14. b) What is the diameter of a circle with a radius of 7 inches? The values shown are useful particularly for calculations of vapor liquid equilibrium wherein liquid being condensed from gas systems. That means y varies directly with x.
Find The Value Of K For Which The Equation
This correlation is applicable to low and moderate pressure, up to about 3. Therefore, in equation, we cannot have k =0. I have been told that the circle with equation $x^2 + y^2 - 12x -10y + k=0$ meets the co-ordinate axes exactly three times, and I have to find the value of $k$. T. T is the temperature of the reaction in Kelvin. Find the value of k for each of the following quadratic equations, so that they have two equal roots. For what value of k do the equations 3x-y+8 0. In the nomograph, the K-values of light hydrocarbons, normally methane through n-decane, are plotted on one or two pages. Yet, $k$ cannot equal $61$ since that would imply the radius of the circle is zero, a contradiction to the fact that the equation is a circle. It is important to realise that we are talking about standard free energy change here - NOT the free energy change at whatever temperature the reaction was carried out. The EoS method has been programmed in the GCAP for Volumes 1 & 2 of Gas Conditioning and Processing Software to generate K-values using the SRK EoS [10]. P: The sun is shining.
This is also provable since. Example 4: Given that y varies directly with x. For what value of #k# does the equation #4x^2 - 12x + k# have only one solution? In the equilibrium constant expression, there must be hardly any products at the top and lots of reactants at the bottom. We don't have to use the formula y = k\, x all the time. This gives us 10 inches for the diameter. Let p and q denote the following statements. The Antoine [5] equation is recommended for calculating vapor pressure: Values of A, B, and C for several compounds are reported in the literature [5]. This approach is widely used in industry for polar systems exhibiting highly non-ideal behavior. Let A and B be non empty sets in R and f: is a bijective function. A relatively simple nomograph is normally presented in undergraduate thermodynamics and unit operations text books. Algebra precalculus - Finding the value of $k$ for the equation of a circle. In general K-values are function of the pressure, temperature, and composition of the vapor and liquid phases. Some of these are polynomial or exponential equations in which K-values are expressed in terms of pressure and temperature.
Alternatively, there are several graphical or numerical tools that are used for determination of K-values. Find the ratio of y and x, and see if we can get a common answer which we will call constant k. It looks like the k-value on the third row is different from the rest. If yours is different and it isn't obvious, read the instruction book! Modeling and design of many types of equipment for separating gas and liquids such as flash separators at the well head, distillation columns and even a pipeline are based on the phases present being in vapor-liquid equilibrium. The fugacity coefficients for each component in the vapor phase are represented by fi V. The saturation fugacity coefficient for a component in the system, fi Sat is calculated for pure component i at the temperature of the system but at the saturation pressure of that component. Questions from AIEEE 2012. The value of k for which the equation (K - 2)x2 + 8x + K + 4 = 0 has both roots real, distinct and negative is. Application of Derivatives. For calculation purposes, Eq. The graph only has one solution.
What Is The Value Of K K
Remember that diameter is twice the measure of a radius, thus 7 inches of the. At temperatures above the critical point of a component, one must extrapolate the vapor pressure which frequently results in erroneous K-values. Find the value of k for which the equation. If we isolate k on one side, it reveals that k is the constant ratio between y and x. The table does not represent direct variation, therefore, we can't write the equation for direct variation.
When an equation that represents direct variation is graphed in the Cartesian Plane, it is always a straight line passing through the origin. R. R is the gas constant with a value of 8. Think of it as the Slope-Intercept Form of a line written as. How to find value of k if given quadratic equation has equal roots. The quotient of y and x is always k = - \, 0. It is a powerful tool and relatively accurate if used appropriately. This pressure was termed the "Convergence Pressure" of the system and has been used to correlate the effect of composition on K-values, thus permitting generalized K-values to be presented in a moderate number of charts. Now, I don't know if their solutions are correct or not, because they don't exactly show that their obtained value of $k$ satisfies the condition on the circle (that it meets the co-ordinate axes exactly three times). 1) is transformed to a more common expression which is. Wilson, G., "A modified Redlich-Kwong equation of state applicable to general physical data calculations, " Paper No15C, 65th AIChE National meeting, May, (1968).
