*Only need help with (d), I already have (a) (b) and (c)* Beer brewing begins wi
ID: 1529014 • Letter: #
Question
*Only need help with (d), I already have (a) (b) and (c)*
Beer brewing begins with steeping grains in hot water, releasing the sugars inside. The sugar water is then heated to a boil and hops added. The hot temperature of the boil extracts oils from the hops and provides sanitation from unwanted bacteria. The whole mess is cooled down and once it is safe enough for yeast to survive, they are added. The yeast convert the sugars to alcohol, and the oils from the hops provide many things including flavor and antibacterial benefits.
(a) If 16.5 lbs of grain at 67 ºF are added to 5 gal of hot water and the equilibrium temperature of the mixture is to be 154 ºF, what must the initial temperature (strike temp) of the hot water be? The specific heat of malt grains is about 0.44 times that of water. Also assume no energy is lost during the time the system comes to equilibrium. Ti = 169.2 ºF
(b) How much did it cost to heat the 5 gals of tap water from 110 ºF up to the strike temp? Assume the heating takes 47 minutes, electricity costs 15 ¢ per kilowatt-hour, and only 10% energy is lost during heating. 12.2 ¢
(c) During the one hour steeping stage, where the water and grain mixture started at 154 ºF, the mixture only lost 2 ºF. What was the average energy per time lost by the mixture. -1.03e5 J/hr
(d) The steeping was done in a cylindrical vessel (cooler) with outside dimensions 20 inches tall and 15 inches in diameter. The thickness of the walls is 1 inch. Estimate the thermal conductivity of the steeping vessel assuming a room temperature of 67 ºF.
Explanation / Answer
We know that,
Q/t = k A (Th - Tc)/d
where, Q/t is the heat energy over time ; k is the thermal condutivity ; Th is the hot temp and Tc is the cold temp.
A is the area = 2 pi r h + 2 pi r^2 = 2 x 3.14 ( 0.51 x 0.19 + 0.19^2) = 2.12 m^2 [h = 20 in = 0.51 ; r = 15/2 in = 0.38 m]
1.03 x 10^-5/3600 = k x 2.12 (76.22 - 19.44)/0.025
k = 0.0059 W/m deg C
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