specifically, it deals with the relations between heat and other forms of energy (such as mechanical, electrical, or chemical energy), and, by extension, of the relationships between all forms of energy.

QUASISTATIC SYSTEMS
Quasistatic systems mean that they are in mechanical, chemical, and thermal equilibrium, or that their properties vary so slowly that they can be described at any instant as if in equilibrium.

THERMODYNAMIC VARIABLES
Thermodynamic variables (or macroscopic variables) are physical properties, such as, volume and internal energy, which describe the system as a whole. Most other thermodynamic variables, such as, pressure and temperature can be defined only if the system is quasistatic.

MECHANICAL EQUILIBRIUM
This is understood to mean not only that the system as a whole does not accelerate, but that within the system the different parts are in mechanical equilibrium with each other —no churning of fluids and no pressure imbalances.

CHEMICAL EQUILIBRIUM
A system in mechanical equilibrium may still undergo change through a chemical reaction. The system is in chemical equilibrium when there is no change in chemical composition taking place.

THERMAL EQUILIBRIUM
A system in mechanical and chemical equilibrium may still undergo change in temperature. Two objects in thermal equilibrium with each other are also said to be at the same temperature.

THERMODYNAMIC EQUILIBRIUM
A system that is in mechanical, chemical and thermal equilibrium with its surroundings, as well as internally is said to be in thermodynamic equilibrium. Thermodynamic equilibrium means that there is no change on the macroscopic level.

TEMPERATURE
Temperature is a numerical value that we assign to each thermal equilibrium state of a system as determined by some agreed-upon procedure.

ZEROTH LAW OF THERMODYNAMICS
If two systems A and B are each found to be in thermal equilibrium with a third system C, then when the two systems A and B are brought into contact with each other, they are themselves found to be in thermal equilibrium.

THERMOMETRIC PROPERTY
A thermometric property is a property that varies with the thermal equilibrium states in a well-defined and reproducible way. For example, mercury in a sealed hollow bulb attached to a long, thin hollow glass stem. When mercury expands or contracts with change in the thermal equilibrium state, small changes in its volume are observable from its height in the thin stem.

CELSIUS SCALE
This is the most widely used temperature scale that assigns the number tC = 0°C for the ice point, and tC =100°C for steam point at atmospheric pressure. The distance between these two points is divided into 100 equal marked intervals labeled in 1°C steps.

ICE POINT
The point at which ice and water are in thermal equilibrium at atmospheric pressure.

STEAM POINT
The point at which steam, and water are in thermal equilibrium at atmospheric pressure.

FAHRENHEIT SCALE
On this scale the ice point and steam point are defined as tF = 32°F and tF = 212°F respectively, and the distance between these two points is divided into 180 equal marked intervals labeled in 1°F steps.

THERMOMETER
A thermometer is a temperature-calibrated mercury system, which can be used to measure the temperature of any other object. However, the temperature scale shall be dependent on the material being used to define it.

CONSTANT VOLUME GAS THERMOMETER
This thermometer consists of a gas confined to a fixed volume, with an open-tube manometer used to measure the pressure of the gas inside. Constant volume gas thermometer is often considered the “standard” against which other thermometers are calibrated.

KELVIN TEMPERATURE SCALE
The graphs of pressure vs. temperature of all very low-density gases at fixed volumes are straight lines. When extrapolated these straight lines intersect the temperature axis at the same point: -273.15°C. On the basis of this result, one defines the Kelvin (or absolute) temperature scale. It is same as the Celsius Scale with its zero shifted to “-273.15°C”.

T = tC + 273.15

RANKINE TEMPERATURE SCALE
This is the Kelvin scale using the Fahrenheit degree rather than the Celsius degrees.

TR = tF + 459.67

TRIPLE POINT
The triple point is the temperature, tC = 0.01°C, at which all three phases of water—solid, liquid, and vapor—coexist.

COEFFICIENT OF LINEAR EXPANSION
If we have a rod of length L at a given absolute temperature and we increase the temperature by a small amount ∆T, we find that the length of the rod increases b an amount ∆L that is proportional to the original length L and to the temperature increase ∆T:

∆L = a L∆T

The proportionality constant a is called the coefficient of linear expansion; it depends on the material of which the rod is made.

CALORIC
Early scientists believed that some invisible and weightless substance, which they called caloric, flows from a hotter to cooler object until both objects reach thermal equilibrium.

THERMAL ENERGY
It became clear through the efforts of Joule and others that it is not caloric but thermal energy that is transferred between two macroscopic systems in contact.

