A hollow sphere with inner and outer radii of R1 and R2, respectively, is covered with a layer of insulation having an outer radius of R3. Derive an expression for the rate of heat transfer through the insulated sphere in terms of the radii, the thermal conductivities, the heat transfer coefficients, and the temperatures of the interior and the surrounding medium of the sphere.
> A copper wire, 0.8-mm OD, 5 cm long, is placed in an air stream whose temperature rises at a rate given by where t is the time in seconds. If the initial temperature of the wire is 10°C, deter- mine its temperature after 2s, 10s, and 1 min. T
> A spherical stainless steel vessel at 93°C contains 45 kg of water initially at the same temperature. If the entire system is suddenly immersed in ice water, determine (a) the time required for the water in the vessel to cool to 16°C, and (b) the temper
> A thermocouple (0.8-mm-diameter wire) used to measure the temperature of the quiescent gas in a furnace gives a reading of 165°C. It is known, how- ever, that the rate of radiant heat flow per meter length from the hotter furnace walls to the
> In the heat treating process in a sheet-metal manufacturing plant, brass plates are annealed by first heating them in an industrial furnace oven the inside of which is maintained at a constant uniform temperature of 550°C. If the surface of the brass pla
> A spherical shell satellite (3-m-OD, 1.25-cm-thick stainless steel walls) re-enters the atmosphere from outer space. If its original temperature is 38°C, the effective average temperature of the atmosphere is 1093°C, and the effective heat transfer coeff
> Consider a flat plate or a plane wall with a thickness L and a long cylinder of radius ro. Both of these are made of materials such that they can be treated as lumped capacitances (Bi < 0.1) . Show that in each case, the characteristic length lc, defin
> In a large chemical factory, hot gases at 2273 K are cooled by a liquid at 373 K with gas-side and liquid- side convection heat transfer coefficients of 50 and 1000 W/m2. K, respectively. The wall that separates the gas and liquid streams is composed of
> A thin, flat plate integrated circuit is cooled on its upper surface by a dielectric liquid. The heat dissipation rate from this chip is 20,000 W/m2 and with the coolant flow at a free-stream temperature of , the convective heat transfer coefficient bet
> A very thin silicon chip is bonded to a 6-mm thick aluminum substrate by a 0.02-mm thick epoxy glue. Both surfaces of this chip-aluminum system are cooled by air at 258C, where the convective heat transfer coefficient of air flow is 100 W/m2. K. If the h
> Calculate the rate of heat transfer between a 15-cm- OD pipe at 1208C and a 10-cm-OD pipe at 408C. The two pipes are 330 m long and are buried in sand (k = 0.33 W/m K) 12 m below the surface (Ts = 25°C ) . The pipes are parallel and are separated by 23 c
> A 2.5-cm-OD hot steam line at 100oC runs parallel to a 5.0-cm-OD cold water line at 15oC. The pipes are 5 cm apart (center to center) and deeply buried in concrete with a thermal conductivity of 0.87 W/m K. What is the heat transfer per meter of pipe bet
> A 15-cm-OD pipe is buried with its centerline 1.25 m below the surface of the ground (k of soil is 0.35 W/(m K)). An oil having a density of 800 kg/m3 and a specific heat of 2.1 kJ/(kg K) flows in the pipe at 5.6 L/s. Assuming a ground surface temperatur
> A radioactive sample is to be stored in a protective box with 4-cm-thick walls and interior dimensions of 4 cm * 4 cm * 12 cm. The radiation emitted by the sample is completely absorbed at the inner surface of the box, which is made of concrete. If the o
> Using Table 1.4 as a guide, prepare a similar table showing the orders of magnitude of the thermal resistances of a unit area for convection between a surface and various fluids.
> Two long pipes, one having a 10-cm OD and a sur- face temperature of 300oC, the other having a 5-cm OD and a surface temperature of 100oC, are buried deeply in dry sand with their centerlines 15 cm apart. Determine the rate of heat flow from the larger t
> A plane wall of thickness 2L has internal heat sources whose strength varies according to where qo is the heat generated per unit volume at the center of the wall (x = 0) and a is a constant. If both sides of the wall are maintained at a constant tempera
> A 30-cm-OD pipe with a surface temperature of 90oC carries steam over a distance of 100 m. The pipe is buried with its centerline at a depth of 1 m, the ground surface is 26°C, and the mean thermal conductivity of the soil is 0.7 W/m K. Calcul
> Determine the temperature distribution and heat flow rate per meter length in a long concrete block having the shape shown below. The cross-sectional area of the block is square and the hole is centered.
