Question: Exhaust gases from a manufacturing plant are
Exhaust gases from a manufacturing plant are being discharged through a 10-m-tall exhaust stack with outer diameter of 1 m. The exhaust gases are discharged at a rate of 0.125 kg/s, while temperature drop between inlet and exit of the exhaust stack is 30°C, and the constant pressure specific heat of the exhaust gases is 1600 J/kgâ‹…K. On a particular calm day, the surrounding quiescent air temperature is 33°C. Solar radiation is incident on the exhaust stack outer surface at a rate of 500 W/m2, and both the emissivity and solar absorptivity of the outer surface are 0.9. Determine the exhaust stack outer surface temperature. Assume the film temperature is 60°C. 
> Ethane at 10 MPa and 100°C is heated at constant pressure until its volume has increased by 60 percent. Determine the final temperature using (a) the ideal-gas equation of state and (b) the compressibility factor. Which of these two results is the more a
> A 3-mm-thick glass window transmits 90 percent of the radiation between λ = 0.3 and 3.0 μm and is essentially opaque for radiation at other wavelengths. Determine the rate of radiation transmitted through a 3-m × 3-m glass window from blackbody sources a
> The sun can be treated as a blackbody at an effective surface temperature of 10,400 R. Determine the rate at which infrared radiation energy (λ = 0.76 − 100 μm) is emitted by the sun, in Btu/h⋅ft2.
> What is thermal radiation? How does it differ from the other forms of electromagnetic radiation?
> It is desired that the radiation energy emitted by a light source reach a maximum in the blue range (λ = 0.47 μm). Determine the temperature of this light source and the fraction of radiation it emits in the visible range (λ = 0.40 − 0.76 μm).
> Reconsider Prob. 21–27. Using appropriate software, investigate the effect of temperature on the fraction of radiation emitted in the visible range. Let the surface temperature vary from 1000 K to 4000 K, and plot the fraction of radiation emitted in the
> The temperature of the filament of an incandescent lightbulb is 2800 K. Treating the filament as a blackbody, determine the fraction of the radiant energy emitted by the filament that falls in the visible range. Also, determine the wavelength at which th
> The temperature of the filament of an incandescent lightbulb is 2500 K. Assuming the filament to be a blackbody, determine the fraction of the radiant energy emitted by the filament that falls in the visible range. Also, determine the wavelength at which
> We wish an incandescent lightbulb to emit at least 15 percent of its energy at wavelengths shorter than 0.8 μm. Determine the minimum temperature to which the filament of the lightbulb must be heated.
> A circular ceramic plate that can be modeled as a blackbody is being heated by an electrical heater. The plate is 30 cm in diameter and is situated in a surrounding ambient temperature of 15°C where the natural convection heat transfer coeffic
> A thin vertical copper plate is subjected to a uniform heat flux of 1000 W/m2 on one side, while the other side is exposed to ambient surroundings at 5°C. The surface of the plate is oxidized black and can be treated as a blackbody. The heat t
> On the property diagrams indicated below, sketch (not to scale) with respect to the saturated liquid and saturated vapor lines and label the following processes and states for refrigerant 134a. Use arrows to indicate the direction of the process, and lab
> Consider a black spherical ball, with a diameter of 25 cm, that is suspended in air. Determine the surface temperature of the ball that should be maintained in order to heat 10 kg of air from 20 to 30°C in 5 minutes.
> A small body is placed inside a spherical stainless steel chamber with a diameter of 3 m. The chamber is evacuated and has a constant surface temperature of 500 K. Determine the radiation incident on the surface of the small body inside the chamber if th
> The sun can be treated as a blackbody at 5780 K. Using appropriate software, calculate and plot the spectral blackbody emissive power Ebλ of the sun versus wavelength in the range of 0.01 μm to 1000 μm. Discuss the results.
> By what properties is an electromagnetic wave characterized? How are these properties related to each other?
> At a wavelength of 0.7 μm, the blackbody emissive power is equal to 108 W/m3. Determine (a) the temperature of the blackbody and (b) the total emissive power at this temperature.
> A flame from a match may be approximated as a black body at the effective surface temperature of 1700 K, while moonlight may be approximated as a blackbody at the effective surface temperature of 4000 K, respectively. Determine the peak spectral blackbod
> Consider a surface at a uniform temperature of 1000 K. Determine the maximum rate of thermal radiation that can be emitted by this surface, in W/m2.
> Why did we define the blackbody radiation function? What does it represent? For what is it used?