Reference: - Natural Gasoline Supply Men's Association, 20th Annual Convention, April 23-25, 1941. Having a negative value of k implies that the line has a negative slope. Now, I first found the centre of the circle, with the information given, to be $(6, 5)$, and substituing this into the equation, we obtain $k=61$. Solution: To show that y varies directly with x, we need to verify if dividing y by x always gives us the same value. I is the acentric factor, P is the system pressure, in psi, kPa or bar, T is the system temperature, in ºR or K. (P and Pc, T and Tc must be in the same units. ) Statement 2: The function f is continuous and differentiable on (-°o, oo) and/'(0) = 0. What is the value of k k. With general quadratic equation, we get.
For What Value Of K Do The Equations 3X-Y+8 0
Solution: If real roots then, If both roots are negative then is. As you can see, the line is decreasing from left to right. The determination of convergence Pressure is a trial-and-error procedure and can be found elsewhere [6]. This approach is applicable to polar systems such as water – ethanol mixtures from low to high pressures. The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is. What happens if you change the temperature? As mentioned earlier, determination of K-values from charts is inconvenient for computer calculations. Example 6: The circumference of a circle (C) varies directly with its diameter.
Appendix 5B is based on the data obtained from field tests and correlations on oil-gas separators. As is the case for the EoS approach, calculations are trial and error. Therefore, scientists and engineers have developed numerous curve fitted expressions for calculation of K-values. This method is simple but it suffers when the temperature of the system is above the critical temperature of one or more of the components in the mixture. Prausnitz, J. M. ; R. N. Lichtenthaler, E. G. de Azevedo, "Molecular Thermodynamics of Fluid Phase Equilibria, ", 3rd Ed., Prentice Hall PTR, New Jersey, NY, 1999. Maddox, R. and L. L. Lilly, "Gas conditioning and processing, Volume 3: Advanced Techniques and Applications, " John M. Campbell and Company, Norman, Oklahoma, USA, 1994. Complex vapor pressure equations such as presented by Wagner [5], even though more accurate, should be avoided because they can not be used to extrapolate to temperatures beyond the critical temperature of each component. Under these conditions the fugacities are expressed by.
The thermodynamic equilibrium between vapor and liquid phases is expressed in terms equality of fugacity of component i in the vapor phase, fi V, and the fugacity of component i in the liquid phase, fi L, is written as. Relations and Functions - Part 2. We know that quadratic equation has two equal roots only when the value of discriminant is equal to zero. Substitution of fugacities from Eqs (12) and (13) in Eq (1) gives. 35 MPa) or to systems whose components are very similar such as benzene and toluene. But we can use it to come up with a similar set-up depending on what the problem is asking. By Dr. Mahmood Moshfeghian.
The southern tribes surrendered, but the northern Xiongnu tribes moved westward away from Han forces, toward the Mediterranean, where they were eventually to threaten the stability of the eastern flank of the Roman Empire. Now, seizing that "one moment in ten thousand ages, " the Qin king relied on his massive army of conscripted peasant farmers to make. Lewis, Bernard (trans. Worlds together worlds apart 6th edition. The Zhou initially swore allegiance to the Shang and allied with them in their fight against nomadic incursions on the western borderlands.
Worlds Together Worlds Apart Concise 3Rd Edition Combined Volume Pdf
A fundamental guide to all aspects of the Roman army. Claimed to have met at least sixty rulers, and in his book he recorded the names of more than 2, 000 persons whom he knew personally. What aspects of Hellenistic culture held broad appeal for diverse groups? Over the course of two centuries, these major powers learned how to settle their differences through treaties and diplomatic negotiations rather than on the battlefield. And because their ancestors were pastoralists, the Persians had no highly developed urban tradition of their own to draw on. Analyze the extent to which the diverse peoples of subSaharan Africa were connected to each other and the larger world during the first millennium BCE. First investigated by the German archaeologist Heinrich Schliemann in the 1870s, Troy level I was identified as a third-millennium BCE fortified settlement with monumental stone gateways and stone-paved ramps. Worlds Together, Worlds Apart (3rd ed.) by Jeremy Adelman (ebook. And like peasants from its devotees; it became a religion of traders and many contemporary scholars and philosophers elsewhere, a other city dwellers whose occupations allowed them to follow new group of South Asian scholars and religious leaders took its precepts. The Leakeys nicknamed it "Dear Boy. "
Worlds Together Worlds Apart 6Th Edition
A thought-provoking essay on the social, economic, and political development of the wider Near East during the fourth and third millennia BCE. From K'ung-chia's time to the time of Emperor Chieh, the feudal lords had revolted many times against the Hsia. Compare and contrast the islands of the South Pacific to those in the eastern Mediterranean during the second millennium BCE. "The outward forms of this art will not of course be everywhere the same. Because the cities that the Bactrian Greeks founded included a substantial number of Indian residents, and thus were a mix of cultural influences, they have been called "Indo-Greek. " The Celts, Gauls, Germans, Scythians, and other northerners came to the Mediterranean first as conquerors. However, the iconography of bodhisattvas was not clearly established at the time that this frieze was carved. Registration, required of all males when they reached maturity (at age sixteen or seventeen, and five feet in height), provided the lists from which men were taxed and conscripted. Klein, Jacob, "The Marriage of Martu: The Urbanization of 'Barbaric' Nomads, " in Mutual Influences of Peoples and Cultures in the Ancient Near East, ed. A fine collection of original sources that portray various aspects of classical Islamic society. Worlds together worlds apart 3rd edition pdf free download. How was the mandate of heaven used to justify the defeat of the Qin by rebels? From the navel was the atmosphere created, from the head the heaven issued forth; from two feet was born the earth and the quarters (the cardinal directions) from the ear. That spread made Buddhism, for the first time, a. major world religion.