HEAT
Heat is the thermal energy transfer from one system to another. Heat is actually the statistical “summing up” of the mechanical work done by the random interactions of the individual atoms and molecules of the two systems.

INTERNAL ENERGY
Related to heat is the internal energy that resides in a system due to the random motion and jiggling of the myriad atoms and molecules making up that system.

CALORIE (CAL)
A calorie is defined as the “amount of heat” (thermal energy in transit) necessary (at atmospheric) to raise the temperature of 1 gram of water 1°C. 1 cal = 4.184 J

BRITISH THERMAL UNIT (BTU)
A Btu is the amount of heat necessary to raise 1 lb of water 1°F. The conversion is 1 Btu = 252 cal.

SPECIFIC HEAT (c)
The specific heat is the characteristic amount of heat that flows into a unit mass of a given substance and raises its temperature by 1°. For solids and liquids, heat is transferred under constant atmospheric pressure.

HEAT CAPACITY (C)
Heat capacity is the total amount of heat needed to produce a degree rise in temperature.

CALORIMETRY
Calorimetry is the experimental measurements of specific heats and other heat constants.

HEAT OF FUSION (Lf)
Heat of fusion is the amount of heat added to melt each unit mass of substance at the melting point (under normal atmospheric pressure).

HEAT OF VAPORIZATION (Lv)
Heat of vaporization is the amount of heat added to vaporize each unit mass of substance at the boiling point (under normal atmospheric pressure).

HEAT OF SUBLIMATION (Ls)
Heat of sublimation is the amount of heat added to sublimate each unit mass of substance at the sublimation point (under normal atmospheric pressure).

P-T DIAGRAM
The P-T diagram keeps track of phase changes. For a pure substance the diagram will resemble the following.

EVAPORATION
Evaporation takes place at the surface of the liquid in contact with a gas at a given pressure. At temperatures well below the boiling point, molecules from the liquid that are particularly energetic can break free and rise above the liquid to form a vapor. The evaporating molecules take away the thermal energy with them—on average the amount of energy per unit mass is the same order of magnitude as the heat of vaporization for boiling. Thus the evaporation process removes heat from the liquid, cooling it and anything in contact with it.

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December 21, 2022 – 10:34 AM Categories: Physics | Post a comment

JUDAISM: Meaning in Messianism

Reference: Judaism

[NOTE: In color are Vinaire’s comments.]

Whether we read it in its Jewish, its Christian, its secular, or its heretical version, the underlying messianic theme has always been that of hope. 

Though the Jews were able to find their suffering meaningful, meaning for them did not end there. It climaxed in Messianism. 

We can work our way into this concept by way of an arresting fact. The idea of progress—belief that the conditions of life can improve, and that history can in this sense get somewhere—originated in the West. Insofar as other peoples have come to this notion, they have acquired it from the West.

The idea of progress—belief that the conditions of life can improve, and that history can in this sense get somewhere—originated in the West.

Striking as this fact is, it seems explicable. If we confine ourselves to the two other enduring civilizations—South Asian, centering in India, and East Asian, centering in China and its cultural offshoots—we find that their presiding outlooks were forged by people who were in power; in India these were the brahmins, and in China the literati. By contrast, the West’s outlook was decisively shaped in this matter by the Jews, who for most of their formative period were underdogs. Ruling classes may be satisfied with the status quo, but underdogs are not. Unless their spirits have been crushed, which the Jewish spirit never was, oppressed people hope for improvement. This hope gave the biblical Jews a forward and upward looking cast of mind. They were an expectant people—a people who were waiting, if not to throw off the yoke of the oppressor, then to cross over into the promised land.

The West’s outlook was decisively shaped in this matter by the Jews, who for most of their formative period were underdogs. 

Sweet, sweet the open spreading fields
Lay decked in shining green;
So to the Jews fair Canaan stood,
While Jordan rolled between.

To sum up the matter: Underdogs have only one direction to look, and it was the upward tilt of the Jewish imagination that eventually led the West to conclude that the conditions of life as a whole might improve. 

Oppressed people hope for improvement. The Biblical Jews were waiting, if not to throw off the yoke of the oppressor, then to cross over into the promised land.

Hope has more purchase on the human heart when it is rendered concrete, so eventually Jewish hope came to be personified in the figure of a coming Messiah. Literally, Messiah (from the Hebrew mashiah) means “anointed”; but as kings and high priests were anointed with oil, the terms became a title of honor, signifying someone who had been elevated or “chosen.” During the Babylonian Exile the Jews began to hope for a redeemer who would effect the “ingathering of the exiles” to their native homeland. After the second destruction of the Temple (70 C.E.), the honorific title “Messiah” was used to designate the person who would rescue them from that diaspora. 

