The Kelvin equation

The Kelvin equation The Kelvin equation relates the vapour pressure of a liquid to the effect of surface curvature i.e. a meniscus with radius. The equation illustrates that due to the surface tension and the surface being larger than the volume, there is much higher evaporation rate for smaller droplet liquids when compared to that of larger droplets. ln(P/P0 ) = 2?Vm /rRT The Kelvin equation also shows that smaller particles exhibits higher solubility than larger particles. This occurs because of much greater pressure inside the droplet than outside and therefore gas diffusion can occur across the plateau borders of the droplet, weakening the walls (from high to low pressure). The vapour pressure of that over the droplet of water of radius r and inside a bubble in water at a specific temperature could be calculated using the Kelvin equation below. KELVIN EQUATION PARAMETERS P: Actual vapour pressure P0: Saturated vapour pressure Surface tension of liquid MW: Molecular weight r: Radius Density R: Universal gas constant (8.314 J K-1 mol-1) T: Temperature in Kelvin The Kelvin equation has a variety of significant effects as it provides clarifications for such phenomena including supersaturation of vapours, superheating, Ostwald ripening and capillary condensation. This effect is known as Kelvin effect and also Gibbs-Kelvin effect or Gibbs-Thomson effect. (Barnes 2005) Supersaturation The effect on the Kelvin equation could be explained in terms of supersaturation of vapour. The term of supersaturation refers to the state in which a solution has overly dissolved material than that of a saturated solution. Supersaturation could also be referred to the compounds vapour having greater partial pressure than that of the vapour pressure of the compound. In the solid form, the small particles can lead to crystallites or large single crystals formation. In a polydisperse suspension the material will dissolve until it has reached its saturated level at that temperature. When the sample is stored, the temperature will fluctuate slightly regardless of storage location. For example, if the sample is stored in the fridge, the temperature could vary and so the temperature of suspension could increase leading to a rise in saturation level allowing smaller particles to further dissolve until a new saturation level is reached. When the temperature drops, the suspension is affected in terms of consisting more than usual of the dissolved species. The new concentration is described as supersaturation. The remaining dissolved species would precipitate back on all the particles, the smaller particles preferentially dissolve and so larger particles having a coat will enlarge. Hence, supersaturated solutions are a result because of alteration of the saturated solution, i.e. temperature, volume or pressure. Some examples of supersaturation are beer and carbonated water. Water is able to dissolve a lot of carbon dioxide than at atmospheric pressure, which happens at the elevated pressure in bottle. At the state of atmospheric pressure, the escape of the carbon dioxide gas from the supersaturated liquid is quite slow. This process is advanced by the existence of small bubbles which is caused by shaking the product. Rock candy Rock candy is a type of confectionery mineral composed of relatively large sugar crystals. The candy is formed by allowing a supersaturated solution of sugar and water to crystallize onto a surface suitable for crystal nucleation, such as a string or stick In the phenomenon of superheating, the homogeneous substance without boiling is heated at a temperature in which is greater than the liquids normal boiling point. In order for a vapour bubble to expand and consequently burst at the surface (to boil), the temperature heating must be highly sufficient (raised above the boiling point) that the vapour pressure will go beyond the atmospheric pressure. (Patrick 2006) An insufficient temperature that is below will cause the vapour bubble to decrease and so disappear. However, in terms of superheating, the liquid is seen that it does not boil despite having the vapour pressure exceeding the atmospheric pressure. As a result, the surface tension restrains the growth of the bubbles. Boiling chips which are also known as boiling stones or anti-bumping granules are purposely added to the liquid to make boiling easier without the liquid becoming superheated. They are small and insoluble porous stones composing of calcium carbonate or silicon carbide. Inside the stones, they have pores that allow cavities to trap air and supply spaces in which the solvent bubbles can develop (nucleation sites i.e. formation of the vapour bubbles in on cavities). When there is an addition of boiling chips to a solvent and is heated, it would release very small bubbles. These tiny bubbles prevent bumping, loss of solution and hence allows liquid to boil easier without being superheated. Without the addition of boiling chips in a solvent, the heated liquid could be defined as superheated, an unstable state and therefore would be able to release a quantity of bubble of gas all of a sudden or perhaps violently. As a consequence of the sudden expel of vapour from the container of the liquid, it could lead to from ruining of the experiment to causing harsh burns. Ostwald ripening In regards to droplets that are spherical and being in contact with their vapour, the two radii situated in the liquid phase are equal and so maintain positive signs. Therefore in reference to the Kelvin equation, the droplets vapour pressure will be higher than the same liquid with a flat surface. An example is that for a radius of water droplet of 10nm, the increase in vapour pressure is approximately 10%. The smaller the droplets radius, the greater the vapour pressure. (Barnes 2005) For instance, in the case a polydispersion system (droplets with different sizes), the smaller particles has the tendency to dissolve (i.e. have greater solubility) or evaporate attaching themselves onto the