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physics
thermodynamics

Questions and Answers of Thermodynamics

A truncated cone 30 cm high is constructed of aluminum. The diameter at the top is 7.5 cm, and the diameter at the bottom is 12.5 cm. The lower surface is maintained at 93ºC; the upper surface, at
A vertical square plate, 30 cm on a side, is maintained at 50ºC and exposed to room air at 20ºC. The surface emissivity is 0.8. Calculate the total heat lost by both sides of the plate.
A black 20-by-20-cm plate has air forced over it at a velocity of 2 m/s and a temperature of 0ºC. The plate is placed in a large room whose walls are at 30ºC. The back side of the plate is
Two large black plates are separated by a vacuum. On the outside of one plate is a convection environment of T = 80ºC and h = 100 W/m2 · ºC, while the outside of the other plate is exposed to
Using the approximate values of convection heat-transfer coefficients given in Table 1-3, estimate the surface temperature for which the free convection heat loss will just equal the radiation heat
A woman informs an engineer that she frequently feels cooler in the summer when standing in front of an open refrigerator. The engineer tells her that she is only "imagining things" because there is
A woman informs her engineer husband that "hot water will freeze faster than cold water." He calls this statement nonsense. She answers by saying that she has actually timed the freezing process for
An air-conditioned classroom in Texas is maintained at 72ºF in the summer. The students attend classes in shorts, sandals, and tee shirts and are quite comfortable. In the same classroom during the
A vertical cylinder 6 ft tall and 1 ft in diameter might be used to approximate a man for heat-transfer purposes. Suppose the surface temperature of the cylinder is 78ºF, h = 2 Btu/h · ft2 · ºF,
An ice-skating rink is located in an indoor shopping mall with an environmental air temperature of 22ºC and radiation surrounding walls of about 25ºC. The convection heat-transfer coefficient
Using information developed in Problem 1-42, investigate the energy cost saving that results from the installation of a layer of glass wool 15 cm thick on a steel building 12 by 12 m in size and 5 m
A certain super insulation material having a thermal conductivity of 2 × 10−4W/m · ºC is used to insulate a tank of liquid nitrogen that is maintained at −196ºC; 199 kJ is required to
A 50-cm-diameter pipeline in the Arctic carries hot oil at 30ºC and is exposed to a surrounding temperature of −20ºC.Aspecial powder insulation 5 cm thick surrounds the pipe and has a thermal
Some people might recall being told to be sure to put on a hat when outside in cold weather because "you lose all the heat out the top of your head." Comment on the validity of this statement.
A wall 2 cm thick is to be constructed from material that has an average thermal conductivity of 1.3 W/m· ºC. The wall is to be insulated with material having an average thermal conductivity of
A certain material has a thickness of 30 cm and a thermal conductivity of 0.04 W/m · ºC. At a particular instant in time, the temperature distribution with x, the distance from the left face, is T
A straight fin having a triangular profile has a length of 5 cm and a thickness of 4 mm and is constructed of a material having k = 23 W/m ∙ ºC. The fin is exposed to surroundings with a
A circumferential aluminum fin is installed on a 25.4-mm-diameter tube. The length of the fin is 12.7 mm and the thickness is 1.0 mm. It is exposed to a convection environment at 30ºC with a
A circumferential fin of rectangular profile is constructed of stainless steel (18% Cr, 8% Ni). The thickness of the fin is 2.0 mm, the inside radius is 2.0 cm, and the length is 8.0 cm. The base
A rectangular fin has a length of 2.5 cm and thickness of 1.1 mm. The thermal conductivity is 55 W/m · ºC. The fin is exposed to a convection environment at 20ºC and h = 500 W/m2 · ºC. Calculate
A 1.0-mm-thick aluminum fin surrounds a 2.5-cm-diameter tube. The length of the fin is 1.25 cm. The fin is exposed to a convection environment at 30ºC with h = 75 W/m2 · ºC. The tube surface is
A glass rod having a diameter of 1 cm and length of 5 cm is exposed to a convection environment at a temperature of 20ºC. One end of the rod is maintained at a temperature of 180ºC. Calculate the
A stainless steel rod has a square cross section measuring 1 by 1 cm. The rod length is 8 cm, and k = 18 W/m · ºC. The base temperature of the rod is 300ºC. The rod is exposed to a convection