During the Babylonian Exile the Jews began to hope for a redeemer who would effect the “ingathering of the exiles” to their native homeland. 

Things, though, are never this simple, and in the course of time the messianic idea became complex. Its animating concept was always hope, and this hope always had two sides to it: the politico-national side (which foresaw the triumph of the Jews over their enemies and their elevation to a position of importance in world affairs), and a spiritual-universal side (in which their political triumph would be attended by a moral advance of worldwide proportions).

They shall beat their swords into plowshares, and their spears
into pruning hooks;
nation shall not lift up sword against nation,
neither shall they learn war any more. (Isaiah 2:4)

These three features of the messianic idea—hope, national restitution, and world upgrade—remained constant, but within this stable framework differing scenarios were scripted. 

The messianic idea had the stable framework of hope, national restitution, and world upgrade.

One important difference concerned the way the messianic age would arrive. Some expected an actual Messiah to appear—a priest or king who, as God’s deputy, would effect the new order. On the other side were those who thought God would dispense with a human agent and intervene directly. The latter view, appropriately called the messianic expectation, hoped for “an age in which there would be political freedom, moral perfection, and earthly bliss for the people of Israel in their own land, and also for the entire human race.” The first concept includes everything in the second, but adds the figure of a lofty and exalted political and spiritual human personality, who comes to prepare the world for the Almighty’s kingdom. 

It hoped for an age in which there would be political freedom, moral perfection, and earthly bliss for the people of Israel in their own land, and also for the entire human race.

A second tension reflected the restorative and utopian impulses within Judaism generally. Restorative Messianism looked for the recreation of past conditions, typically the Davidic monarchy but now idealized. Here hope turned backward to the reestablishment of an original state of things and to a “life lived with the ancestors.” But Messianism also accommodated Judaism’s forward-looking impulse, so there were versions that were utopian in envisioning a state of things that never before existed.

Restorative Messianism looked for the recreation of past conditions, typically the Davidic monarchy but now idealized. But Messianism also envisioned a state of things that never before existed.

Finally, Messianists differed concerning whether the new order would be continuous with previous history or would shake the world to its foundations and replace it (in the End of Days) with an aeon that was supernaturally different in kind. As the power of the Jews dwindled in the face of a rising Europe, and hope of political restoration in Israel seemed increasingly impossible, the expectation of a miraculous redemption strangled political yearnings. Apocalypticism, elements of which are visible in the prophets themselves, replaced hopes for military victory. The Messianic Age would break in at any moment, abruptly and cataclysmically. Mountains would crumble and the seas boil. The laws of nature would be abrogated to make way for a divine order that was unimaginable save that the “birth pangs of the Messianic Age”—its fearful images excited by terrors the Jews were actually experiencing—would be followed by peace. Thus even this apocalyptic version contained a utopian element. Peril and dread were balanced by consolation and redemption.

Finally, there was also an element of the Messianic Age breaking in at any moment, abruptly and cataclysmically, and to be followed by peace. 

In all three of these polarities the alternatives were deeply intertwined, while being contradictory by nature. The messianic idea crystallized and retained its vitality out of the tensions created by its ingredient opposites. Nowhere do we find a pure case of one without the other; only the proportions between them fluctuated, often wildly. The direction in which the pendulum swung was determined by historical events and the individual character of their proclaimers, a number of whom—the “false messiahs”—assumed the messianic title for themselves and in several instances attracted large followings. In periods when the Israelites were still living an independent political life in their own land, ethical perfection and earthly bliss were emphasized; whereas in periods of subjugation and exile the yearning for political freedom was more prominent. In times of national freedom the worldwide, universalistic part of the hope was basic; but in times of trouble and distress the nationalistic element came to the fore. Throughout, however, the political component went arm in arm with the ethical, and the nationalistic with the universal. Political and spiritual longings united, as did hopes for themselves and the world at large. Both themes figure in Zionism, the modern movement for political and spiritual renewal of the Jewish people, which helped the Jews return to Palestine and found the State of Israel in 1948.

Throughout, however, the political component went arm in arm with the ethical, and the nationalistic with the universal. Political and spiritual longings united, as did hopes for themselves and the world at large. 

So we return to the underlying messianic theme, which is hope. Moving into Christianity, it took the form of the Second Coming of Christ. In seventeenth—century Europe it surfaced as the idea of historical progress, and in the nineteenth century it assumed Marxist idiom in the vision of a coming classless society. But whether we read it in its Jewish, its Christian, its secular, or its heretical version, the underlying theme is the same. “There’s going to be a great day!” That says it prosaically. Martin Luther King, Jr., drawing his images from the Prophet Isaiah, said it rhetorically in his address to the audience of 200,000 in the 1968 civil rights March on Washington.