surface of the larger ones, leading the larger particles to continue to grow with time but the smaller particles disappearing. This spontaneous process known as Ostwald ripening was first recognised in 1896 by Wilhelm Ostwald. (Ostwald 1896) A real life effect of the Kelvin equation occurs in clouds in which the larger droplets grow expecting to be heavy enough to fall as rain. Similarly, this process also exists for crystals contained in solutions. The larger crystals will tend to grow rather than the smaller ones resulting in a process of Ostwald ripening. This process is an important ageing effect occurring in any polydisperse systems. It could be observed in foams, emulsions as well as aqueous sols. (Adamson 1990) In terms of foam instability, the reason of instability could be due to Ostwald ripening. The Ostwald ripenings driving force arises because of the variation of Laplace pressure between bubbles of unequal size that is the smaller and larger foam bubbles. (Barnes 2005) The smaller bubbles having a greater gas pressure than the larger bubbles causes an effect on the foam stability. For the period of foam storage, the bubbles rise in the gravity field to the top of the liquid due to the large density existing between the liquid and the gas phases. From here, they shape a loosely closed-packed or honeycomb like structure from which the liquid drains forming foam that turns out to be dryer. The thin films created can collapse due to gravity and causing coalescence of bubbles. When increased of gas solubility with pressure happens, gas between bubbles are able to diffuse from the smaller to the larger bubbles. A large bubble in the foam that is surrounded by smaller bubbles could ultimately cause a big hole in the structure of the foam. (Hubbard 2002) Ostwald ripening is the cause of foam instability when a larger pressure difference of foam bubbles that are spherical cam be seen. In the case of polyhedral foam (with planar liquid lamella), the foam bubbles pressure difference is not great and so foam instability is not because of the Ostwald process. (Tadros 2005) Since the surface of the bubble behaves like viscoelastic behaviour, the process of Ostwald ripening in foam bubbles could be reduced by addition of a gas that is only soluble in the liquid. As a result of this process, it also has an effect of decreasing of specific surface area in time due to the highly soluble particles. (Lyklema 2005) The Ostwald ripening is important as it is used to increase the efficiency in both industrial and analytical filtration. (Barnes 2005) Capillary Condensation The Kelvin effect can also be observed in terms of capillary condensation due to the existence of a curvature, a meniscus. Capillary condensation arises because of the vapours adsorption in a capillary which creates a liquid surface with tiny radius of curvature. (Fisher 2002) The liquids vapour pressure being lower than that of the same liquid with a flat surface is a consequence of the radii being positioned in the vapour phase. If the actual vapour pressure is greater than the vapour pressure calculated from using the Kelvin equation for the curved surface than condensation would likely to occur. The actual vapour pressure for a flat surface may possibly be lower than its saturation vapour pressure. (Patrick 2006) As the capillary filled by capillary condensation occurs, immediately a meniscus is generated (which depends on the liquids surface tension) at the liquid-vapour interface enabling the equilibrium to be under the Psat (saturation vapour pressure). At low vapour pressure, the liquid condenses in smaller radius of the capillary. As the vapour pressure increases, further condensation of the liquid at the larger radius capillary is filled causing the radius of the meniscus to increase (capillary becoming full). The Kelvin equation implies that the Pv/Psat rises inside a capillary and the meniscus radius will further expand causing a creation of more flat surface. Hence, the vapour condensation is able to occur smoothly over the range of vapour pressures. For any liquid-vapour interface involving a meniscus, the Kelvin equation therefore relates the change between the equilibrium vapour pressure and the saturation vapour pressure. Capillary condensation as an important factor, is significant by means in both naturally and synthetic occurring porous structures. These structures allow scientists to recognize the concept of capillary condensation to determine pore size distribution as well as surface area through adsorption isotherms. (Barnes, 2005) References Adamson, W 1990, Physical chemistry of surfaces, 5th edn, John Wiley Sons, Canada Barnes, G.T 2005, Interfacial science, Ist edn, Oxford University press, United States CUBoulder Organic Chemistry, 2007, Boiling Chips, viewed 28 March, 2010 Economic expert, 2010, Supersaturation, viewed 28 March, 2010 Farlex, 2010, Kelvin equation, the free encyclopedia viewed 25 March, 2010, Fisher, LR Israelachvili JN 2002, Colloid Interfacial science, 3rd edn, Elsevier LTD, United States Gordon, M 1988, Physical Chemistry, 5th edn, McGraw-Hill, United States Hiemenz, CP 1997, Principles of Colloid and Surface, 3rd edn, Marcel Dekker, United States Hubbard, T 2002, Encyclopedia of Surface and Colloid Science: Por Z, 2nd edn, Marcel Dekker, New York Lyklema, J 2005, Fundamentals of interface and colloid science, 2nd edn, Academic press, London, vol. 2, p. 24 Ostwald, W 1896. Lehrbuch der Allgemeinen Chemie, vol. 2, part 1. Leipzig, Germany. Sinko, PJ 2006, Martins physical pharmacy and pharmaceutical sciences, 5th edn, Lippincott Williams and Wilkins, Philadelphia Tadros, F.T 2005, Applied Surfactants: principles and application 4th edn, edn, Wiley-VCH, Germany. The engineering toolbox, 2005, Introduction to vapor and steam, viewed 28 March, 2010, UBC Chemistry Department, 2002, Boiling Chips, viewed 28 March, 2010 Uci education, 2005, Boiling point and distillation, RDG, viewed 28 March, 2010 https://eee.uci.edu/programs/hongchem/RDGbpdostill.pdf

