Question

A "calorie" is a unit of energy, defined as the amount of energy needed to raise the temperature of one gram of water by one degree Celsius. The nutritional labels on food products typically tell you how many calories of digestible energy are in one serving of food, where "digestible" means that the energy stored in the chemical bonds of the molecules comprising the food can be extracted by your body. (Water for example has energy, but that energy is not chemically accessible via digestion.) To simplify understanding for typical consumers, the "calories" reported on nutritional labels actually represent kilocalories: a 170 calorie can of beer actually contains 170,000 calories of digestible energy i) If a student foolishly decides to binge drink 21 beers on their 21t birthday, how many gallons of water could they have heated from room temperature (24 °C) to boiling (100 C) using an equivalent amount of digestible energy in the beer? Recall that one gallon of water is roughly 8 pounds ii) What is this energy equivalent to in BTU? A "BTU" or British Thermal Unit is also a unit of energy, defined as the amount of energy needed to raise the temperature of one pound of water by one degree Fahrenheit iii) If you had purchased an equivalent amount of electrical energy in kW-hr from the utility company, how much would you have to pay? Is this cheaper than buying beer? A kW-hr ypically costs 10 cents

Answer 1

Answer & Explanation:

i) If a student foolishly decides to binge drink 21 beers on their 21st birthday, they would consume a total of 21 x 170 = <<21*170=3570>>3570 calories of digestible energy. Since one calorie is equivalent to raising the temperature of one gram of water by one degree Celsius, and one gallon of water is equivalent to 3,785 grams, the student would have consumed enough energy to raise the temperature of 3,785 grams x 3570 calories = 13,678,950 calories of water from 24 °C to 100 °C. This means that the student could have heated 13,678,950 / 100 = <<136789500/100=136789.5>>136789.5 grams of water from room temperature to boiling, which is equivalent to 136789.5 / 3,785 = <<136789.5/3785=36.19>>36.19 gallons of water.

ii) The energy equivalent of the beer consumed by the student is 3570 calories x 4.184 joules/calorie = 14,889.48 joules. Since one BTU is equivalent to 1,055 joules, this energy is equivalent to 14,889.48 joules / 1,055 joules/BTU = <<14889.48/1055=14.15>>14.15 BTU.

iii) If the student had purchased an equivalent amount of electrical energy from the utility company, they would have to pay 14.15 kW-hr x $0.10/kW-hr = $<<14.15*0.1=1.42>>1.42. This is cheaper than buying beer, as a can of beer typically costs more than $1.42.