I have a dream today.
I have a dream that one day every valley shall be exalted, every hill
and mountain shall be made low, the rough places will be made plain,
and the crooked places will be made straight, and the glory of the Lord
shall be revealed, and all flesh shall see it together.

The underlying messianic theme has always been that of hope. 

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December 19, 2022 – 6:04 AM Categories: Religion | Post a comment

HINDUISM: The Stations of Life

Reference: Hinduism

Note: The original Text is provided below.
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People are different. The point of caste is the natural differences in dispositions that put people into classes as seers, administrators, producers, and followers. Insofar as caste has come to mean rigidity, exclusiveness, and undeserved privilege, Hindus today are working to clear the corruption from their polity.

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Summary

People are different. They occupy different stations in the social order. This brings us to the Hindu concept of caste. Caste contains both point and perversion. It emerged from the clash between the invading Aryan culture and the indigenous Indian culture during the second millennium B.C. The outcome was a society that was divided into four groups: seers, administrators, producers, and unskilled laborers.

A fifth group of outcastes , or untouchables, is looked upon as a perversion of the caste system as their lot through India’s history has been a wretched one. Many religious reformers have sought to remove untouchability from the caste system. Other perversions have been the proliferation of castes into subcastes, proscriptions against intermarriage and inter-dining, higher castes benefiting at the expense of the lower, and one remaining in the caste into which one was born.

But, in its basic format, the caste system recognizes that, with respect to the ways they can best contribute to society and develop their own potentialities, people fall into four groups:

(1) Brahmins or seers. Into their province fall the functions distributed among philosophers, artists, religious leaders, and teachers. Things of the mind and spirit are their raw materials. 

(2) Kshatriyas or administrators. They are born with a genius for orchestrating people and projects in ways that makes the most of available human talents.

(3) Vaishyas or producers. They are artisans and farmers, skillful in creating the material things on which life depends.

(4) Shudras or unskilled laborers. Such people are better off, and actually happier, working for others than being on their own.

Unequal castes were thus separated so the weak did not have to compete against the strong across the board. Within each caste there was equality, opportunity, and social insurance. 

Justice was defined as a state in which privileges were proportionate to responsibilities. The brahmins stood supreme in honor and psychological power, and the kshatriyas stood supreme In salary and social power, since they had responsibilities far beyond average at the cost of considerable self-sacrifice. The same offense elicited much higher punishment for those with higher responsibilities compared with those with lower responsibilities.

India considered Plato’s dream of the philosopher king unrealistic, and it is true that when brahmins assumed social power, they became corrupt. But it came in time to neglect Plato’s insight that the son could be of a different “caste” than his father.

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Comments

The caste system, as practiced today, contains many perversions; but the basic theses of caste continue to warrant attention.

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Original Text

People are different—we are back a third time to this cardinal Hindu tenet. We have traced its import for the different paths people should follow toward God, and the different patterns of life appropriate at various stages in the human career. We come now to its implications for the station the individual should occupy in the social order.

This brings us to the Hindu concept of caste. On no other score is Hinduism better known or more roundly denounced by the outside world. Caste contains both point and perversion. Everything in the discussion of this subject depends on our ability to distinguish between the two.

How caste arose is one of the confused topics of history. Central, certainly, was the fact that during the second millennium B.C. a host of Aryans possessing a different language, culture, and physiognomy (tall, fair-skinned, blue-eyed, straight-haired) migrated into India. The clash of differences that followed burgeoned the caste system, if it did not actually create it. The extent to which ethnic differences, color, trade guilds harboring professional secrets, sanitation restrictions between groups with different immunity systems, and magico-religious taboos concerning pollution and purification contributed to the pattern that emerged may never be fully unraveled. In any event the outcome was a society that was divided into four groups: seers, administrators, producers, and followers.

Let us record at once the perversions that entered in time, however they originated. To begin with, a fifth group—of outcastes or untouchables—appeared. Even in speaking of this category there are mitigating points to be remembered. In dealing with her lowest social group, India did not sink to slavery as have most civilizations; outcastes who in their fourth stage of life renounced the world for God were regarded as outside social classifications and were revered, even by the highest caste, the brahmins; from Buddha through Dayananda to Gandhi, many religious reformers sought to remove untouchability from the caste system; and contemporary India’s constitution outlaws the institution. Still, the outcaste’s lot through India’s history has been a wretched one and must be regarded as the basic perversion the caste system succumbed to. A second deterioration lay in the proliferation of castes into subcastes, of which there are today over three thousand. Third, proscriptions against intermarriage and inter-dining came to complicate social intercourse enormously. Fourth, privileges entered the system, with higher castes benefiting at the expense of the lower. Finally, caste became hereditary. One remained in the caste into which one was born.