The Elderly and Malnutrition Essay -- Health Nutrition Pyramid Diet

The Elderly and Malnutrition      Ã‚  Ã‚  Ã‚  Ã‚   At any age, nutrition is vital to maintaining health and enhancing quality of life.   However, achieving good nutrition can be especially difficult for the elderly, the fastest growing portion of America's population.   Many factors, including physiological changes, changes in nutritional needs, illness and physical limitations, food-medication interactions, depression and loneliness, and food insecurity are common causes of malnutrition in the elderly.   This paper will explore factors affecting elderly nutrition, provide suggestions for obtaining and maintaining good nutrition after age 65, and describe the services available to help the elderly meet their nutritional needs.  Ã‚        Ã‚  Ã‚  Ã‚  Ã‚   A number of factors influence the nutritional status of the elderly.   First, several physiological changes impact elderly nutritional requirements.   Changes in taste and smell may decrease an individual's appetite or desire for food.   Gastro-intestinal motility decreases with age and may lead to constipation, decreased nutrient absorption, and a decrease in fat and protein absorption.   Metabolism also slows with age; this results in a decrease of lean body mass and an increase in body fat (8).   Lastly, bone mass decreases, leaving the elderly vulnerable to bone fractures from falls and osteoporosis.      Ã‚  Ã‚  Ã‚  Ã‚   Ultimately, these physiological changes result in different nutritional needs for the elderly.   The Food and Nutrition Board of the National Academy of Sciences issues the Recommended Daily Allowances for healthy people over the age of 51.   However, these RDAs are limited in that they have been derived from studies of younger, healthy populations and do not account ... ...;. 5) Good Nutrition is Ageless. Egg Nutrition Center. 22 Jan. 2002 <http://www.enc-online.org/elderly.htm>. 6) Good Nutrition for Seniors Caregiver Fact Sheet. 9 Aug. 2001. National Network for Health. 22 Jan. 2002 <http://www.nnh.org/products/gnfs.htm>. 7) Home page. Meals on Wheels Association of America. 22 Jan. 2000.   <http://www.projectmeal.org/mowaa.html>. 8) "Nutrition Index."   Gerontology and Geriatric Dentistry n.d.: n. pag. Columbia University Dental Education Software. N.d. 9) A Profile on Older Americans: 2001. 10 Jan. 2002. Administration on Aging. 22 Jan. 2002 <http://www.aoa.gov/default.htm>. 10) The Warning Signs. New York State Office for the Aging. 22 Jan. 2002 <http://agingwell.state.ny.us/eatwell/warning.htm>. 11) Wieand, Jane. Telephone Interview. 22 Jan. 2002.      

