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As shown in Fig. P3.90, a system consists of a copper tank

Fundamentals of Engineering Thermodynamics | 8th Edition | ISBN: 9781118412930 | Authors: Michael J. Moran ISBN: 9781118412930 139

Solution for problem 3.90 Chapter 3

Fundamentals of Engineering Thermodynamics | 8th Edition

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Fundamentals of Engineering Thermodynamics | 8th Edition | ISBN: 9781118412930 | Authors: Michael J. Moran

Fundamentals of Engineering Thermodynamics | 8th Edition

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Problem 3.90

As shown in Fig. P3.90, a system consists of a copper tank whose mass is 13 kg, 4 kg of liquid water, and an electrical resistor of negligible mass. The system is insulated on its outer surface. Initially, the temperature of the copper is 278C and the temperature of the water is 508C. The electrical resistor transfers 100 kJ of energy to the system. Eventually the system comes to equilibrium. Determine the final equilibrium temperature, in 8C.

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ECON 2306 Test #2 PREVIEW SHEET 1. What is meant by utility Satisfaction …isoutility Equal Satisfaction 2. What is meant by marginal utility Additional Satisfaction 3. What is the formula for marginal utility ΔTU/ΔQ (change in total utility divided by change in quantity) 4. What is the formula for a budget constraint if only two goods may be purchased I = Px Qx + Py Qy 5. What is the slope of the budget constraint Price x ÷ Price y 6. What is the slope of the isoutility curve MRSxy= MUx ÷ MUy 7. What are the characteristics of an isoutility curve *all points on an indifference curve produce equal levels of satisfaction *indifference curves must not cross because this leads to an INTRANSITIVITY. *Higher curves are preferred to lower curves because they are closer to bliss point and farther away from its origin. *Slopes are negative and represent the marginal rate of substitution of good x for good y. *Shape of curve refers to the law of diminishing marginal utility 8. What is meant by “intransitivity” when two indifference curves cross 9. What is the formula for consumer equilibrium MUx/Px=MUy/Py … Producer equilibrium MPL/PL=MPk/Pk (where MP= marginal product, L= labor, K= capital) 10. What happens to a budget constraint when the price of one good changes The higher good “x” goes in price, the steeper the budget constraint. … When more income is received When nominal income doubles, and prices fall in half, both will cause a shift in the budget constraint to the right (in real graph terms). 11. How are the vertical and horizontal intercepts of a budget constraint determined Vertical: Income/Price of good y Horizontal: Income/Price of good x 12. How can an individual’s demand curve for a good be determined using isoutility curves and budget constraints The demand curve can be derived from the indifference curves and budget constraints by changing the price of the good. For example, if the price of pizza is $4, the quantity demanded of pizza is two. If the price of pizza decreases, the budget constraint becomes flatter and the consumer can purchase more pizza, say the price of pizza drops to $2 and consumer purchases 4 units. If the price drops to $1.33, the quantity demanded increases to 5. Plotting each of the price and quantity demanded points creates the demand curve for pizza. 13. What is meant by the law of demand The law of demand is a microeconomic law that states, all other factors being equal, as the price of a good or service increases, consumer demand for the good or service will decrease, and vice versa. 14. What is meant by production The processes and methods used to transform tangible inputs (raw materials, semi-finished goods, subassemblies) and intangible inputs (ideas, information, knowledge) into outputs (goods or services). 15. What is the formula for a Cobb-Douglas Production Function Q=F(K,L) Where: - Q is the quantity of products, which is the function of K,L. - L the quantity of labor applied to the production of Q, for example, hours of labor in a month. - K the hours of capital applied to the production of Q, for example, hours a machine has been working for the production of Q. 16. What is meant by returns to scale The relationship between inputs and outputs in the long run. 17. How can a Cobb-Douglas Production function be used to determine returns to scale 18. What is meant by the marginal product of labor (MPL) The increase in the amount of output from an additional unit of labor 19. What is meant by the marginal product of capital (MPK) The increase in the amount of output from an additional unit of capital. 