> Define the total and spectral blackbody emissive powers. How are they related to each other? How do they differ?
> What is a blackbody? Does a blackbody actually exist?
> A tank contains helium at 37°C and 140 kPa gage. The helium is heated in a process by heat transfer from the surroundings such that the helium reaches a final equilibrium state at 200°C. Determine the final gage pressure of the helium. Assume atmospheric
> The electromagnetic spectrum that lies between 0.40 and 0.76 μm is what we call visible light. Within this spectrum, the color violet has the shortest wavelength while the color red has the longest wavelength. Determine which of these colors, violet (λ =
> A furnace is of cylindrical shape with a diameter of 1.2 m and a length of 1.2 m. The top surface has an emissivity of 0.60 and is maintained at 450 K. The bottom surface has an emissivity of 0.50 and is maintained at 800 K. The side surface has an emiss
> Consider a cubical furnace with a side length of 3 m. The top surface is maintained at 700 K. The base surface has an emissivity of 0.90 and is maintained at 950 K. The side surface is black and is maintained at 450 K. Heat is supplied from the base surf
> Two concentric spheres of diameters D1 = 15 cm and D2 = 25 cm are separated by air at 1 atm pressure. The surface temperatures of the two spheres enclosing the air are T1 = 350 K and T2 = 275 K, respectively, and their emissivities are 0.75. Determine th
> A 2-m-internal-diameter double-walled spherical tank is used to store iced water at 0°C. Each wall is 0.5 cm thick, and the 1.5-cm-thick airspace between the two walls of the tank is evacuated in order to minimize heat transfer. The surfaces s
> An electromagnetic wave with a wavelength of 0.5 μm is being propagated in different media: air, water, and glass. The refractive index of air, water, and glass are 1, 1.33, and 1.5, respectively. Determine the photon energy, in eV, of the electromagnet
> A solar collector consists of a horizontal aluminum tube of outer diameter 5 cm enclosed in a concentric thin glass tube of 7 cm diameter. Water is heated as it flows through the aluminum tube, and the annular space between the aluminum and glass tubes i
> A vertical 2-m-high and 5-m-wide double-pane window consists of two sheets of glass separated by a 3-cm-thick air gap. In order to reduce heat transfer through the window, the air space between the two glasses is partially evacuated to 0.3 atm pressure.
> A solar collector consists of a horizontal copper tube of outer diameter 5 cm enclosed in a concentric thin glass tube of 9 cm diameter. Water is heated as it flows through the tube, and the annular space between the copper and glass tube is filled with
> A large number of long tubes, each of diameter D, are placed parallel to each other and at a center to-center distance of s. Since all of the tubes are geometrically similar and at the same temperature, these could be treated collectively as one surface
> Does the amount of heat absorbed as 1 kg of saturated liquid water boils at 100°C have to be equal to the amount of heat released as 1 kg of saturated water vapor condenses at 100°C?
> Consider a 1.2-m-high and 2-m-wide double-pane window consisting of two 3-mm-thick layers of glass (k = 0.78W/m⋅K) separated by a 2.5-cm-wide airspace. Determine the steady rate of heat transfer through this window and the temperature of its inner surfac
> A dryer is shaped like a long semicylindrical duct of diameter 1.5 m. The base of the dryer is occupied by water-soaked materials to be dried, and it is maintained at a temperature of 370 K and emissivity of 0.5. The dome of the dryer is maintained at 1
> A spherical vessel with a 30.0-cm outside diameter is used as a reactor for a slow endothermic reaction. The vessel is completely submerged in a large water-filled tank, held at a constant temperature of 30°C. The outside surface temperature of the vess
> Two parallel concentric disks, 20 cm and 40 cm in diameter, are separated by a distance of 10 cm. The smaller disk (ε = 0.80) is at a temperature of 300°C. The larger disk (ε = 0.60) is at a temperature of 800°C. (a) Calculate the radiation view factors.
