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Question
Energy that is not utilized for work or heat transfer is converted to the chemical energy of body fat containing about 39 kJ/g. How many grams of fat will you gain if you eat 10,000 kJ (about 2500 kcal) one day and do nothing but sit relaxed for 16.0 h and sleep for the other 8.00 h? Use data from Table 7.5 for the energy consumption rates of these activities.
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Final Answer
$17.9 \textrm{ g}$
Solution Video

OpenStax College Physics Solution, Chapter 7, Problem 48 (Problems & Exercises) (2:20)

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Video Transcript

This is College Physics Answers with Shaun Dychko. In this question we are going to determine the amount of weight a person will gain due to consuming 10,000 kilojoules of energy and then sitting at rest for 16 hours and then sleeping for 8 hours and using up a total of less energy than what's consumed and then this excess energy will be converted into mass of fat and fat has about 39 kilojoules for every gram. Okay! So we have 10,000 kilojoules of energy consumed and from that we'll take the energy expended and so they are going to be sitting at rest which has an energy consumption of 120 watts and that's for 16 hours and so this gives us energy after multiplying by watts multiplied by hours is an energy unit of watt-hours which we'll convert into kilojoules with these factors here and I'll explain that in a second. But add to this the 83 watts—rate of energy use—multiplied by 8 hours while sleeping and then this sum gets multiplied by 3600 seconds per hour and then that gives us units of watt-seconds but a watt-second is the same as joules per second since that's what a watt is multiplied by seconds which is joules. So after multiplying by this factor here, we are left with joules and then we want kilojoules to match with this kilojoules here. So we multiply by 1 kilojoule for every 1000 joules and we are left with 697.6 kilojoules and so there's a net energy consumption here or leftover after expending energy from sitting and sleeping and consuming 10,000 kilojoules initially. So the mass gain of the person will be 1 gram for every 39 kilojoules not burned multiplied by 697.6 kilojoules giving us a mass gain of 17.9 grams of fat.