Copper fins with a thickness of 1.0 mm are installed on a 2.5-cm-diameter tube. The length of each fin is 12 mm. The tube temperature is 275ºC and the fins are exposed to air at 35ºC with a
A straight fin of rectangular profile is constructed of stainless steel (18% Cr, 8% Ni) and has a length of 5 cm and a thickness of 2.5 cm. The base temperature is maintained at 100ºC and the fin is
A circumferential fin of rectangular profile is constructed of duralumin and surrounds a 3-cm-diameter tube. The fin is 3 cm long and 1mmthick. The tube wall temperature is 200ºC, and the fin is
A 0.025-mm-diameter stainless steel wire having k = 16W/m ∙ ºC is connected to two electrodes. The length of the wire is 80 cm and it is exposed to a convection environment at 20ºC with h = 500
A circular fin of rectangular profile is attached to a 3.0-cm-diameter tube maintained at 100ºC. The outside diameter of the fin is 9.0 cm and the fin thickness is 1.0 mm. The environment has a
A circumferential fin of rectangular profile having a thickness of 1.0mmand a length of 2.0 cm is placed on a 2.0-cm-diameter tube. The tube temperature is 150ºC, the environment temperature is
Two 1-in-diameter bars of stainless steel [k = 17 W/m ∙ ºC] are brought into end-to-end contact so that only 0.1 percent of the cross-sectional area is in contact at the joint. The bars are 7.5 cm
Two aluminum plates 5 mm thick with a ground roughness of 100 μ in are bolted together with a contact pressure of 20 atm. The overall temperature difference across the plates is 80ºC. Calculate the
Fins are frequently installed on tubes by a press-fit process. Consider a circumferential aluminum fin having a thickness of 1.0 mm to be installed on a 2.5-cm-diameter aluminum tube. The fin length
An aluminum fin is attached to a transistor that generates heat at the rate of 300 mW. The fin has a total surface area of 9.0 cm2 and is exposed to surrounding air at 27ºC. The contact conductance
A plane wall 20 cm thick with uniform internal heat generation of 200 kW/m3 is exposed to a convection environment on both sides at 50ºC with h = 400 W/m2 · ºC. Calculate the center temperature of
A circumferential fin of rectangular profile is constructed of aluminum and placed on a 6-cm-diameter tube maintained at 120ºC. The length of the fin is 3 cm and its thickness is 2 mm. The fin is
A wall is constructed of 2.0 cm of copper, 3.0 mm of asbestos sheet [k = 0.166 W/m ∙ ºC], and 6.0 cm of fiberglass. Calculate the heat flow per unit area for an overall temperature difference of
A straight aluminum fin of triangular profile has a base maintained at 200ºC and is exposed to a convection environment at 25ºC with h = 45 W/m2 · ºC. The fin has a length of 8 mm and a thickness
One hundred circumferential aluminum fins of rectangular profile are mounted on a 1.0-m tube having a diameter of 2.5 cm. The fins are 1 cm long and 2.0 mm thick. The base temperature is 180ºC, and
The cylindrical segment shown in Figure P2-122 has a thermal conductivity of 100 W/m · ºC. The inner and outer radii are 1.5 and 1.7 cm, respectively, and the surfaces are insulated.
The truncated hollow cone shown in Figure P2-123 is used in laser-cooling applications and is constructed of copper with a thickness of 0.5 mm. Calculate the thermal resistance for one-dimensional
A tube assembly is constructed of copper with an inside diameter of 1.25 cm, wall thickness of 0.8 mm, and circumferential fins around the periphery. The fins have a thickness of 0.3 mm and length of
Calculate the R value for the fin-tube combination in Problem 2-116. Problem 2-116 An aluminum fin is attached to a transistor that generates heat at the rate of 300 mW. The fin has a total surface
Repeat Problem 2-124 for aluminum fins installed on a copper tube. Problem 2-124 A tube assembly is constructed of copper with an inside diameter of 1.25 cm, wall thickness of 0.8 mm, and
Repeat Problem 2-125 for aluminum fins installed on a copper tube. Problem 2-125 Calculate the R value for the fin-tube combination in Problem 2-116. Problem 2-116 An aluminum fin is attached to a
A stainless-steel rod having a length of 10 cm and diameter of 2 mm has a resistivity of 70 μΩ ∙ cm and thermal conductivity of 16 W/m ∙ ºC. The rod is exposed to a convection environment with
Suppose the rod in Problem 2-128 is very long. What would the zero-voltage heat transfer be in this case? Problem 2-128 A stainless-steel rod having a length of 10 cm and diameter of 2 mm has a
