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$\bullet$ Bicycling on a warm day. If the air temperature is the same as the temperature of your skin (about $30^{\circ} \mathrm{C}$ ), your body cannot get rid of heat by transferring it to the air. In that case, it gets rid of the heat by evaporating water (sweat). During bicycling, a typical 70 kg person's body produces energy at a rate of about 500 $\mathrm{W}$ due to metabolism, 80$\%$ of which is convertedto heat. (a) How many kilograms of water must the person's body evaporate in an hour to get rid of this heat? The heat of vaporization of water at body temperature is $2.42 \times 10^{6} \mathrm{J} / \mathrm{kg}$ (b) The evaporated water must, of course, be replenished, or the person will dehydrate. How many 750 $\mathrm{mL}$ bottles of water must the bicyclist drink per hour to replenish the lost water? (Recall that the mass of a liter of water is 1.0 kg.)

(a) 0.6 $\mathrm{kg}$ (b) 0.80 bottles/hr

Physics 101 Mechanics

Chapter 14

Temperature and Heat

Thermal Properties of Matter

The First Law of Thermodynamics

Cornell University

Rutgers, The State University of New Jersey

University of Sheffield

Lectures

02:20

A solid, liquid, or gas is one of the three main states of matter. Solids have a definite shape and volume, and retain their shape when a force is applied to them. They are rigid, and do not flow to take on the shape of a container, but retain their own shape. Solids are held together by intermolecular forces, which are usually chemical bonds. Liquids have a free-flowing, continuous surface, and take the shape of a container. They flow to fill an available space. Their particles do not have a definite shape or volume, and they are not rigid. Gases have no definite shape or volume. They are not held together, and are not rigid. They flow to fill an available space. Gases are often described as being the state of matter with the lowest density.

03:25

The First Law of Thermodynamics is an expression of the principle of conservation of energy. The law states that the change in the internal energy of a closed system is equal to the amount of heat energy added to the system, minus the work done by the system on its surroundings. The total energy of a system can be subdivided and classified in various ways.

03:08

If the air temperature is …

03:30

09:08

The metabolic rate (i.e. t…

02:04

Evaporation of water from …

01:47

A cyclist with a total ski…

0:00

Maintaining body temperatu…

03:54

08:44

Jogging in the heat of the…

06:51

You have probably seen peo…

06:41

Jogging in the Heat of the…

02:47

Overheating. (a) By how mu…

in this problem, we're going to talk about the latent heat. So what we need to remember is that the latent heat is the energy necessary to transfer to transfer to a system or from a system in order to change its phase of matter. And que is equal to the latent heat Constant l A times the mass of the object. And what we have in our problem is a cyclist, uh, who, um, produces energy at a rate at a power off 500 watts and about 80% off. This energy is produced in the form of the heat and in question A. We have to calculate how much mass of water a person must, uh, evaporate in order to lose all this heat that was produced. So first notice that the power that is produced in the form of heat is actually 80% off 500 and that is 400 watts and in one hour because we want to calculate the mass of water that must be evaporated in one hour in one hour. The total energy is 400 watts times 360 uh, 3600, uh, second. So this is equal to 1.44 times 10 to the sixth Jews in one hour. The person must the person produces in heat an energy that is equal to 1.44 times 10 to the sixth jewel, the mass of water times The latent heat must be equal to this energy e Okay, because this s O that the water they evaporated water can take away the heat from the person's body. So before we want to contemplate M, this is equal to the energy divided by L. So that's 1.44 times 10 to the sixth Jewels divided by the latent heat and exercise gives us the latent heat off authorization of the water. That's 2.42 time sent to the sixth jewels for meter. We have to divide it by 2.42 times since of the six use for actually said juice perimeter should be Yukos per kilogram. So the mass is equal to 0.6 kg. And then in question be you have to calculate how much how many bottles of water, each one having a volume of 750 mL. Must this, uh, cyclist drink in order to replenish the water that was lost in went out. Well, uh, noticed that 750 mL of water is equal to 750 g of water or 0.75 kg. Because one leader of water is it. Which 1 kg? Uh, then this corresponds to 0.75 kg. Wrote grams. But it should be kilograms cage. So the number of bottles of water is equal to the mass of one bottle. We'll call it envy. Divided by am. Actually, I'm sorry. The mass of water divided by the mass of one model. So this is 0.6 kg. The vital is your 0.75 kg. And this is 0.8. Okay, So a man, the man needs to drink 80% of a bottle of water.

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