20. How can a Cobb-Douglas Production Function be used to calculate MPL & MPK MPL=ΔQ/ΔL, MPK=ΔQ/ΔK 21. How does a short-run production function differ from a long-run production function (graphically) In a short run production function, capital is held constant. In a long run production function, both capital and labor are held constant. 22. What is meant by “isoquant” Meaning equal quantity or equal output, is a graph of all possible combinations of inputs that result in the production of a given level of output. Used in the study of microeconomics to measure the influence of inputs on the level of production or output that can be achieved. 23. How does “isoquant” differ from “isoutility” An isoquant shows the various combination of two inputs (capital and labor) on an equal output, while an isoutility curve shows the various combinations of two commodities; good x and good y. 24. What is meant by the law of diminishing marginal utility In economics, the law of diminishing marginal utility states that the marginal utility of a good or service declines as its available supply increases. That is, the additional satisfaction gained from consuming more of a product reduces as we consume more units of that product. 25. What is meant by the law of diminishing marginal product The law of diminishing marginal productivity is an economic principle that states that while increasing one input and keeping other inputs at the same level may initially increase output, further increases in that input will have a limited effect, and eventually no effect or a negative effect, on output. The law of diminishing marginal productivity helps explain why increasing production is not always the best way to increase profitability. 26. How does the concept in #24 differ from that of #25 (above) The law of diminishing marginal utility is related to a consumer. The law of diminishing marginal productivity is related to a producer. 27. What are the three stages of production in a short-run production function  Increasing at an increasing rate  Increasing at a decreasing rate  decreasing 28. How can a production function be used to determine the marginal product of labor ... Average product of labor 29. What is the formula for MPL ΔQ/ΔL … APL Q/L 30. How do MPL and APL relate to the cost curves When MPL is at its peak, MC curve is at its minimum. When APL is at its peak, AVC curve is at its minimum. 31. How does the Total Product curve relate to the cost curves TP has the height of TVC and TC and the height of TFC 32. What ways can production be related to cost TC and TVC have the same shape 33. What are meant by fixed costs A fixed cost is a cost that does not change with an increase or decrease in the amount of output produced. … Variable costs Variable costs are those costs that vary depending on a company's production volume; they rise as production increases and fall as production decreases. 34. What are the formulae for TC TFC + TVC or ATC × Q…TFC TC – TVC or AFC × Q …TVC TC – TFC or AVC × Q 35. What are the formulae for ATC AFC + AVC or TC/Q …AFC ATC – AVC or TFC/Q …AVC ATC – AFC or TVC/Q 36. What are the formulae for MC ΔTVC/ΔQ or ΔTC/ΔQ …MR ΔTR/ΔQ 37. What is the formula for profit maximization MR=MC 38. What is the formula for cost-minimization of all inputs MPK/PK= MPL/PL 39. What is known about TC and TFC when output is equal to zero When Q=0, TFC=TC …Why TVC=0 40. In terms of types of cost, what things are equal when output is equal to zero TFC=TC …to one TFC=AFC, TVC=AVC=MC, TC=ATC. 41. What are the shapes of TC, TFC, and TVC TC and TVC are shaped like waves while TFC is horizontal. 42. What are the shapes of ATC, AFC, and AVC, MC Think of NIKE check mark for MC, then ATC has a bowl-like shape to it and would always be above AVC 43. How does MC relate to ATC and AVC MC always intersects ATC and AVC at their minimum points. It leads them. 44. How does ATC relate to AVC (graphically) ATC hits its minimum after AVC. 45. How does the MPL curve relate to MC MPL is at its peak when MC is at its minimum 46. How does the APL curve relate to AVC APL is at its peak when AVC is at its minimum 47. How is a long-run ATC curve derived The long-run average total cost curve is derived from the minimum points of tangency of each of the short-run ATC curves. 48. What is meant by “lumpy facilities” Lumpy inputs are inputs whose quantity cannot be changed gradually as output increases, but rather must be adjusted in large jumps. Moreover, this category of inputs can exist in either the short run or the long run. 49. What is meant by increasing returns to scale When inputs are doubled up, output more than doubles. 