A 0.15-kg of aluminum contains 0.2 kg of water. Initially, the water and the cup
ID: 1528845 • Letter: A
Question
A 0.15-kg of aluminum contains 0.2 kg of water. Initially, the water and the cup have a common temperature of 18 degree C. An unknown material (m = 00.04 kg) is heated to a temperature of 97 degree C and then added to the water. The temperature of the water, the cup, and the unknown material is 22 degree C after thermal equilibrium is reestablished. Ignoring the small amount of heat gained by the thermometer, find the specific heat capacity of the unknown material. 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. If 16.5 lbs of grain at 67 degree F are added to 5 gal of hot water and the equilibrium temperature of the mixture is to be 154 degree F, 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. How much did it cost to heat the 5 gals of tap water from 110 degree F 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. During the one hour steeping stage, where the water and grain mixture started at 154 degree F, the mixture only lost 2 degree F. What was the average energy per time lost by the mixture. 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 degree F.Explanation / Answer
3.
ma = mass of aluminium = 0.15 kg
ca = specific heat of aluminium = 900
mw = mass of water = 0.2 kg
cw = specific heat of water = 4186
m = mass of unknown material = 0.04 kg
c = specific heat of unknown material
using conservation of heat
heat gained by water and aluminium = heat lost by unknown material
ma ca (22 - 18) + mw cw (22 - 18) = m c (97 - 22)
(0.15) (900) (22 - 18) + (0.2) (4186) (22 - 18) = (0.04) c (97 - 22)
c = 1296.3
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