Each pound of fat contains 3500 food calories. When the body...

Each pound of fat contains 3500 food calories. When the body metabolizes food, $80 \%$ of this energy goes to heat. Suppose you decide to run without stopping, an activity that produces $1290 \mathrm{~W}$ of metabolic power for a typical person. (a) For how many hours must you run to burn up 1 lb of fat? Is this a realistic exercise plan? (b) If you followed your planned exercise program, how much heat would your body produce when you burn up a pound of fat? (c) If you needed to get rid of all of this excess heat by evaporating water (i.e., sweating), how many liters would you need to evaporate? The heat of vaporization of water at body temperature is $2.42 \times 10^{6} \mathrm{~J} / \mathrm{kg}$

Key Concepts

Conversion between Calories and Joules

Converting between food calories and joules is essential because it allows for a standardized assessment of energy across different scientific contexts. While food calories are commonly used in nutrition, the joule is the SI unit for energy, making the conversion crucial for applying principles of physics and engineering to biological processes.

Heat of Vaporization

The heat of vaporization is the amount of energy required to change a substance from a liquid to a vapor without a temperature change. In the context of exercise physiology, it is significant because it quantifies the energy needed for the body to dissipate excess heat through sweating. Understanding this concept is important for linking thermal regulation with metabolic activity during physical exertion.

Power and Energy Relationship

This key concept deals with the relationship between power, defined as the rate of energy expenditure, and total energy consumed over time. Power is typically measured in Watts (joules per second), and integrating this rate over a period provides the total energy expended. This relationship is fundamental when determining the duration of exercise necessary to meet a specific energy expenditure goal.

Energy Content of Fat

This concept refers to the caloric value of fat, which is often quantified in food calories. It serves as a measure of the energy available from adipose tissue and is critical when calculating energy expenditure for weight loss and metabolism. It also connects nutritional intake with the body's energy consumption during physical activity.

Metabolic Efficiency

Metabolic efficiency describes how effectively the body converts the energy from food into useful work versus heat. In many cases, only a fraction of the energy consumed results in mechanical work; a significant portion is inevitably lost as heat due to biological inefficiencies. This concept is key in understanding why energy balance and heat production are important in exercise physiology.

Transcript

00:01 Here we will determine how long you must run in order to burn off one pound of fat, which is assumed to be 3 ,500 food calories.

00:13 What many people don't realize is that 3 ,500 is actually in kilo calories.

00:21 It gets a little bit confusing because that is usually written as a calorie with a capital c, but it really is 3 ,500 times 1 ,000 times more calories.

00:40 And in order to convert that to joules, there are 4 .184 joules per calorie, little calorie.

00:53 Okay, so the idea is that we know the power at which the energy is getting expended, and we will assume that goes right into the fat, which may not be perfectly true.

01:08 But we have basically q.

01:10 Dot times delta t in seconds is equal to the full amount of calories.

01:25 Because we have the power in watts, we do want the energy in joules, because a watt is the same as 8 jule per second.

01:41 And that's a lot of joules, 1 .46 times 10 to the 7th joules.

01:49 A jewel, by the way, is a very small unit.

01:53 So therefore, we can solve for the time to burn that off.

02:11 Simply divide that by the rate in joules per second.

02:16 And we get of the order of 11 ,000 seconds, which if we convert that to hours, we see that it's about three hours, a little bit over.

02:32 So 3 .15 hours.

02:37 And the question is, is this a reasonable plan? well, most people would have a hard time running at that metabolic rate for three hours.

02:48 If you're a trained runner doing a marathon, yes, you can expect to be doing that, but usually people do not run to burn off fat.

02:59 They're doing it for other reasons.

03:02 So that does not seem very reasonable.

03:06 The next thing that's really interesting is that 80 % of the heat that is generated over that three hours, sorry, 80 % of the energy that comes out during that three hours is in the form of heat.

03:26 So the question is, where does that heat go? and of course, this is why you sweat.

03:36 The heat generated goes to evaporation.

03:48 And so we want to pretend that that sweat is water and how much evaporates during the three -hour run.

04:06 So we're going to take the metabolic energy and the rule of thumb is that 80 % of that goes into heat.

04:21 And we're running for 11 ,400 seconds, and that will give us the energy and jewels.

04:37 Using q equals m latent heat of vaporization during a phase change, we are going to assume that the temperature of the water is, of course, raise to the evaporation point, so we won't use any of it to raise it up...

Please give Ace some feedback