In a highly competitive game, a basketball player can produce 300 W of power. Assuming the effi

In a highly competitive game, a basketball player can...

In a highly competitive game, a basketball player can produce $300 \mathrm{~W}$ of power. Assuming the efficiency of the player's "engine" is $15 \%$ and heat dissipates primarily through the evaporation of perspiration, what mass of perspiration is evaporated per hour?

Key Concepts

Efficiency

Efficiency refers to the ratio of useful output energy or work to the total energy input. In a biological or mechanical system, only a fraction of the total energy consumed is converted into mechanical work, with the remainder typically lost as heat. This concept is crucial for understanding how much energy is available for performing work versus being dissipated as waste heat.

Power and Energy Conversion

Power is defined as the rate at which energy is used or produced, commonly measured in watts (joules per second). Converting power into energy over a period involves multiplying power by time. This conversion is essential when calculating total energy expenditure in scenarios extended over time, such as energy output per hour.

Latent Heat of Vaporization

Latent heat of vaporization is the amount of energy required to convert a unit mass of a liquid into vapor without changing its temperature. In contexts where heat dissipation occurs primarily through the evaporation of perspiration, knowing the latent heat allows one to determine the mass of sweat that must evaporate to dissipate a given amount of thermal energy.

Transcript

00:01 So here we're going to do an interesting back -the -envelope calculation.

00:06 So let's suppose that a professional basketball player generates 300 watts as power.

00:17 Okay, so that is power that's doing useful work during the game.

00:22 And we're going to ask how much heat gets exhausted from their body.

00:27 And furthermore, a more interesting question is how much.

00:31 Much perspiration could they vaporize? how much perspiration could they vaporize? so sort of an interesting calculation will let us know why you have to drink a lot of fluids while you're doing such an activity.

00:59 So we are told that this power is generated at 15 % capacity, at 15 % efficiency.

01:15 And we want to know how much perspiration is vaporized in one hour.

01:21 So let's say that this person could keep up their activity fully for one hour.

01:27 So we want to start with the definition of efficiency of a heat engine is the amount of work produced divided by the amount of heat absorbed.

01:40 And to conserve energy that work is the difference between the heat absorbed, minus the heat exhausted.

01:54 And these are, of course, absolute values.

02:03 Okay, so we can start off, and let's assume we're thinking about just the power.

02:10 Of course, everything could have time dependence on top of it.

02:16 So what i mean by that dot is take a jewel and turn it into a jewel per second or a watt.

02:25 Okay, so we can do the same with our efficiency.

02:31 And using our 15 % efficiency, we can use our work of 300 watts and solve for the amount of heat absorbed.

02:54 And we find that to be 1 ,700, 2 ,000.

02:59 One step at a time.

03:13 My napkin is getting a little seedy looking.

03:18 Here we go...

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