Worlds Together Worlds Apart 5Th Edition
Teotihuacán A city-state in a large, mountainous valley in present-day Mexico; the first major community to emerge after the Olmecs. "This is what my master has spoken, this is what he has said. The seaborne peoples from all around the Mediterranean Sea basin—Phoenicians, Greeks, Cretans, Cypriots, Lydians, Etruscans, and many others—shared common characterisA N E W W O R L D O F C I T Y- S TAT E S tics. The reigning sultan, Alaud din Khalji (ruled 1296–1316), was able to raise a sufficiently powerful army to drive the Mongols, who were. The most complete discovery from Southeast Asia, it dates from about 800, 000 years ago. MAP 1-6 THE SPREAD O F FA R M I N G I N E A S T A S I A. l Yel. Thus, gradually, a network of educated men and women formed that was not wholly dependent on either the church or the state, but which, increasingly, had the power to debunk old truths and create new beauties. 10.1525 9780520933057-008.pdf - III. From The Pyramid Texts T h e Pyramid T e x t s are carved on the walls of the sarcophagus chambers and adjoining | Course Hero. In India, Buddhists had adopted a form of dome-shaped tombs called stupas into shrines used to house relics of the Buddha. Art Library; p. 406: akg-images; p. 407 (both): Alamy; p. 408 (top): The Art Archive; (bottom): Werner Forman/Art Resource; p. 410: Alamy; p. 411: Greg Probst/Corbis. Frequently several households would operate as a closed economic unit, producing most of the necessities within a closed system. They were part of the foundation of the Roman Empire. They must do this because they must create an idea to match every substance that exists in our real everyday world... and also one in the realm of the eternal heavenly entities.
Worlds Together Worlds Apart 3Rd Edition Pdf Free
Although no traveler crossed the Atlantic or Pacific oceans, an increasing number ventured through the lands of Africa, Europe, and Asia. Ancient Egyptian history can be told as a struggle of sharply competing dualistic forces: the north or Lower Egypt versus the south or Upper Egypt; the sand, the so-called red part of the earth, versus the rich soil, described as black; life versus death; heaven versus earth; and order versus disorder. Determined to ensure their religion's survival and restoration in Jerusalem, priests in exile in Babylon combined and finalized writings that had begun to be recorded in the tenth century BCE. Metallurgy developed both in Crete and in the Cyclades. Clans, ordered in a hierarchy determined by seniority. Usually administrative centers where farmers and traders gathered to take advantage of the regional states' political and military protection. Yan g. G U P TA L E M P I R E Ganges R. R kong. Worlds together worlds apart concise 3rd edition combined volume free pdf. Dni ep e. Milan 1339 1204 Toulouse 1229 1248 Venice c. 12th C. Avignon PY 1250 REN Bologna 1088 Genoa 1303 EES c. 1218 Florence 1215 CASTILE c. 1300 1246 Marseille 1308 AR. Ideas of freedom, as manifested in trading relations, labor, and political activities, clashed with a traditional world based on inherited rights and statuses and further challenged the way men and women had lived in earlier times. Even more radical were thinkers like Pythagoras from Samos, who held that a wide range of physical phenomena in the world, from masks to music, were in fact based in numbers; thus in a sense he foreshadowed the modern-day digital revolution.