> A long, 1-cm-diameter electric cable is embedded in a concrete wall ( k 5 0.13 W/m K ) that is 1 m * 1 m, as shown in the sketch. If the lower surface is insulated, the surface of the cable is 100oC, and the exposed surface of the concrete is 25oC, estim
> A large number of 3.8-cm-OD pipes carrying hot and cold liquids are embedded in concrete in an equilateral staggered arrangement with centerlines 11.2 cm apart as shown in the sketch. If the pipes in rows A and C are at 16oC while the pipes in rows B and
> A long, 1-cm-diameter electric copper cable is embedded in the center of a 25-cm-square concrete block. If the outside temperature of the concrete is 25oC and the rate of electrical energy dissipation in the cable is 150 W per meter length, determine tem
> Determine the rate of heat flow per meter length from the inner to the outer surface of the molded insulation in the sketch on the next page. Use k = 0.17 W ( m K ) .
> Determine the rate of heat transfer per meter length from a 5-cm-OD pipe at 150oC placed eccentrically within a larger cylinder of 85% magnesia wool as shown in the sketch. The outside diameter of the larger cylinder is 15 cm and the surface temperature
> Use a flux plot to estimate the rate of heat flow through the object shown in the sketch. The thermal conductivity of the material is 15 W/m K. Assume no heat is lost from the sides.
> If the outer air temperature in Problem 1.11 is 22°C, calculate the convection heat transfer coefficient between the outer surface of the window and the air, assuming radiation is negligible.
> Determine by means of a flux plot the temperatures and heat flow per unit depth in the ribbed insulation shown in the accompanying sketch.
> Compare the rate of heat flow from the bottom to the top of the aluminum structure shown in the sketch below with the rate of heat flow through a solid slab. The top is at -10°C, the bottom at 0oC. The holes are filled with insulation that doe
> Derive an expression for the temperature distribution in a plane wall in which there are uniformly distributed heat sources that vary according to the linear relation where qw is a constant equal to the heat generation per unit volume at the wall tempera
> A 0.3-cm-thick aluminum plate has rectangular fins 0.16 cm * 0.6 cm, on one side, spaced 0.6 cm apart. The finned side is in contact with low pressure air at 38oC, and the average heat transfer coefficient is 28.4 W/m2 K. On the un finned side, water flo
> The handle of a ladle used for pouring molten lead is 30 cm long. Originally the handle was made of 1.9 cm * 1.25 cm mild steel bar stock. To reduce the grip temperature, it is proposed to form the handle of tubing 0.15 cm thick to the same rectangular s
> The top of a 30-cm I-beam is maintained at a temperature of 260oC, while the bottom is at 93oC. The thick- ness of the web is 1.25 cm. Air at 260oC is blowing along the side of the beam so that / The thermal conductivity of the steel may be assumed const
> The wall of a liquid-to-gas heat exchanger has a sur- face area on the liquid side of 1.8 m2 (0.6 m * 3.0 m)with a heat transfer coefficient of 255 W/m2 K. On the other side of the heat exchanger wall flows a gas, and the wall has 96 thin rectangular ste
> Heat is transferred from water to air through a brass wall (k = 54 W/m K) . The addition of rectangular brass fins, 0.08 cm thick and 2.5 cm long, spaced 1.25 cm apart, is contemplated. Assuming a water-side heat transfer coefficient of 170 W/m2 K and an
> To determine the thermal conductivity of a long, solid 2.5-cm-diameter rod, one half of the rod was inserted into a furnace while the other half was projecting into air at 27oC. After steady state had been reached, the temperatures at two points 7.6 cm a
> A turbine blade 6.3 cm long, with cross-sectional area A = 4.6 3 10-4 m2 and perimeter P = 0.12 m, is made of stainless steel (k = 18 W/m K) . The temperature of the root, Ts, is 482oC. The blade is exposed to a hot gas at 871oC, and the heat transfer co
> A wall with a thickness L is made of a material with a thermal conductivity that varies with its thickness x according to the equation, k=(ax +b) W/mK, where a and b are constants. If the heat flux applied at the surface of one end (x =0) of the wall is
> A circumferential fin of rectangular cross section, 3.7-cm OD and 0.3 cm thick, surrounds a 2.5-cm- diameter tube as shown below. The fin is constructed of mild steel. Air blowing over the fin produces a heat transfer coefficient of 28.4 W/m2 K. If the t
> Both ends of a 0.6-cm copper U-shaped rod are rigidly affixed to a vertical wall as shown in the accompanying sketch. The temperature of the wall is maintained at 93oC. The developed length of the rod is 0.6 m, and it is exposed to air at 38oC. The combi
> One end of a 0.3-m-long steel rod is connected to a wall at 204oC. The other end is connected to a wall that is maintained at 93oC. Air is blown across the rod so that a heat transfer coefficient of 17 W/m2 K is maintained over the entire surface. If the
> A plane wall 15 cm thick has a thermal conductivity given by the relation where T is in kelvin. If one surface of this wall is maintained at 1508C and the other at 508C, determine the rate of heat transfer per square meter. Sketch the temperature distrib
> The tip of a soldering iron consists of a 0.6-cm- diameter copper rod, 7.6 cm long. If the tip must be 204oC, what are the required minimum temperature of the base and the heat flow, in watts, into the base? Assume that W/m2 K and Tair 5 21°C
> The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1 m wide and 1 m tall. The fins are to be rectangular in cross section, 2.5 cm long and 0.25 cm thick, as shown in the figure.
