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Numerade Educator

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Problem 8 Easy Difficulty

(a) The number of kilocalories in food is determined by calorimetry techniques in which the food is burned and the amount of heat transfer is measured. How many kilocalories per gram are there in a 5.00-g peanut if the energy from burning it is transferred to 0.500 kg of water held in a 0.100-kg aluminum cup, causing a $54.9^{\circ} \mathrm{C}$ temperature increase? (b) Compare your answer to labeling information found on a package of peanuts and comment on whether the values are consistent.

Answer

(a) 28.6 $\mathrm{KCal}$
(b) The number of calories per gram is 5.68 .

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Video Transcript

for this question, we want to find out how many kill a cop kill Oh, calories per gram. There are in a five gram peanut. If the energy from burning it is transferred to ah container of water and aluminum. So we have a five grand Peanut. We have a mass of water that is your 0.5 kilograms. We have a mass of aluminum in the cup that is your 0.1 kilograms, and we have a temperature change in the cup from the heat received from burning the peanut. That is a positive temperature change of 54.9 degrees Celsius. So we want to determine the heat, um, transferred to the cups. So that equation is Q. The heat or energy equals mass time specific eat times Delta T. So in our case, we have to materials with two different specific heats. So we want to write this as m water specific. It ofwater times Delta T plus, um of aluminum sea of aluminum times Delta T, where Delta T is the same for both of them. So we need to look up the specific heat of water, which is just one kill a cow per kilogram degrees Celsius and the specific heat of aluminum is 0.22 Killer Cal's per kilogrammes degrees Celsius. Hooves. Okay, so we can start plugging numbers in so he burned where he can pull out the delta t out here since assessing for both and water sea water plus AM aluminum see aluminum, which is delta T is 54.9 m of water. One Kill Kao kilogram degrees Celsius Times the mass of the water, which is 2.5 kilograms, plus specific heat of aluminum, which we wrote your point to to kill a cow's per kilogram degree. Celsius times the mass of the aluminum, which is your 0.1 kilograms kilograms cancel out in both cases. More left with 54.9 degrees Celsius times to your 0.5 to 2 killa cows over degrees Celsius. So we multiply these degrees Celsius cancels out more left with five. Oops, we're left with 28.66 chemicals. So that's the amount of heat burned for the entire five grand peanut. So in order to find the, uh, Kilic calories per gram, we need to do 20.66 kilocalories burned for the whole peanut divided by the five grams of the peanut, which is 5.73 Kill a cow's program, says the answer to the first part. In the second part asked you to compare to a regular package of peanuts and the one that I have says for 170 kilocalories. They call that just capital C calories and packages, um, divided by. So this is killer cows or on your package it'll look like regular calories on the package is 28 grams, which comes out to about six Killer Cal's program, which is perfectly in line with her answer.