Worlds Together Worlds Apart Concise 3Rd Edition Combined Volume Free Pdf
The Western Pure Land. How did Roman attitudes toward military service influence the growth of the empire? Chosen by the whole people, Va¯, is what is meant by Maha¯ Sammata; so Maha¯ Sammata (the Great Elect) was the first standing phrase to arise [for such an one]. Commanderies Han Empire in 1st Century BCE Major trade center Area of intensive agriculture. Chinese and other merchants expanded trade across the Silk Road and the South China Sea.
Worlds Together Worlds Apart 3Rd Edition Pdf Free Download
To many outsiders, especially Europeans whose own end of Afro-Eurasia was in a state of constant war, Ming stability and centralization appeared to be political wizardry. The famous Barmaki family, who for several generations held high administrative offices during the Abbasid caliphate, came from the central Asian city of Balkh. Cartledge, Paul (ed. The hominids soon learned to communicate Also, recent discoveries of the bones of five individuals in the mainly through gestures, but they also may have developed a Afar depression in Ethiopia (in an area just south of where simple early form of language that facilitated the establishLucy was found) have revealed the existence of bipedal ho-. In one infamous "crusade" Frankish armies went on a rampage in the Byzantine capital and sacked Constantinople in 1204. At the height of the Shang state, circa 1200 BCE, its rulers erected massive palaces at the capital of Yin, which required bronze foundries for its wine and food vessels. RELI G I ON S, EM PI RES, AN D AG RI C U LT U RAL REVOLU T I ONS. He moved the capital eastward from its former location, Chang'an, to Luoyang on the North China plain. The prosperity and cultural vitality of the heavily populated regions of China and India spilled over into the maritime and Asian mainland worlds of Southeast Asia, especially benefiting the Thai, Vietnamese, and Burmese peoples who gradually emerged as the largest population groups on the mainland. And like Byzantine rulers, Abbasid Turks would become the successor state to the Umayyad dycaliphs lived in secluded palaces, cut off from their subjects nasty and rule over stretches of southern Europe and Southand protected by eunuchs and professional bodyguards. Spanish silks also passed through Alexandria on their way to eastern Mediterranean markets.
And challenged from below, both by individuals pursuing alternative kinds of spirituality and by increasing demands on the clergy and church administration. And while the connections between this northern frontier zone and other parts of the AfroEurasian world began to multiply, it was still too dispersed and unruly a region to give rise to integrated kingdoms. Through its evangelizing efforts, the Christianity of the West bridged the ancient gulf between the Mediterranean world and the non-Roman world of the north. The world was being carved up into culturally distinct regions. The paradoxical result was that the world was becoming more interconnected, while its regions became more clearly differentiated. Unlike other Muslim authors of his time, however, Usa¯mah does not refer to the Franks in derogatory terms such as "infidels" or "devils. " Your chief descendant has not as much talent and skill as I and cannot serve the spirits!... " 100 BCE, carries an image of Zeus, surrounded by the Greek The coming of the many nomadic groups did not underinscription ΒΑΣΙΛΕΩΣ ΒΑΣΙΛΕΩΝ ΜΕΓΑΛΟΥ ΜΑΥΟΥ mine local cultural traditions or the Hellenistic heritage, but it (King of Kings, the Great Maues). The Austronesians then ventured further eastward into the South Pacific, apparently arriving in Samoa and Fiji in 1200 BCE and on mainland Southeast Asia in 1000 BCE. Chapter 11, "Crises and Recovery in Afro-Eurasia, 1300s–1500s, " describes how the Mongol warriors, through their conquests and the integration of the Afro-Eurasian world, spread the bubonic plague, which brought death and depopulation to much of Afro-Eurasia. In East Asia, rugged nomadic people from the steppes of Inner Eurasia tangled with Shang. The war economy also provoked universal demand for these better weapons; smiths therefore began to produce them in bulk—as evidenced by the great hoards of copper and bronze tools and weapons from the period found in several archaeological sites in central Europe. These new rulers gradually rebuilt state institutions. Therefore literacy, though a fundamental part of the.
Similarly, solid wood wheels that easily shattered gave way to spokes and hooped bronze and later iron rims. The Chinese from East Asia, who did not appear to have an indigenous creation story, and Buddhists believed in an apparently endlessly repeated reappearance of human and animal souls over time. As in Mesopotamia, such population densities were unprecedented departures from the common dispersal of peoples into self-sufficient agrarian hamlets, villages, or nomadic communities. What can we perceive more generally about the differences between these societies?