> In cryogenic surgery, a small spherical probe is bought into contact with the diseased tissue which is frozen and thereby destroyed. One such probe can be modeled as a 3-mm diameter sphere whose surface is maintained at 240 K when the surrounding tissue
> The development of contact lenses has transformed the solutions that are available today for vision impairments. However, wearing them also poses several problems that includes the condition of dry eyes due to lack of cooling, oxygenation, and moisturizi
> Liquid oxygen is to be stored on the service module of NASA’s new Orion Spacecraft (NASA, “Orion Quick Facts,” FS-2014-08-004-JSC, Lyndon B. Johnson Space Center, Houston, TX)* in a spherical stainles
> Show that the temperature distribution in a sphere of radius ro, made of a homogeneous material in which energy is released at a uniform rate per unit volume qG , is
> Calculate the heat loss through a 1m*3m glass window 7-mm thick if the inner surface temperature is 20°C and the outer surface temperature is 17°C. Comment on the possible effect of radiation on your answer.
> For the system outlined in Problem 2.31, determine an expression for the critical radius of the insulation in terms of the thermal conductivity of the insulation and the surface coefficient between the exterior surface of the insulation and the surroundi
> The thermal conductivity of a material can be determined in the following manner. Saturated steam at 2.41 * 105 N/m2 is condensed at the rate of 0.68 kg/h inside a hollow iron sphere that is 1.3 cm thick and has an internal diameter of 51 cm. The sphere
> An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of 80 * 10-6 ohm-centimeter. The operating temperature of the stainless steel is to be no more tha
> The shield of a nuclear reactor is idealized by a large 25-cm-thick flat plate having a thermal conductivity of 3.5 W/(m K). Radiation from the interior of the reactor penetrates the shield and there produces heat generation that decreases exponentially
> In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of 26 W/(m K) if the rate of
> Heat is generated uniformly in the fuel rod of a nuclear reactor. The rod has a long, hollow cylindrical shape with its inner and outer surfaces at temperatures of Ti and To, respectively. Derive an expression for the temperature distribution.