A certain building wall consists of 6.0 in of concrete [k = 1.2 W/m ∙ ºC], 2.0 in of fiberglass insulation, and 38 in of gypsum board [k = 0.05 W/m ∙ ºC]. The inside and outside convection
Suppose the cylindrical segment of Problem 2-122 has a periphery exposed to a convection environment with h = 75 W/m2 · ºC and T∞ = 30ºC instead of to the insulated surface. For this case, one
Suppose you have a choice between a straight triangular or rectangular fin constructed of aluminum with a base thickness of 3.0 mm. The convection coefficient is 50 W/m2 · ºC. Select the fin with
Consider aluminum circumferential fins with r1 = 1.0 cm, r2 = 2.0 cm, and thicknesses of 1.0, 2.0, and 3.0 mm. The convection coefficient is 160 W/m2 · ºC. Compare the heat transfers for six 1.0-mm
"Pin fins" of aluminum are to be compared in terms of their relative performance as a function of diameter. Three "pins" having diameters of 2, 5, and 10 mm with a length of 5 cm are exposed to a
Insulating materials are frequently installed with a reflective coating to reduce the radiation heat transfer between the surface and the surroundings. An insulating material is installed on a
A thin-wall stainless-steel tube is to be used as an electric heating element that will deliver a convection coefficient of 5000 W/m2 · ºC to water at 100ºC. Devise several configurations to
A wall is constructed of a section of stainless steel [k = 16 W/m ∙ ºC] 4.0 mm thick with identical layers of plastic on both sides of the steel. The overall heat-transfer coefficient, considering
Consider a pin fin as shown in Figure 2-10d. Assume that the fin is exposed to an evacuated space such that convection is negligible and that the radiation loss per unit surface area is given bywhere
An ice chest is constructed of Styrofoam [k = 0.033 W/m ∙ ºC] with inside dimensions of 25 by 40 by 100 cm. The wall thickness is 5.0 cm. The outside of the chest is exposed to air at 25ºC with h
A spherical tank, 1 m in diameter, is maintained at a temperature of 120ºC and exposed to a convection environment. With h = 25W/m2 ∙ ºC and T∞ = 15ºC, what thickness of urethane foam should
A hollow sphere is constructed of aluminum with an inner diameter of 4 cm and an outer diameter of 8 cm. The inside temperature is 100ºC and the outer temperature is 50ºC. Calculate the heat
Suppose the sphere in Problem 2-16 is covered with a 1-cm layer of an insulating material having k = 50 m W/m ∙ ºC and the outside of the insulation is exposed to an environment with h = 20 W/m2
In Appendix A, dimensions of standard steel pipe are given. Suppose a 3-in schedule 80 pipe is covered with 1 in of an insulation having k = 60 m W/m ∙ ºC and the outside of the insulation is
A certain material 2.5 cm thick, with a cross-sectional area of 0.1 m2, has one side maintained at 35ºC and the other at 95ºC. The temperature at the center plane of the material is 62ºC, and the
A steel pipe with 5-cm OD is covered with a 6.4-mm asbestos insulation [k = 0.096 Btu/h ∙ ft ∙ ºF] followed by a 2.5-cm layer of fiberglass insulation [k = 0.028 Btu/h ∙ ft ∙ ºF]. The
Derive an expression for the thermal resistance through a hollow spherical shell of inside radius ri and outside radius ro having a thermal conductivity k.
A 1.0-mm-diameter wire is maintained at a temperature of 400ºC and exposed to a convection environment at 40ºC with h = 120 W/m2 ∙ ºC. Calculate the thermal conductivity that will just cause an
A 2.0-in schedule 40 steel pipe (see Appendix A) has k = 27 Btu/h ∙ ft ∙ ºF. The fluid inside the pipe has h = 30 Btu/h ∙ ft2 ∙ ºF, and the outer surface of the pipe is covered with 0.5-in
Derive a relation for the critical radius of insulation for a sphere.
A cylindrical tank 80 cm in diameter and 2.0 m high contains water at 80ºC. The tank is 90 percent full, and insulation is to be added so that the water temperature will not drop more than 2ºC per
A hot steam pipe having an inside surface temperature of 250ºC has an inside diameter of 8 cm and a wall thickness of 5.5 mm. It is covered with a 9-cm layer of insulation having k = 0.5 W/m ∙
A house wall may be approximated as two 1.2-cm layers of fiber insulating board, an 8.0-cm layer of loosely packed asbestos, and a 10-cm layer of common brick. Assuming convection heat-transfer
Calculate the R value for the following insulations: (a) urethane foam, (b) fiberglass mats, (c) mineral wool blocks, (d) calcium silicate blocks.
