Question

A container has a flat bottom made of aluminum that is 1.18 -cm thick. The walls are insulated with thick styrofoam. The exterior bottom of the container is in continual contact with boiling water. Inside the container, ethanol (ethyl alcohol) is boiling. How long until the alcohol completely boils away if initially it has a depth of 5 cm? Assume that the thermal conductivity of aluminum is 220 W/m· ◦C, the latent heat of vaporization of ethanol is 854 kJ/kg, the boiling point of ethanol is 78.2 ◦C, and the density of ethanol is 785 kg/m3 . [50, 80 s]

Answer 1

d = thickness of bottom of container = 1.18 cm = 0.0118 m

A = area of the bottom

T = Change in temperature = 100 - 78.2 = 21.8 ^oC

k = thermal conductivity of aluminum = 220 W/mC

t = time taken

Q = heat provided to ethanol

Heat provided is given as

Q = k A T t/d

= density of ethanol = 785

h = depth = 5 cm = 0.05 m

mass of ethanol is given as

m = Ah

L = latent heat of vaporization of ethanol = 854 x 10³ J/kg

Heat of vaporization is given as

Q' = m L

Using conservation of heat

Q' = Q

m L = k A T t/d

Ah L = k A T t/d

h L = k T t/d

(785) (0.05) (854 x 10³) = (220) (21.8) t/(0.0118)

t = 82.5 sec