With these heavy counts against it, it may come as a surprise to find that there are contemporary Indians, thoroughly familiar with Western alternatives, who defend caste—not, to be sure, in its entirety, especially what it has become, but in its basic format. What lasting values could such a system possibly contain?

What is called for here is recognition that with respect to the ways they can best contribute to society and develop their own potentialities, people fall into four groups. (1) The first group India called brahmins or seers. Reflective, with a passion to understand and a keen intuitive grasp of the values that matter most in human life, these are civilization’s intellectual and spiritual leaders. Into their province fall the functions our more specialized society has distributed among philosophers, artists, religious leaders, and teachers; things of the mind and spirit are their raw materials. (2) The second group, the kshatriyas, are born administrators, with a genius for orchestrating people and projects in ways that makes the most of available human talents. (3) Others find their vocation as producers; they are artisans and farmers, skillful in creating the material things on which life depends. These are the vaishyas. (4) Finally, shudras, can be characterized as followers or servants. Unskilled laborers would be another name for them. These are people who, if they had to carve out a career for themselves, commit themselves to long periods of training, or go into business for themselves, would founder. Their attention spans are relatively short, which makes them unwilling to sacrifice a great deal in the way of present gains for the sake of future rewards. Under supervision, however, they are capable of hard work and devoted service. Such people are better off, and actually happier, working for others than being on their own. We, with our democratic and egalitarian sentiments, do not like to admit that there are such people, to which the orthodox Hindu replies: What you would like is not the point. The question is what people actually are.

Few contemporary Hindus defend the lengths to which India eventually went in keeping the castes distinct. Her proscriptions regulating intermarriage, inter-dining, and other forms of social contact made her, in her first prime minister’s wry assessment, “the least tolerant nation in social forms while the most tolerant in the realm of ideas.” Yet even here a certain point lies behind the accursed proliferations. That proscriptions against different castes drinking from the same source were especially firm suggests that differences in immunity to diseases may have played a part. The presiding reasons, however, were broader than this. Unless unequals are separated in some fashion, the weak must compete against the strong across the board and will stand no chance of winning anywhere. Between castes there was no equality, but within each caste the individual’s rights were safer than if he or she had been forced to fend alone in the world at large. Each caste was self-governing, and in trouble one could be sure of being tried by one’s peers. Within each caste there was equality, opportunity, and social insurance.

Inequalities between the castes themselves aimed for due compensation for services rendered. The well-being of society requires that some people assume, at the cost of considerable self-sacrifice, responsibilities far beyond average. While most young people will plunge early into marriage and employment, some must postpone those satisfactions for as much as a decade to prepare themselves for demanding vocations. The wage earner who checks out at five o’clock is through for the day; the employer must take home the ever-present insecurities of the entrepreneur, and often homework as well. The question is partly whether employers would be willing to shoulder their responsibilities without added compensation, but also whether it would be just to ask them to do so. India never confused democracy with egalitarianism. Justice was defined as a state in which privileges were proportionate to responsibilities. In salary and social power, therefore, the second caste, the administrators, rightly stood supreme; in honor and psychological power, the brahmins. But only (according to the ideal) because their responsibilities were proportionately greater. In precise reverse of the European doctrine that the king could do no wrong, the orthodox Hindu view came very near to holding that the shudras, the lowest caste, could do no wrong, its members being regarded as children from whom not much should be expected. Classical legal doctrine stipulated that for the same offense “the punishment of the Vaishya [producer] should be twice as heavy as that of the shudra, that of the kshatriya [administrator] twice as heavy again, and that of the brahmin twice or even four times as heavy again.” In India the lowest caste was exempt from many of the forms of probity and self-denial that the upper castes were held to. Its widows might remarry, and proscription against meat and alcohol were less exacting.

Stated in modern idiom, the ideal of caste emerges something like this: At the bottom of the social scale is a class of routineers—domestics, factory workers, and hired hands—who can put up with an unvaried round of duties but who, their self-discipline being marginal, must punch time clocks if they are to get in a day’s work, and who are little inclined to forego present gratification for the sake of long-term gains. Above them is a class of technicians. Artisans in preindustrial societies, in an industrial age they are the people who understand machines, repair them, and keep them running. Next comes the managerial class. In its political wing it includes party officials and elected representatives; in its military branch, officers and chiefs-of-staff; in its industrial arm, entrepreneurs, managers, board members, and chief executive officers.

