∙Burning fat by exercise. Each pound of fat contains 3500...

$\bullet$ Burning fat by exercise. 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

Heat of Vaporization and Cooling

The heat of vaporization is the energy required to convert a given amount of water from liquid to vapor without a temperature change. In the context of exercise and thermoregulation, it is critical for understanding how much water must evaporate through sweating to dissipate excess metabolic heat and maintain body temperature.

Heat Production During Exercise

During exercise, a significant proportion of the energy derived from metabolism is dissipated as heat. This heat production is intrinsic to the body's energy conversion processes and has implications for thermal regulation, exercise performance, and overall metabolic demands.

Metabolic Power

Metabolic power is the rate at which the body converts stored energy (from food or fat) into work and heat, typically measured in watts. In exercise physiology, it quantifies how quickly energy is used during physical activity and helps determine the duration of activity required to expend a set amount of energy.

Energy Content of Fat

The energy content of fat refers to the amount of stored energy per unit mass, usually expressed in calories or joules. This concept is crucial for understanding how much energy can be released from fat when it is metabolized, and it serves as a basis for calculating energy deficits in weight management.

Conversion Efficiency in Metabolism

This concept involves the fraction of chemical energy from food that is converted into useful work versus the amount lost as heat during metabolism. The efficiency plays a key role in determining how much of the energy stored in fat actually contributes to physical work, with the remainder typically released as heat.

Transcript

00:01 Hey everyone.

00:01 This is question number 70 from chapter 14.

00:04 In this problem where it's about the body, we're told that one pound of fat equals 3 ,500 food calories, not very comforting.

00:11 We're told that 80 % of metabolized food goes to heat, and we're given a situation that you're going to run, and running produces a metabolic rate of 1 ,090 watts of metabolic power, excuse me.

00:25 We're asked to find the hours to burn 1 pound of fat, how much heat produced by burning, one pound of fat and how many liters of sweat you would need to evaporate to get rid of that heat.

00:36 Okay, so pert a.

00:44 We're asked to find out hours we need to run to burn one pound of fat.

00:49 So first we need to figure out how much heat this pound of fat actually is.

00:58 We can convert food calories to joules.

01:03 You can find that conversion in your book, but essentially one food calorie.

01:11 I'm just going to put fc is equal to 4 .186 times 10 to the third joules.

01:26 Okay.

01:28 So the energy released with that 3 ,500 is just 3 ,500.

01:41 Times that amount 4 .186 times 10 to the third joules and that gives us 1 .47 times 10 to the 7th joules and then we are trying to solve for time we have energy we have a power which we're given in watts and we know that power equals q over t energy or in this case heat over time so we rearrange this equation and solve for t.

02:18 T equals q over p.

02:23 This is part a, t equals q.

02:28 We just found it, 1 .47 times 10 to the 7th jules over 1 ,090 watts we know is a jewel per second.

02:42 Jules cancel, you're left with seconds, equals 1 .13 times 10 to the fourth second.

02:53 And we're asked to find an hour, so you divide by 3 ,600, and you get 3 .2 hours.

03:01 So this is not really realistic for a normal person.

03:05 You'd have to be very, very in shape...