Theme Elements in Chinua Achebes Things Fall Apart :: Things Fall Apart essays

Theme Elements in Things Fall Apart Achbe, in the novel Things Fall Apart, conveys a flavor of traditional African culture in the 1800`s. But despite this, it seems the tragedy of okonkwo that embodies the theme of the novel. Many of Achebe`s themes are not limited to the events in his novel, but relate to SITUATIONS, in which traditional values are questioned and people from different cultures meet, the most profound impact being related to the themes of religion and justice.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚     Like any good religion, the Igbo religion comes with many superstitions. Personal chi is one of the superstitions in the Igbo tribe. Chi can be a personal fragment of the Supreme Being, unique for each individual. It determines much of a person's success and character. "When a man says yes his chi says yes also" (19). But at the same time a man does not challenge his chi. "The evil you have done can ruin the whole clan. The earth goddess whom you have insulted may refuse to give us her increase, and we shall all perish" (22). Ezeani said this to okonkwo in response to his challenge against his chi, by beating his wife during the week of peace. Okonkwo BECAME THE EXAMPLE OF A person challenging his own chi. His desperate desire to succeed his chi, does not let him go any further than failure, destruction and death. Chi is simultaneously a destiny and an internal commitment, WHICH cannot be denied.   Ã‚  Ã‚     The Igbo religion has a tendency to symbolize numerous amounts of divine gods. They HAD a god for every different natural phenomenon that occurred. These things of worship were things such as trees, pieces of wood, hills, caves etc.    For every symbolic god there was a being in the clan that represented it. Ezeani the priestess, of the goddess of the earth, represented the goddess of earth (Ani). The clan seeks knowledge from the god through the oracle of the hills and caves. Other symbols in the Igbo religion are the sacred silk cotton tree and the evil forest.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚     The festivals, in the novel contribute to the development of this theme as well.   The two festivals "Week of peace" and "The Feast of the New Yam" ARE SYMBOLS OF IMPORTANCE TO the clan and OF THE power WHICH gods have. The week of peace was one of the means of unification FOR the clan and appeasement for the gods in control over the crops.

Essays --

Role of Open Design in Engineering â€Å"Before I start teaching you all Industrial Revolution, I have a question?†. My history teacher drifted towards the blackboard and wrote - â€Å"Who invented the Steam Engine?† I raised my hand promptly. â€Å"Yes, Ankit.† I stood up - â€Å"James Watt, maam!† â€Å"You are correct. It was the invention of Steam Engine by James Watt that changed the world and led to the industrial revolution.† I gave a equanimous smile and took my seat. Boldrin and Levine mentioned in their book Against Intellectual Monopoly how James Watt got the idea of allowing steam to expand and condense in separate containers while repairing a small Newcomen steam engine. In 1768, he applied for a patent on the idea after doing a series of improvements. He spent the next six months working hard to obtain his patent, made an alliance with the rich industrialist Matthew Boulton and even secured an act of Parliament extending his patent until the year 1800. In the name of economic freedom, the great statesman Edmund Burke spoke eloquently in Parliament against the creation of this unnecessary ...

The Power of Light in The Scarlet Letter Essay -- Scarlet Letter essay

The Power of Light in The Scarlet Letter   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚     Ã‚  Ã‚   Since the conception of humanity, man has been fascinated with that presence which illuminates, yet cannot be touched.   Mankind has brought it into his religions, giving it a great deal of importance in his creed.   Following in the footsteps of his ancestors, Nathaniel Hawthorne uses light as a tool of God that illuminates the darkness of human iniquity and exposes its permanence.   He studies the psychological theme of the impossibility of eradicating sin from the human heart in his novel The Scarlet Letter.   The use of light in order to fortify this psychological theme confirms its significance in the novel.   As though he were weaving an elaborate tapestry, Hawthorne meshes light's intense symbolism into his characters' natures until a chef d'oeuvre manifests itself upon the loom of the reader's intellect.   This tapestry serves as a subtle background upon which the characters' sinful hearts are bared.         Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   As Hawthorne navigates the reader through th...

