Question

3. You are outside a vacation cabin in Alaska where the outdoor temperature is -20°C. You left a bottle of water outside when you go back to the house. You had the bottle in the inside pocket of your jacket so the temperature of the water is 20°C when you left it outside. The bottle is 20.0cm high and it has a diameter of 6.0 cm. How long does it take for the 100.0 g water to become ice? The emissivity of the bottle is 0.8. Assume the only heat transfer between the can and the surrounding air is by radiation. (10 points)

Answer 1

biven, outside temp. T T =-20°c = 253K inside temp. T2 = 200 = 293k Height of botie, - 20.0cm Diameter d - 6.0cm radius, r = a = 3.0cm mass of water, m = 100.0 g E = 0.8 Emissivity, change in tempreature. AT = T2-T = 293-253 - 40K -2 Total surface area of bottle, A= 2a8(rth) = 2x3.14x 3.0x10 (3.0+20.0) x 10 -4 2 = 433.32 x 10 By stefan's law, total energy radiated per Unit time is given by - E = TE A[AT.34 -1,9] -8 -4 253 - 1965.54 x 10 [7.378109 -4.09x109 -12 1965.54 T10 9 = 6446.97 x 10 - 3 = 6.845ls - 12 x 3.28 xlos

to Heat Heat required to convert water at 20°c ice. of fusion L. = 334 Jlg Specific heat c = 4179.6 J1kg Ik Heat arequired = MCAT +ML = 0.1 X 4179.6 X 20 t Boo Loa 334 - 8359.2 7.33,400 = 8292.6F Heat required Q , Q = 41,759.2 J Heat radiated per second, E = 6.4.5/sec water at 20°c Time required to converte to ice is given by - 41759.2 t E 6.4 = 6524.8 sec 108.7 minute Time required, t = 108.7 minute