An insulation system is to be selected for a furnace wall at 1000ºC using first a layer of mineral wool blocks followed by fiberglass boards. The outside of the insulation is exposed to an
Derive an expression for the temperature distribution in a plane wall having uniformly distributed heat sources and one face maintained at a temperature T1 while the other face is maintained at a
A5-cm-diameter steel pipe is covered with a 1-cm layer of insulating material having k = 0.22 W/m · ºC followed by a 3-cm-thick layer of another insulating material having k = 0.06 W/m · ºC. The
Derive an expression for the temperature distribution in a plane wall in which distributed heat sources vary according to the linear relationwhere w is a constant and equal to the heat generated per
A circumferential fin of rectangular profile is constructed of stainless steel with k = 43 W/m ∙ ºC and a thickness of 1.0 mm. The fin is installed on a tube having a diameter of 3.0 cm and the
A plane wall 6.0 cm thick generates heat internally at the rate of 0.3 MW/m3. One side of the wall is insulated, and the other side is exposed to an environment at 93ºC. The convection heat-transfer
Consider a shielding wall for a nuclear reactor. The wall receives a gamma-ray flux such that heat is generated within the wall according to the relationwhere 0 is the heat generation at the inner
Repeat Problem 2-35, assuming that the outer surface is adiabatic while the inner surface temperature is maintained at Ti.Problem 2-35Consider a shielding wall for a nuclear reactor. The wall
Rework Problem 2-32 assuming that the plate is subjected to a convection environment on both sides of temperature Tˆž with a heat-transfer coefficient h. Tw is now some reference
Heat is generated in a 2.5-cm-square copper rod at the rate of 35.3MW/m3. The rod is exposed to a convection environment at 20ºC, and the heat-transfer coefficient is 4000 W/m2 ∙ ºC. Calculate
A plane wall of thickness 2L has an internal heat generation that varies according to = 0 cos ax, where 0 is the heat generated per unit volume at the center of the wall (x = 0) and a is a
Find the heat transfer per unit area through the composite wall in Figure P2-4. Assume one dimensional heat flow.
A certain semiconductor material has a conductivity of 0.0124 W/cm ∙ ºC. A rectangular bar of the material has a cross-sectional area of 1 cm2 and a length of 3 cm. One end is maintained at 300ºC
The temperature distribution in a certain plane wall iswhere T1 and T2 are the temperatures on each side of the wall. If the thermal conductivity of the wall is constant and the wall thickness is L,
Electric heater wires are installed in a solid wall having a thickness of 8 cm and k = 2.5W/m ∙ ºC. The right face is exposed to an environment with h = 50W/m2 ∙ ºC and T∞ = 30ºC, while the
Two 5.0-cm-diameter aluminum bars, 2cmlong, have ground surfaces and are joined in compression with a 0.025-mm brass shim at a pressure exceeding 20 atm. The combination is subjected to an overall
A plate having a thickness of 4.0 mm has an internal heat generation of 200MW/m3 and a thermal conductivity of 25 W/m ∙ ºC. One side of the plate is insulated and the other side is maintained at
A 3.2-mm-diameter stainless-steel wire 30 cm long has a voltage of 10 V impressed on it. The outer surface temperature of the wire is maintained at 93ºC. Calculate the center temperature of the
The heater wire of Example 2-7 is submerged in a fluid maintained at 93ºC. The convection heat transfer coefficient is 5.7 kW/m2 ∙ ºC. Calculate the center temperature of the wire.
An electric current is used to heat a tube through which a suitable cooling fluid flows. The outside of the tube is covered with insulation to minimize heat loss to the surroundings, and
Derive an expression for the temperature distribution in a sphere of radius r with uniform heat generation and constant surface temperature Tw.
A stainless-steel sphere [k = 16 W/m ∙ ºC] having a diameter of 4 cm is exposed to a convection environment at 20ºC, h = 15 W/m2 ∙ ºC. Heat is generated uniformly in the sphere at the rate of
An aluminum-alloy electrical cable has k = 190 W/m ∙ ºC, a diameter of 30 mm, and carries an electric current of 230 A. The resistivity of the cable is 2.9 μΩ ∙ cm, and the outside surface
Derive an expression for the temperature distribution in a hollow cylinder with heat sources that vary according to the linear relation = a + br with i the generation rate per unit volume at r =
The outside of a copper wire having a diameter of 2 mm is exposed to a convection environment with h = 5000 W/m2 ∙ ºC and T∞ = 100ºC. What current must be passed through the wire to produce a
A hollow tube having an inside diameter of 2.5 cm and a wall thickness of 0.4 mm is exposed to an environment at h = 100 W/m2 · ºC and T∞ = 40ºC. What heat-generation rate in the tube will
Water flows on the inside of a steel pipe with an ID of 2.5 cm. The wall thickness is 2 mm, and the convection coefficient on the inside is 500 W/m2 · ºC. The convection coefficient on the outside
The pipe in Problem 2-56 is covered with a layer of asbestos [k = 0.18 W/m · ºC] while still surrounded by a convection environment with h = 12W/m2 · ºC. Calculate the critical insulation radius.
Calculate the overall heat-transfer coefficient for Problem 2-5. Problem 2-5 One side of a copper block 5 cm thick is maintained at 250ºC. The other side is covered with a layer of fiberglass 2.5 cm
Air flows at 120ºC in a thin-wall stainless-steel tube with h = 65 W/m2 · ºC. The inside diameter of the tube is 2.5 cm and the wall thickness is 0.4 mm. k = 18 W/m · ºC for the steel. The tube

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