Gas Laws Lab Essay

Introduction: The four basic physical properties of a gas sample are pressure, volume, temperature, and number of moles. The volume simply indicates the volume of the container since a gas will take up all space available to it. The temperature indicates the average kinetic energy of the gas particles. For gases, the temperature must be converted to the Kelvin unit. The pressure of the gas indicates the number of collisions with each other and the wall of the container. The number of moles indicates the amount of gas particles. Gases do not have a definite shape of volume. Gases spread out into their container and occupy the entire volume available, which means they are free to move around and have large amounts of empty space. In many chemical reactions, gases are produced; for example, reactions involving metal carbonates that react with an acid produce gaseous carbon dioxide. Objective: To determine the volume of gas produced from a reaction between a metal carbonate and acid and to determine the identity of an unknown carbonate salt. Pre-Lab Questions: 1. If you increase the temperature what happens to the speed of the particles? Explain. 2. What is the formula to convert Celsius temperature to Kelvin? a. Â °C+273.15=K 3. What are the standard conditions for a gas? Are you at standard conditions in the lab? 4. Boyle’s Law – The principle that the volume of a given mass of an ideal gas is inversely proportional to its pressure, as long as temperature remains constant. Boyle’s law is a subcase of the ideal gas law. P1V1 = P2V2 Charles’ Law – The law of volumes. The volume of a fixed amount of gas at constant pressure is directly proportional to the Kelvin temperature of the gas. (Temperature must be in Kelvin). V1T1= V2T2 V/T = K V1T2 = V2T1 Gay-Lussac’s Law – Pressure is directly proportional to temperature if the volume is constant. P1/T1 = P2/T2 5. What is the Ideal Gas Law in formula form? What is the value for the proportionality constant with units? Why are those units so important? b. PV = nRT c. C = PV / T 6. Write the balanced equations for CaCO3, BaCO3, Li2CO3, and Na2CO3 reactions with hydrochloric acid. 7. Calculate the molar mass of these same four metallic carbonates. LiCo3 = mass/mole; 3.0036g/0.0344 mol = 87.31 g/mol Materials/Equipment: * 3.0 M HCl (aq) * 5 ml graduated cylinder * Balloon String * Scissors * Weighing paper * 3g of unknown #2 carbonate salt * Funnel Procedures: First measure out 5ml of 3.0 M HCl into the graduated cylinder and weigh 3 g of the unknown carbonate salt. Using the funnel, pour the unknown carbonate salt into the balloon and put the open end of the balloon over the graduated cylinder and secure with a string. It is important to make sure the string is very tight to prevent the gas from leaking. Empty the contents of the balloon into the graduated cylinder that contains the 3.0 M HCl. After the gas fills the balloon, use a string and measure the circumference of the balloon.| Observations:Carbonate is limiting reactant.| Conclusion: Based upon our experiment, equations, and calculations that our unknown Carbonate Salt for Unknown # D was Li2CO3 – Lithium Carbonate. There could be a number of factors that could have caused us to receive an 18.1% error. How we held the balloon when tipping it over the acid could greatly affect the radius of our balloon.

Customer benefit package (CBP) diagram for Gold’s Gym Essay

Gold’s Gym International, Inc. is an American chain of international co-ed fitness centers (commonly referred to as â€Å"gyms†). Each gym features with a wide array of exercise equipment, group exercise classes and personal trainers to assist clients. So the primary services of the Gyms is to provide a wonderful and professional environement for people who want to do bodybuilding and physical education. It is considered a landmark in the bodybuilding subculture. Gold’s Gym locations are equipped with cardiovascular and strength training equipment and offer group exercise classes such as group cycling, pilates, Latin dance, yoga and stretching through the company GGX (Gold’s Group Exercise) program. Many gyms also offer basketball, swimming pools and boxing studios so these are Gold’gyms’s peripheral service. 2. The mission of the Gold’gyms is to help people find their inner strengths to achieve goals. No matter what your fitness level is. Anything is possible when coming to Gold’gyms. 3. The strategy of the Gold’Gyms is to provide the best facilities for trainers and also bring benefits to membership. They focus on 4 â€Å"P†. Product : Equipment and training programs for health and fitness vary among facilities Certified staff and employees. Price: Membership fees and plans range depending on gym  $34.99 for a two-year commitment to $569 for a one-year membership that includes group sessions. Promotion: Gold’s Gym have their own website so we can easily find infortmation, searching for training progames and applying the a training course, also they have Tumblr, Facebook, Twitter Gold’s Gym Spotter App and Commercials. Everything is public so it gets closer to customers. Place : with 600+ gyms in 37 states and 30 different countries. Gold’gyms are gaining more and more customers every single year. 4. The competitive priorities of Gold’gym are: Currently have the 3rd largest market share. Has 600+ gyms in 30 countries. Have a history of being a body-building gym Recognizable logo. Large line of products in store. The favorite place for many celebrities. 5. The core competencies of Gold’gym is :  They encourage people to define their own strength no matter what their fitness level is. 6. The strategy that they used to win customers is : Providing the best environment for people who want to do bodybuilding. With their reputation, the Gyms always provide most professional space for trainer. With well-trained staffs and employees. Gold’s gyms have built their own images without any kind of lobby or PR. 7. Two key perfomances matrix which could be useful are : Full body analysis : This will help the Gyms to what will be the best method to people to train in the whole body. The body will be trained in fully and healthiest way. Focus on the 18-34 year olds : When people reach to 18, and from 18 to 25 years old: bonds and body structure are built quite good so it is the best time for them to do a professional bodybuilding, in additional, they also have many free time than others. From 25 to 34: They already have jobs so the pressure of job may effect their body so they really need to practice to relax and become healthier in order to work better. If the Gyms can focus on these two things, I believe that they can even gain more profits and become the best fitness centers in the world