50. How does returns to scale differ from economies of scale Returns to scale is the relationship between inputs and outputs in the long-run, while economies of scale is the relationship between cost and output (as Q↑ ATC↓ in the long run). 51. What are the reasons for economies of scale  Geometric growth  Specialization of labor  Increased use of capital equipment  Managerial specialization 52. What is meant by MES Minimum Efficient Scale is the smallest amount of production a company can achieve while still taking full advantage of economies of scale with regards to supplies and costs. In classical economics, the minimum efficient scale is defined as the lowest production point at which long-run total average costs (LRATC) are minimized. 53. What is meant by diseconomies of scale Diseconomies of scale is an economic concept referring to a situation in which economies of scale no longer function for a firm. Rather than experiencing continued decreasing costs per increase in output, firms see an increase in marginal cost when output is increased. 54. What are the formulae for profit TR-TC or Q×(P – ATC) 55. What is the formula for profit-maximization (i.e., a profit-maximizing condition) MR=MC 56. What is meant by MR and MC MARGINAL REVENUE is the increase in revenue that results from the sale of one additional unit of output AND MARGINAL COST is the change in total cost that comes from making or producing one additional item. 57. What should a profit-maximizing firm do if MR>MC The firm is producing too little and can increase profit by increasing output …MRATC... normal profit P=ATC … loss-minimization PAVC, keep operating at a loss. 63. In terms of high-fixed cost or low fixed cost firms, what types of firms are more likely to shut down high 64. In terms of high-fixed cost or low fixed cost firms, what types of firms are more likely to operate at a loss low 65. In the short run, a firm must be able to cover which type of cost in order for it to make sense for the firm to operate variable 66. Be able to fill out a COST TABLE! Remember formula. Solve for TFC and AFC first using any method you can find. When Q=0 TVC=0 therefore TFC=TC. When Q=0 MC, ATC, AFC and AVC are not present because you can’t divide by 0. When Q=1 TFC=AFC, TVC=AVC=MC, TC=ATC. Remember graph. Use averages and marginal to find totals. Use totals to find averages. 67. What are the types of market structures Monopoly, duopoly, oligopoly, monopolistic competition, perfect competition. 68. What is meant by monopoly One firm…duopoly Two firms…oligopoly Few firms…monopolistic competition Many firms 69. What is meant by a price-taker Firms cannot control the market price of their product … price maker A price maker is a monopoly or a firm within monopolistic competition that has the power to influence the price it charges as the good it produces does not have perfect substitutes 70. How is the demand curve for a firm in perfect competition determined It’s determined by the market. The demand curve for the market, which includes all firms, is downward sloping, while the demand curve for the individual firm is flat or perfectly elastic. 71. What are the various things that the demand curve for a PC firm equals D=AR=MR=P 72. What is one item which a PC firm controls in the marketplace they can sell any quantity of the product at the market price 73. Graphically, what determines the level of output which a PC firm should produce price 74. What are the various misperceptions regarding firms operating as a monopoly Monopolies charge the highest price, Monopolists maximize unit profit (monopolists are interested in total profit not profit per unit, and want to operate where marginal revenue = marginal cost), Monopolists always earn a profit. 75. How does one determine the level of output and price for a monopoly TR=P×Q 76. How does one determine profit for a firm in monopoly Profit = Total revenue – Total Cost 77. What is the formula for profit TR-TC or Q×(P-ATC) 78. Graphically, how can the formula for profit be used in the case of monopoly 79. What is the MR curve for a Perfectly Competitive firm 80. What is the MR curve for a monopoly 81. Why might one describe a monopoly as being “evil” Monopolies are considered evil depending on how they are formed. If formed through irrational political policies they are objectively evil. 82. What is the formula for “allocative efficiency” P=MC…productive efficiency P= Min ATC

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Chapter 3, Problem 3.90 is Solved
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Textbook: Fundamentals of Engineering Thermodynamics
Edition: 8
Author: Michael J. Moran
ISBN: 9781118412930

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As shown in Fig. P3.90, a system consists of a copper tank