> A 6-m-internal-diameter spherical tank made of 1.5-cm thick stainless steel (k = 15 W/m⋅K) is used to store iced water at 0°C in a room at 20°C. The walls of the room are also at 20°C. The outer surface of the tank is black (emissivity ε = 1), and heat t
> Two parallel black disks are positioned coaxially with a distance of 0.25 m apart. The lower disk is 0.2 m in diameter and the upper disk is 0.4 m in diameter. If the lower disk is heated electrically at 20 W to maintain a uniform temperature of 500 K, d
> Consider an industrial furnace that resembles a 13-ft long horizontal cylindrical enclosure 8 ft in diameter whose end surfaces are well insulated. The furnace burns natural gas at a rate of 48 therms/h. The combustion efficiency of the furnace is 82 per
> Consider a cylindrical enclosure with A1, A2, and A3 representing the internal base, top, and side surfaces, respectively. Using the length-to-diameter ratio, K = L/D, determine (a) the expression for the view factor from the side surface to itself F33 i
> Hot water is flowing at an average velocity of 4 ft/s through a cast iron pipe (k = 30 Btu/h⋅ft⋅°F) whose inner and outer diameters are 1.0 in and 1.2 in, respectively. The pipe passes through a 50 ft-long section of a basement whose temperature is 60°F.
> Consider an enclosure consisting of eight surfaces. How many view factors does this geometry involve? How many of these view factors can be determined by the application of the reciprocity and the summation rules?
> Reconsider Prob. 4–108. Using appropriate software, investigate the effect of the initial pressure of refrigerant-134a on the volume of the tank. Let the initial pressure vary from 0.5 to 1.5 MPa. Plot the volume of the tank versus the
> A 12-cm-diameter and 15-m-long cylinder with a surface temperature of 10°C is placed horizontally in air at 40°C. Calculate the steady rate of heat transfer for the cases of (a) free-stream air velocity of 10 m/s due to normal winds and (b) no winds and
> A horizontal opaque flat plate is well insulated on the edges and the lower surface. The top surface has an area of 5 m2, and it experiences uniform irradiation at a rate of 5000 W. The plate absorbs 4000 W of the irradiation, and the surface is losing h
> A 40-cm-diameter, 110-cm-high cylindrical hot-water tank is located in the bathroom of a house maintained at 20°C. The surface temperature of the tank is measured to be 44°C and its emissivity is 0.4. Taking the surrounding surface temperature to be als
> Solar radiation is incident on the front surface of a thin plate with direct and diffuse components of 300 and 250 W/m2, respectively. The direct radiation makes a 30° angle with the normal of the surface. The plate surfaces have a solar absor
> The surface in Prob. 21–109 receives solar radiation at a rate of 470 W/m2. Determine the solar absorptivity of the surface and the rate of absorption of solar radiation.
> The density of liquid water can be correlated as ρ(T) = 1000 − 0.0736T − 0.00355T2 where ρ and T are in kg/m3 and °C, respectively. Determine the volume expansion coefficient at 70°C. Compare the result with the value tabulated.
> A radio station is broadcasting radio waves at a wavelength of 150 m. Determine the frequency of these waves.
> Repeat Prob. 20–87E for a circular horizontal duct of diameter 4 in. Evaluate air properties at a film temperature of 115°F and 1 atm pressure. Is this a good assumption? Data from Prob. 20-87: The components of an electroni
> The spectral absorptivity of an opaque surface is as shown in Fig. P21-109. Determine the absorptivity of the surface for radiation emitted by a source at (a) 1000 K and (b) 3000 K.
> A tank whose volume is unknown is divided into two parts by a partition. One side of the tank contains 0.03 m3 of refrigerant-134a that is a saturated liquid at 0.9 MPa, while the other side is evacuated. The partition is now removed, and the refrigerant
> Repeat Prob. 20–87E assuming the fan fails and thus all heat generated inside the duct must be rejected to the ambient air by natural convection through the outer surfaces of the duct. Evaluate air properties at a film temperature of 12
> The spectral emissivity of an opaque surface at 1200 K is approximated as; ε1 = 0 for λ < 2 μm ε2 = 0.85 for 2 ≤ λ ≤ 6 μm ε3 = 0 for λ > 6 μm Determine the total emissivity and the emissive flux of the surface.
> The human skin is “selective” when it comes to the absorption of the solar radiation that strikes it perpendicularly. The skin absorbs only 50 percent of the incident radiation with wavelengths between λ1 = 0.517 μm and λ2 = 1.552 μm. The radiation with
> The components of an electronic system dissipating 150 W are located in a 5-ft-long horizontal duct whose cross section is 6 in × 6 in. The components in the duct are cooled by forced air, which enters at 85°F at a rate of 22 cfm
> An automotive engine can be approximated as a 0.4-m-high, 0.60-m-wide, and 0.7-m-long rectangular block. The bottom surface of the block is at a temperature of 75°C and has an emissivity of 0.92. The ambient air is at 5°C, and the r
> Daylight and incandescent light may be approximated as blackbodies at the effective surface temperatures of 5800 K and 2800 K, respectively. Determine the wavelength at maximum emission of radiation for each of the lighting sources.