If, however, society is to be not only complex but good, if it is to be wise and inspired as well as efficient, there must be above the administrators—in esteem but not in pay, for one of the defining marks of this class must lie in its indifference to wealth and power—a fourth class, which in our specialized society would include religious leaders, teachers, writers, and artists. Such people are rightly called seers in the literal sense of this word, for they are the eyes of the community. As the head (administrators) rests on the body (laborers and technicians), so the eyes are placed at the top of the head. Members of this class must possess enough willpower to counter the egoism and seductions that distort perception. They command respect because others recognize both their own incapacity for such restraint and the truth of what the seer tells them. It is as if the seer sees clearly what other types only suspect. But such vision is fragile; it yields sound discernments only when carefully protected. Needing leisure for unhurried reflection, the seer must be protected from over-involvement in the day-to-day exigencies that clutter and cloud the mind, as a navigator must be free from serving in the galley or stoking in the hold in order to track the stars to keep the ship on course. Above all, this final caste must be protected from temporal power. India considered Plato’s dream of the philosopher king unrealistic, and it is true that when brahmins assumed social power, they became corrupt. For temporal power subjects its wielder to pressures and temptations that to some extent refract judgment and distort it. The role of the seer is not to crack down but to counsel, not to drive but to guide. Like a compass needle, guarded that it may point, the brahmin is to ascertain, then indicate, the true north of life’s meaning and purpose, charting the way to civilization’s advance.

Caste, when it has decayed, is as offensive as any other corrupting corpse. Whatever its character at the start, it came in time to neglect Plato’s insight that “a golden parent may have a silver son, or a silver parent a golden son, and then there must be a change of rank; the son of the rich must descend, and the child of the artisan rise, in the social scale; for an oracle says ’that the state will come to an end if governed by a man of brass or iron.’” As one of the most thoughtful recent advocates of the basic idea of caste has written, “we may expect that the coming development will differ chiefly in permitting intermarriage and choice or change of occupation under certain conditions, though still recognizing the general desirability of marriage within the group and of following one’s parents’ calling.” Insofar as caste has come to mean rigidity, exclusiveness, and undeserved privilege, Hindus today are working to clear the corruption from their polity. But there remain many who believe that to the problem no country has yet solved, the problem of how society ought to be ordered to insure the maximum of fair play and creativity, the basic theses of caste continue to warrant attention.

Up to this point we have approached Hinduism in terms of its practical import. Beginning with its analysis of what people want, we have traced its suggestions concerning the ways these wants might be met and the responses appropriate to various stages and stations of human life. The remaining sections of this chapter shift the focus from practice to theory, indicating the principal philosophical concepts that rib the Hindu religion.

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December 18, 2022 – 9:12 AM Categories: Hinduism, Religion | Post a comment

Physics I: Chapter 14

Reference: Beginning Physics I

CHAPTER 14: FLUIDS IN MOTION (HYDRODYNAMICS)

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KEY WORD LIST

Viscosity, Viscous Forces, Non-Viscous Fluids, Turbulent Flow, Steady-State Flow, Laminar Flow, Flow Line, Streamline, Flow Tube (Stream Tube), Incompressible Fluid, Ideal Fluid, Equation of Continuity, Bernoulli’s Equation, Torricelli’s Theorem, Venturi Tubes, Stagnation Point, Aerodynamics, Coefficient Of Viscosity, Poiseuille’s Law, Stoke’s Law, Reynold’s Number

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GLOSSARY

For details on the following concepts, please consult CHAPTER 14.

VISCOSITY
In general, there are shear forces between layers of fluids that move past each other and between the moving fluids and boundary surfaces. This property of fluids is called viscosity.

VISCOUS FORCES
The shear forces of viscosity are frictional in nature. They are called viscous forces.

NON-VISCOUS FLUIDS
For some fluids the viscous forces can be quite small, especially when they are moving slowly. In such vases one can ignore viscosity. Such a fluid is known as a non-viscous fluid.

TURBULENT FLOW
Much fluid motion is quite complex, with the flow pattern at any given point changing over time. Such motion is called turbulent flow. Turbulent flow is characterized by swirling and eddies and constantly changing patterns of motion.

STEADY-STATE FLOW
In many cases, however, the flow pattern at any point stays the same from moment to moment. Such motion is called steady-state or just steady flow. It is also called laminar flow.

LAMINAR FLOW
See STEADY-STATE FLOW.

