A \"calorie\" is a unit of energy, defined as the amount of energy needed to rai

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

Explanation / Answer

i) 21 beers x 17 kcal/beer = 357 kcal

Now, heat capacity of water = 1 cal/gram

we have. Q= mcT

357 x 1000 cal = m x 1 cal/gram x (100 - 24)

m=4697.37 grams = 10.3559 pounds

II) 1 kcal = 3.97 BTU

Thus, 357 kcal = 1417.29 BTU

iii) We have 1 kWh = (1000 J/s) x 3600 s = 3600000 J = (4184/3600000) cal

Thus, 357 kcal = 0.412 kWh

Cost = 0.412 x 10 = 4.12 cents

This is much cheaper than the beer bought

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