1) A cylindrical dewar has a height of L=25 cm and a volume of V = 1 liter, but

Question

1) A cylindrical dewar has a height of L=25 cm and a volume of V = 1 liter, but the manufacturer goofed and forgot to apply silver films to the pyrex-glass vacuum walls. (Pyrex has an emissivity e = 0.9.) The dewar is initially filled completely with liquid nitrogen at its boiling point = 77 K. at 1 atm. (The density of liquid nitrogen is 800 kg/m3 and its latent heat of vaporization at 1 at. Lv = 1.99 x 105 J/kg). Consider a day when the outside temperature = 20 celsius.

a) What is the rate that energy is transferred by radiation between the inner and outer vacuum walls? [For the area of the container, it is OK to just consider the lateral area, A = 2(pi)rL.]

b) How long will it take for all the nitrogen to evaporate if radiation is the only source of heat and the inner vacuum walls remain at 77K as the nitrogen evaporates?

Explanation / Answer

rate of energy transer H = dQ/dt = Ae (sigma) T^4

where A = area = 2pir L

e= emissitivity = (1 for black bdoy)

sigma = constant = 5.67*10^-8

T = temperatrue in kelvin

from Volume V = 4pi r^3/3 = 1 L = 1000 m^3

so r^3 = 1000 * 3/(4*3.1)

r = 6.23m

so

H = rate of energy transfer

H = 2*3.14 * 6.23 *6.23 * 0.9 * 5.67 e -8 * 77.1* 77.1 *77.1 *77.1

H   = dQ/dt =    439.52 Watts

-------------------------------

apply heat = mL

as Density D = mass/Volume

mass = DV

mass m = 800 * 1000

mass = 800000 kgs

so

heat Q = 800000 * 1.99 e5

Q = 159200000000 J

so time t    = dQ/H

t = 159200000000/439.52

t =    362213323.625 secs

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