FLOW LINE
The flow line of a particle of water moving in a stream is the path it takes. In steady flow, any particle that is located on the flow line of a previous particle will repeat the motion of that particle.

STREAMLINE
The streamline of a flow is the flow pattern of the entire fluid at a given instant, retaining knowledge of the velocities of all the particles at that instant. In steady flow, the streamlines remain constant in time. For steady-state flow, two streamlines can never cross each other.

FLOW TUBE (STREAM TUBE)
A flow tube is made up of the streamlines that pass through the perimeter of a small cross-sectional area in steady state. The flowing fluid can never cross the boundary of the tube.

INCOMPRESSIBLE FLUID
For an incompressible fluidthe changes in the densities from location to location are so small that we can ignore them.

IDEAL FLUID
An incompressible fluid that has no viscosity is called an ideal fluid.

EQUATION OF CONTINUITY
The mass of fluid that flows into one end of the flow tube in a given time interval must be the same as the mass that flows out the other end in the same time interval.

BERNOULLI’S EQUATION

TORRICELLI’S THEOREM
If you have a container filled with fluid with small hole at the bottom of the container, the fluid leaves through the hole with velocity same as it would experience if dropped from the same height to the hole level.

VENTURI TUBES

(a) The pressure in the pipe is determined by observing the height of water in the tube.
(b) The tube acts like a open-tube manometer and measures the gage pressure of the flowing liquid.z
(c) The height difference of the mercury (corrected for the different heights of fluid above the mercury on the two sides) directly measures P2 — P1. This also yields velocity per P2 — P1 = ½ dv12.

STAGNATION POINT
The stagnation point is a small region or point right in front of the tube at 2 in figure (c) above, where the fluid is at rest since it must go around one or the other side of the tube.

AERODYNAMICS
An airplane in motion is supported by the pressure difference between the top and undersides of the wing. Compression of the streamlines above the wing means that the flow tube above the wing has a smaller cross-sectional area and, therefore, greater velocity of the air. This greater velocity implies lower pressure.

COEFFICIENT OF VISCOSITY
For fluid in steady flow between parallel plates, the stress is proportional to the velocity gradient, where the coefficient of viscosity  is the proportionality constant,

POISEUILLE’S LAW
The volume flow rate depends on the fourth power of the radius of the pipe, as well as on the change in pressure per unit length along the pipe.

STOKE’S LAW
When an object moves through a viscous fluid in such a way that the fluid is in steady flow past it, the viscous forces on the object are, to a good approximation, proportional to the relative velocity and the coefficient of viscosity. The expression for the force will vary with the shape of the object. For sphere,

REYNOLD’S NUMBER

The Reynold’s number is a dimensionless quantity that depends on four factors: the density d of the flowing fluid, the coefficient of viscosity , the average relative velocity of the fluid v, and the characteristic linear dimension L of the solid boundary. For flow through a pipe, L is the diameter of the pipe. For an object moving through a fluid, L can be taken as some average linear dimension of the object facing into the fluid flow. In all cases the expression for the Reynold’s number is

When R exceeds a certain value for the geometry at hand, the flow turns from steady to turbulent. A good rule of thumb for fluids flowing through a pipe is that when R exceeds 2000, the flow becomes turbulent. Similarly for a sphere moving through a fluid, the critical value of R is about 10.

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December 17, 2022 – 6:37 PM Categories: Science | Post a comment

JUDAISM: Meaning in Suffering

Reference: Judaism

Note: The original text is provided below.
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Second Isaiah related this general principle to the experience of his people by envisioning a day when the nations of the earth would see that the tiny nation they once scorned (here personified as an individual) had actually been suffering on their behalf.

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Summary

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Comments

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Original Text

From the eighth to the sixth centuries B.C.E., during which Israel and Judah tottered before the aggressive power of Syria, Assyria, Egypt, and Babylon, the prophets found meaning in their predicament by seeing it as God’s way of underscoring the demand for righteousness. God was engaged in a great controversy with his people, a controversy involving moral issues not evident to the secular observer. To correct a wayward child a parent may coax and cajole, but if words fail action may prove to be necessary. Similarly, in the face of Israel’s indifference to God’s commands and pleadings, Yahweh had no alternative but to let the Israelites know who was God—whose will must prevail. It was to make this point that God was using Israel’s enemies against her.

Thus says the Lord:
For three transgressions of Israel,
and for four, I will not revoke the punishment;
because they sell the righteous for silver,
and the needy for a pair of sandals—
Therefore an adversary shall surround the land,
and strip you of your defense;
and your strongholds shall be plundered. (Amos 2:6; 3:11)

Jeremiah takes up the refrain. Because the Jews had forsaken righteousness, it is God’s decision to “make this city a curse for all the nations of the earth” (Jeremiah 26:6).