> An electronic box that consumes 200 W of power is cooled by a fan blowing air into the box enclosure. The dimensions of the electronic box are 15 cm × 50 cm × 50 cm, and all surfaces of the box are exposed to the ambient environ
> A 1-m-diameter spherical cavity is maintained at a uniform temperature of 600 K. Now a 5-mm-diameter hole is drilled. Determine the maximum rate of radiation energy streaming through the hole. What would your answer be if the diameter of the cavity were
> Consider a house that is maintained at a constant temperature of 22°C. One of the walls of the house has three single-pane glass windows that are 1.5 m high and 1.8 m long. The glass (k = 0.78 W/m⋅K) is 0.5 cm thick, and the heat transfer coefficient on
> Consider a flat-plate solar collector placed horizontally on the flat roof of a house. The collector is 1.5 m wide and 4.5 m long, and the average temperature of the exposed surface of the collector is 42°C. Determine the rate of heat loss from the colle
> A piston–cylinder device initially contains 0.2 kg of steam at 200 kPa and 300°C. Now, the steam is cooled at constant pressure until it is at 150°C. Determine the volume change of the cylinder during this process
> Reconsider Prob. 21–103E. Using appropriate software, investigate the effect of base surface emissivity on the net rates of radiation heat transfer between the base and the side surfaces, between the base and top surfaces, and to the base surface. Let th
> The passenger compartment of a minivan traveling at 70 mph can be modeled as a 3.2-ft-high, 6 ft-wide, and 12-ft-long rectangular box whose walls have an insulating value of R-3 (i.e., a wall thickness-to-thermal conductivity ratio of 3 hâ‹
> Consider an L × L horizontal plate that is placed in quiescent air with the hot surface facing up. If the film temperature is 20°C and the average Nusselt number in natural convection is of the form Nu = CRa Ln, show that the aver
> Consider a 10-ft × 10-ft × 10-ft cubical furnace whose top and side surfaces closely approximate black surfaces and whose base surface has an emissivity ε = 0.4. The base, top, and side surfaces of the furnace are maintained at uniform temperatures of 80
> Repeat Prob. 20–82 assuming the plate to be positioned horizontally with (a) transistors facing up and (b) transistors facing down. Data from Prob. 20-82: A group of 25 power transistors, dissipating 1.5 W each, are to be cooled by att
> Oil at 60°C flows at a velocity of 20 cm/s over a 5.0-m-long and 1.0-m-wide flat plate maintained at a constant temperature of 20°C. Determine the rate of heat transfer from the oil to the plate if the average oil properties are ρ = 880 kg/m3, μ = 0.005
> Consider a circular grill whose diameter is 0.3 m. The bottom of the grill is covered with hot coal bricks at 950 K, while the wire mesh on top of the grill is covered with steaks initially at 5°C. The distance between the coal bricks and the
> A group of 25 power transistors, dissipating 1.5 W each, are to be cooled by attaching them to a black-anodized square aluminum plate and mounting the plate on the wall of a room at 30°C. The emissivity of the transistor and the plate surfaces
> Four power transistors, each dissipating 10 W, are mounted on a thin vertical aluminum plate (k = 237 W/m⋅K) 22 cm × 22 cm in size. The heat generated by the transistors is to be dissipated by both surfaces of the plate to the surrounding air at 20°C, wh
> Consider a 4-m × 4-m × 4-m cubical furnace whose floor and ceiling are black and whose side surfaces are reradiating. The floor and the ceiling of the furnace are maintained at temperatures of 550 K and 1100 K, respectively. Determine the net rate of rad
> A 4-L rigid tank contains 2 kg of saturated liquid–vapor mixture of water at 50°C. The water is now slowly heated until it exists in a single phase. At the final state, will the water be in the liquid phase or the vapor phase
> The gas tank of a car is filled with a nozzle that discharges gasoline at a constant flow rate. Based on unit considerations of quantities, obtain a relation for the filling time in terms of the volume V of the tank (in L) and the discharge rate of gasol
> A plate (0.5 m × 0.5 m) is inclined at an angle of 30°. The top surface of the plate is well insulated. Estimate the rate of heat loss from the plate when the bottom surface is maintained at 60°C and the surrounding atmospheric quiescent air is at 0°C.
