Note: Refer to Tables 18-1 and 18-2 for thermal conductivities and other constants needed in the solution of the problems in this section.
18-1. A block of copper has a cross-section of 20 cm2 and a length of 50 cm. The left end is maintained at 00C and the right end is a 1000C. What is the rate of heat flow in watts?
k = 385W/m K; t = 1000C – 00C = 100 C0; 20 cm2 = 20 x 10-4 m2
; H = 154 W
18-2. In Problem 18-1, what is the heat flow if the copper block is replaced with an block of glass having the same dimensions?
kG = 0.80 W/m K; A = 20 x 10-4 m2; L = 0.50 m; t = 100 C0
; H = 0.320 W
18-3. A 50-cm long brass rod has a diameter of 3 mm. The temperature of one end is 76 C0higher than the other end. How much heat is conducted in one minute?
; L = 0.50 m; t = 76 C0
; H = 0.117 W
; Q = 7.03 J
18-4. A pane of window glass is 10 in. wide, 16 in. long, and 1/8 in. thick. The inside surface is at 600F and the outside surface is at 200F. How many Btu are transferred to the outside in a time of 2 h? [ L = (1/8) in. = 0.125 in.; A = (10in.)(16 in.) = 160 in.2 ]
; t = 600F – 200F = 40 F0
; Q = 3980 Btu
18-5. One end of an iron rod 30 cm long and 4 cm2 in cross-section is placed in a bath of ice and water. The other end is placed in a steam bath. How many minutes are needed to transfer 1.0 kcal of heat? In what direction does the heat flow?
; = 625 s; = 10.4 min
The direction of heat flow isfrom the stem bath to the ice and water.
18-6. A steel plate of thickness 20 mm has a cross-section of 600 cm2. One side is at 1700C and the other is at 1200C. What is the rate of heat transfer?
; H = 7530 W
18-7. How much heat is lost in 12 h through a 3-in. brick firewall 10 ft2 area if one side is at 3300F and the other is at 780F?
t = 3300F – 780F = 252 F0; A = 10ft2; = 12 h; L = 3 in.
; Q = 50,400 Btu
*18-8. A composite wall 6 m long and 3 m high consists of 12 cm of concrete joined with 10 cm of corkboard. The inside temperature is 100C and the outside temperature is 400C. Find the temperature at the interface of the two materials. [ t = 400C – 100C = 30 C0 ]
Hsteel = Hsilver;
;t = 22.80C
*18-9. What is the steady-state rate of heat flow through the composite wall of Problem 10-8?
H1 = H2 = ; H = 4.83 J/s
18-10. What is the power radiated from a spherical blackbody of surface area 20 cm2 if its temperature is 2500C?
T = 2500C + 2730 = 523 K; 20 cm2 = 20 x 10-4 m2
; P = 8.48 W
18-11. What is the rate ofradiation for a spherical blackbody at a temperature of 3270C? Will this rate change if the radius is doubled for the same temperature?
T = 3270C + 2730 = 600 K; e = 1; R = eT4
; R = 7.35 kW/m2
so that changing the radius does NOT change the rate of radiation.
*18-12. The emissivity of a metallic sphere is 0.3 and at a temperature of 500 K its radiates a power of 800 W.What is the radius of the sphere?
; r = 0.489 m
*18-13. A certain body absorbs 20 percent of the incident thermal radiation, what is its emissivity? What energy will be emitted by this body in 1 min if its surface area is 1 m2 and its temperature is 7270C?
e = 20% = 0.2; T = 2730 + 7270 = 1000 K; = 60 s;
R = eT4 = (0.2)(5.67 x 10-8 W/m2 K4)(1000 K)4;R = 11,340 W/m2
; E = 680 kJ
*18-14. The operating temperature of the filament in a 25-W lamp is 27270C. If the emissivity is 0.3, what is the surface area of the filament? [ T = 27270C + 2730 = 3000 K ]
A = 1.81 x 10-5 m2 or A = 0.181 cm2
18-15. A glass window pane is 60 cm wide 1.8 m tall...