> Derive an expression for the temperature distribution in an infinitely long rod of uniform cross section within which there is uniform heat generation at the rate of 1 W/m. Assume that the rod is attached to a surface at Ts and is exposed through a conve
> A long, hollow cylinder is constructed from a material whose thermal conductivity is a function of temperature according to = 5 0.15 + 0.0018T, where T is in oC and k is in W/(m K). The inner and outer radii of the cylinder are 12.5 cm and 25 cm, respect
> Show that the rate of heat conduction per unit length through a long, hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with temperature, is given by
> A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is 20 W/m2. If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer sur
> On a cold winter day, the outer surface of a 0.2-m-thick concrete wall of a warehouse is exposed to a temperature of 25°C, while the inner surface is kept at 20°C. The thermal conductivity of the concrete is 1.2 W/m K. Determine the
> At the beginning of the current fiscal year, the balance sheet of Hughey Inc. showed stockholders’ equity of $350,000. During the year, liabilities increased by $17,000 to $167,000, paid-in capital increased by $30,000 to $120,000, and
> Assume that you own 900 shares of common stock of a company, that you have been receiving cash dividends of $3.15 per share per year, and that the company has a 3-for-2 stock split. Required: a. How many shares of common stock will you own after the stoc
> Assume that you own 14,000 shares of Briant Inc.’s common stock and that you currently receive cash dividends of $1.68 per share per year. Required: a. If Briant Inc. declared a 5% stock dividend, how many shares of common stock would you receive as a di
> Refer to the 2020 Campbell Soup Company annual report. From the table of Quarterly Data (unaudited) and the Selected Financial Data (sometimes called the Five-Year Review) find the information relating to cash dividends on common stock. Required: a. How
> Anglin Inc. expects to incur a loss for the current year. The chairperson of the board of directors wants to have a cash dividend so that the company’s record of having paid a dividend during every year of its existence will continue. What factors will d
> O’Garro Inc. has paid a regular quarterly cash dividend of $0.60 per share for several years. The common stock is publicly traded. On February 27 of the current year, O’Garro’s board of directors declared the regular first-quarter dividend of $0.60 per s
> Dedrick Inc. did not pay dividends in 2021 or 2022, even though 60,000 shares of its 7.5%, $50 par value cumulative preferred stock were outstanding during those years. The company has 900,000 shares of $2 par value common stock outstanding. Required: a.
> Rosie Inc. did not pay dividends on its $3.50, $50 par value, cumulative preferred stock during 2021 or 2022, but had met its preferred dividend requirement in all prior years. Since 2017, 38,000 shares of this stock have been outstanding. Rosie Inc. has
> Calculate the cash dividends required to be paid for each of the following preferred stock issues: Required: a. The semiannual dividend on 7% cumulative preferred, $60 par value, 40,000 shares authorized, issued, and outstanding. b. The annual dividend o
> Calculate the annual cash dividends required to be paid for each of the following preferred stock issues: Required: a. $2.25 cumulative preferred, no par value; 600,000 shares authorized, 525,000 shares issued. (The treasury stock caption of the stockhol
> A number of financial statement captions are listed in the following table. Indicate in the spaces to the right of each caption the category of each item and the financial statement(s) on which the item can usually be found. Use the following abbreviatio
> The balance sheet caption for common stock is the following: Required: a. Calculate the average price at which the shares were issued. b. If these shares had been assigned a stated value of $1 each, show how the caption here would be different. c. If a c
> The balance sheet caption for common stock is the following: Required: a. Calculate the dollar amount that will be presented opposite this caption. b. Calculate the total amount of a cash dividend of $0.40 per share. c. What accounts for the difference b
> From the following data, calculate the Retained Earnings balance as of December 31, 2022:
> At September 30, 2022, the end of the first year of operations at Lukancic Inc., the firm’s accountant neglected to accrue payroll taxes of $4,700 that were applicable to payrolls for the year then ended. Required: a. Use the horizontal model (or write t
> On August 1, 2022, Colombo Co.’s treasurer signed a note promising to pay $2,400,000 on December 31, 2022. The proceeds of the note were $2,340,000. Required: a. Calculate the discount rate used by the lender. b. Calculate the effective interest rate (AP
> On May 15, 2022, Powell Inc. obtained a six-month working capital loan from its bank. The face amount of the note signed by the treasurer was $600,000. The interest rate charged by the bank was 7%. The bank made the loan on a discount basis. Required: a.