> A concentric annulus tube has inner and outer diameters of 25 mm and 100 mm, respectively. Liquid water flows at a mass flow rate of 0.05 kg/s through the annulus with the inlet and outlet mean temperatures of 20°C and 80°C, respect
> A 9-ft-high room with a base area of 12 ft × 12 ft is to be heated by electric resistance heaters placed on the ceiling, which is maintained at a uniform temperature of 90°F at all times. The floor of the room is at 65°F and has an emissivity of 0.8. The
> During a plant visit, it was observed that a 1.5-m-high and 1-m-wide section of the vertical front section of a natural gas furnace wall was too hot to touch. The temperature measurements on the surface revealed that the average temperature of the expose
> Reconsider Prob. 19–92. Using appropriate software, investigate the effect of the volume flow rate of air on the exit temperature of air and the rate of heat loss. Let the flow rate vary from 0.05 m3/s to 0.15 m3/s. Plot the exit temper
> The speed of light in a vacuum is given to be 3.0 × 108 m/s. Determine the speed of light in air (n = 1), in water (n = 1.33), and in glass (n = 1.5).
> Show that the volume expansion coefficient of an ideal gas is β = 1/T, where T is the absolute temperature.
> Hot air at atmospheric pressure and 75°C enters a 10-m-long uninsulated square duct of cross section 0.15 m × 0.15 m that passes through the attic of a house at a rate of 0.2 m3/s. The duct is observed to be nearly isothermal at 7
> What is an electromagnetic wave? How does it differ from a sound wave?
> An 8-m-long, uninsulated square duct of cross section 0.2 m × 0.2 m and relative roughness 10−3 passes through the attic space of a house. Hot air enters the duct at 1 atm and 80°C at a volume flow rate of 0.15 m3/s. The duct surface is nearly isothermal
> A 10-kg mass of superheated refrigerant-134a at 1.2 MPa and 70°C is cooled at constant pressure until it exists as a compressed liquid at 20°C. (a) Show the process on a T-v diagram with respect to saturation lines. (b) Determine the change in volume. (c
> An electric resistance space heater is designed such that it resembles a rectangular box 50 cm high, 80 cm long, and 15 cm wide filled with 45 kg of oil. The heater is to be placed against a wall, and thus heat transfer from its back surface is negligibl
> Two concentric spheres of diameters Di = 20 cm and Do = 30 cm are separated by air at 1 atm pressure. The surface temperatures of the two spheres enclosing the air are Ti = 320 K and To = 280 K, respectively. Determine the rate of heat transfer from the
> Air (1 atm) enters into a 5-cm-diameter circular tube at 20°C with an average velocity of 5 m/s. The tube wall is maintained at a constant surface temperature of 160°C, and the outlet mean temperature is 80°C. Estimate the length of the tube. Is the flow
> Reconsider Prob. 20–76. Using appropriate software, plot the rate of natural convection heat transfer as a function of the hot surface temperature of the sphere as the temperature varies from 250 K to 450 K, and discuss the results. Data from Prob. 20-7
> During air cooling of potatoes, the heat transfer coefficient for combined convection, radiation, and evaporation is determined experimentally to be as shown: Consider an 8-cm-diameter potato initially at 20°C. Potatoes are cooled by refrigera
> Two concentric spheres of diameters 15 cm and 25 cm are separated by air at 1 atm pressure. The surface temperatures of the two spheres enclosing the air are T1 = 350 K and T2 = 275 K, respectively. Determine the rate of heat transfer from the inner sphe
> The hot water needs of a household are to be met by heating water at 55°F to 180°F with a parabolic solar collector at a rate of 5 lbm/s. Water flows through a 1.25-in-diameter thin aluminum tube whose outer surface is anodized blac
> Two concentric spheres with diameters of 5 cm and 10 cm have their surface temperatures maintained at 100°C and 200°C, respectively. The enclosure between the two concentric spherical surfaces is filled with nitrogen gas at 1 atm. D
> Consider a fluid with a Prandtl number of 7 flowing through a smooth circular tube. Using the Colburn, Petukhov, and Gnielinski equations, determine the Nusselt numbers for Reynolds numbers at 3500,104, and 5 × 105. Compare and discuss the results.
> Consider two concentric horizontal cylinders of diameters 55 cm and 65 cm and length 125 cm. The surfaces of the inner and outer cylinders are maintained at 54°C and 106°C, respectively. Determine the rate of heat transfer between the cylinders by natura
> A 9-m3 tank contains nitrogen at 17°C and 600 kPa. Some nitrogen is allowed to escape until the pressure in the tank drops to 400 kPa. If the temperature at this point is 15°C, determine the amount of nitrogen that has escaped.