We can appreciate the moral courage required to come up with this interpretation of impending doom. How much easier to assume that God is on our side, or resign oneself to defeat.

The climax, however, is yet to come. Defeat was not averted. In 721 B.C.E. Assyria “came down like a wolf on the fold” and wiped the Northern Kingdom from the map forever, converting its people into “the Ten Lost Tribes of Israel.” In 586 Judah, the Southern Kingdom, was conquered, though in this case its leadership remained intact as Nebuchadnezzar marched it collectively into captivity in Babylonia.

If ever there was a time when the possibility of meaning seemed unlikely, this was it. The Jews had bungled their opportunity and in consequence had been brought low. Surely now the prophets might be expected to concede their people’s doom with a self-serving “I told you so.”

This retort, a blend of vindictiveness and despair, was not in the prophets’ vocabulary. The most staggering fact in the Jewish quest for meaning is the way in which in this blackest hour, when meaning had been exhausted in the deepest strata the Jews had yet mined, the prophets dug deeper still to uncover an entirely new vein. Not to have done so would have amounted to accepting the prevailing view that the victors’ god was stronger than the god of the defeated, a logic that would have ended the biblical faith and the Jewish people along with it. The rejection of that logic rescued the Jewish future. A prophet who wrote in sixth century Babylonia where his people were captives—his name has been lost, but his words come down to us in the latter chapters of the book of Isaiah—argued that Yahweh had not been worsted by the Babylonian god Marduk; history was still Yahweh’s province. This meant that there must have been point in the Israelites’ defeat; the challenge was again to see it. The point that “Second Isaiah” saw was not this time punishment. The Israelites needed to learn something that their defeat would teach, but their experience would also be redemptive for the world.

On the learning side, there are lessons and insights that suffering illumines as nothing else can. In this case the experience of defeat and exile was teaching the Jews the true worth of freedom, which, despite their early Egyptian captivity, they had come to hold too lightly. Lines have come down to us that disclose the spiritual agony of the Israelites as displaced persons—how heavily they felt the yoke of captivity, how fervently they longed for their homeland.

By the rivers of Babylon—there we sat down
and there we wept when we remembered Zion.
On the willows there we hung up our harps.
For there our captors asked us for songs,
and our tormentors asked for mirth, saying,
“Sing us one of the songs of Zion!”
How could we sing the Lord’s song in a foreign land?
If I forget you, O Jerusalem, let my right hand wither!
Let my tongue cling to the roof of my mouth.(Psalm 137:1–6)

Sometimes a single phrase is enough to convey the poignancy and pathos of their plight: “Is it nothing to you, oh you who pass by”; or “How long, O Lord, how long?” 

When Cyrus, King of Persia, conquered Babylon in 538 and permitted the Jews to return to Palestine, the prophets saw another lesson that only suffering can fully impart: the lesson that those who remain faithful in adversity will be vindicated. In the end their rights will be restored.

Go out from Babylon, declare this
with a shout of joy, proclaim it,
send it forth to the end of the earth;
say, “The Lord has redeemed His servant Jacob.”
(Isaiah 48:20–22)

But what the Jews might themselves learn from their captivity was not the only meaning of their ordeal. God was using them to introduce into history insights that all peoples need but to which they are blinded by ease and complacency. God was burning into the hearts of the Jews through their suffering a passion for freedom and justice that would affect all humankind.

I have given you as a light to the nations,
to open the eyes that are blind,
to bring out the prisoners from the dungeon,
from the prison those who sit in darkness. (Isaiah 42:6–7)

Stated abstractly, the deepest meaning the Jews found in their Exile was the meaning of vicarious suffering: meaning that enters lives that are willing to endure pain that others might be spared it. Second Isaiah related this general principle to the experience of his people by envisioning a day when the nations of the earth would see that the tiny nation they once scorned (here personified as an individual) had actually been suffering on their behalf:

Surely he has borne our infirmities
and carried our diseases;
yet we accounted him stricken,
struck down by God, and afflicted.
But he was wounded for our transgressions,
crushed for our iniquities;
upon him was the punishment that made us whole,
and by his bruises we are healed.
All we like sheep have gone astray;
we have all turned to our own way;
and the Lord has laid on him
the iniquity of us all. (Isaiah 53:4–6)

The deepest meaning the Jews found in their Exile was the meaning of vicarious suffering: meaning that enters lives that are willing to endure pain that others might be spared it.

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December 17, 2022 – 6:46 AM Categories: Religion | Post a comment