> Enter the following column headings across the top of a sheet of paper: Enter the transaction or adjustment letter in the first column and show the effect, if any, of each transaction or adjustment on the appropriate balance sheet category or on net inco
> Enter the following column headings across the top of a sheet of paper: Enter the transaction or adjustment letter in the first column and show the effect, if any, of each transaction or adjustment on the appropriate balance sheet category or on net inc
> Enter the following column headings across the top of a sheet of paper: Enter the transaction or adjustment letter in the first column, and show the effect, if any, of each of the transactions or adjustments on the appropriate balance sheet category or o
> Enter the following column headings across the top of a sheet of paper: Enter the transaction or adjustment letter in the first column and show the effect, if any, of each of the transactions or adjustments on the appropriate balance sheet category or on
> The following are the transactions relating to the formation of Gray Mowing Services Inc. and its first month of operations. Prepare an answer sheet with the columns shown. Record each transaction in the appropriate columns of your answer sheet. Show the
> A firm issues long-term debt with an effective interest rate of 10%, and the proceeds of this debt issue can be invested to earn an ROI of 12%. What effect will this financial leverage have on the firm’s ROE relative to having the same amount of funds in
> Atom Endeavour Co. issued $190 million face amount of 6.5% bonds when market interest rates were 6.71% for bonds of similar risk and other characteristics. Required: a. How much interest will be paid annually on these bonds? b. Were the bonds issued at a
> Reynolds Co. issued $75 million face amount of 6% bonds when market interest rates were 5.81% for bonds of similar risk and other characteristics. Required: a. How much interest will be paid annually on these bonds? b. Were the bonds issued at a premium
> On March 1, 2017, Catherine purchased $450,000 of Tyson Co.’s 10%, 20-year bonds at face value. Tyson Co. has regularly paid the annual interest due on the bonds. On March 1, 2022, market interest rates had risen to 12%, and Catherine is considering sell
> On August 1, 2014, Bonnie purchased $40,000 of Huber Co.’s 10%, 20-year bonds at face value. Huber Co. has paid the semiannual interest due on the bonds regularly. On August 1, 2022, market rates of interest had fallen to 8%, and Bonnie is considering se
> Alexi Co. issued $75 million face amount of 6%, 10-year bonds on June 1, 2022. The bonds pay interest on an annual basis on May 31 each year. Required: a. Assume that the market interest rates were slightly higher than 6% when the bonds were sold. Would
> Jessie Co. issued $3 million face amount of 9%, 20-year bonds on July 1, 2022. The bonds pay interest on an annual basis on June 30 each year. Required: a. Assume that market interest rates were slightly lower than 9% when the bonds were sold. Would the
> Kirkland Theater sells season tickets for six events at a price of $378. For the 2022 season, 1,200 season tickets were sold. Required: a. Use the horizontal model (or write the journal entry) to show the effect of the sale of the season tickets. b. Use
> NightWoundsTime Brewing Co. distributes its products in an aluminum keg. Customers are charged a deposit of $80 per keg; deposits are recorded in the Keg Deposits account. Required: a. Where on the balance sheet will the Keg Deposits account be found? Ex
> Prist Co. had not provided a warranty on its products, but competitive pressures forced management to add this feature at the beginning of 2022. Based on an analysis of customer complaints made over the past two years, the cost of a warranty program was
> Record transactions and calculate financial statement amounts. The transactions relating to the formation of Blue Co. Stores Inc. and its first month of operations follow. Prepare an answer sheet with the columns shown. Record each transaction in the app
> Kohl Co. provides warranties for many of its products. The January 1, 2022, balance of the Estimated Warranty Liability account was $25,100. Based on an analysis of warranty claims during the past several years, this year’s warranty provision was establi
> Glennelle’s Boutique Inc. operates in a city in which real estate tax bills for one year are issued in May of the subsequent year. Thus, tax bills for 2022 are issued in May 2023 and are payable in July 2023. Required: a. Explain how the amount of tax ex
> Dorsey Co. has expanded its operations by purchasing a parcel of land with a building on it from Bibb Co. for $310,000. The appraised value of the land is $105,000, and the appraised value of the building is $245,000. Required: a. Assuming that the build
> Prepare an answer sheet with the following column headings. For each of the following transactions or adjustments, indicate the effect of the transaction or adjustment on assets, liabilities, and net income by entering for each account affected the accou
> Prepare an answer sheet with the column headings that follow. For each of the following transactions or adjustments, indicate the effect of the transaction or adjustment on assets, liabilities, and net income by entering for each account affected the acc
> Goodwill arises when one firm acquires the net assets of another firm and pays more for those net assets than their current fair value. Suppose that Target Co. had operating income of $1,215,000 and net assets with a fair value of $5,400,000. Takeover Co
> Assume that fast-food restaurants generally provide an ROI of 10%, but that such a restaurant near a college campus has an ROI of 16% because its relatively large volume of business generates an above-average turnover (sales/assets). The replacement valu
> Using a present value table, your calculator, or a computer program present value function, calculate the present value of a. A car down payment of $16,000 that will be required in two years, assuming an interest rate of 10%. b. A lottery prize of $28 mi
> Barefoot Industrial acquired a new delivery truck at the beginning of its current fiscal year. The truck cost $117,000 and has an estimated useful life of four years and an estimated salvage value of $18,000. Required: a. Calculate depreciation expense f
