Greg's Challenge Question #1

It depends on what are the sources and the sinks of heat.

If you consider the kitchen as an adiabatic system, the introduction of some people at temperature lower that the kitchen would actually lower the system temperature, initially, by the reason:

Final kitchen temp x (kitchen mass + people mass) = Kitchen tempxKitchen mass + People tempxpeople mass

Like, if you mix 1l of boiling water and 1l of ice about to melt at sea level in an adiabatic pot, you'll end with 2l of water at about 50 deg C, or so. Always use absolute temperatures in the calculus. People breathing, transpiration, all would exchange heat with the ambient, untill the people all die from asphixie and the bodies themselves go to an equilibrium with the surrounding ambient.

Being the system adiabatic and isolated to the ambient, of course.

BUT: A kitchen usually has one heat source, and many sinks, and is not all at 105 F. What you would do introducing people is to increase the number of heat sources comparing to the heat sinks, so, the temperature of the kitchen would actually increase. Maybe imperceptible, maybe some degrees. A lot of people also can block ventilation, and so...

Unfortunately, the answer is "depends".

"Like, if you mix 1l of boiling water and 1l of ice about to melt at sea level in an adiabatic pot, you'll end with 2l of water at about 50 deg C, or so"

You neglected to account for the latent heat of fusion (melting) of the ice, and the the fact that 1 liter of ice will yield less than 1 liter of water after it melts. Therefore you would end up with approximately 1.9 liters of water, and at a temperature around 15 °C.

As to the OP, as you point out there are sources and "sinks", plus we have to assume airflow through the kitchen, along with a temperature gradient from floor to ceiling. In short, there is no way to definitively answer the question with the information provided in a real world, satisfactory way.

However, assuming its an abstract question, one answer would be that people will not raise the temperature, because their body temperature is lower than the air temperature, and they will perspire as necessary to keep it that way, but if their core temperature rises too far, they may collapse before it reaches 105° F. This is where the question is silly, because their bodies are adding heat (latent heat, in the form of increased humidity) to the kitchen all along, but without raising its temperature, at least until they themselves overheat above 105° F, OR the excess humidity they added condenses on a cooler area of the kitchen which is acting as a "heat sink" of sorts, and the latent heat manifests itself by raising the temperature of that cooler area which will then tend to increase the kitchen air temperature.

Greg

The kitchen gets cooler and the bodies get warmer.

That's the answer to your question as you phrased it.

As far as the employees go, which is the real reason driving his action, sure stay out of the kitchen if you can't take the heat. Sorry about the pun.

No, I'm not sorry about the pun on second thought.

Anonymous Hero,

We know that heat moves from the higher temperature to the lower temperature, and your answer certainly has that on its side so you are right I would think if we assumed a closed system ... In any case, you are not wrong because people at body temperature can't raise the temperature of a room that is hotter than they are .. the room would transfer heat to them, and heat would be used to evaporate their perspiration, so the more I think about it, the more I like your answer better than my own.

But, it's such a silly question to begin with because it leaves so many things undefined and in a real situation, it would be extremely difficult to make accurate measurements, unless the room was fully instrumented, and a large number of trials was conducted. And, that would only answer it for that particular case, and those particular trials, since we know things like air circulation, humidity, how the people are dressed, how long they are in there, etc all will have an effect.

Greg

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DISCLAIMER: I AM NOT THE POSTER OF "Greg's Challenge Question #1", although I confess to a certain curiosity since it was posted by Guest yet the name coincidentally matches my own.

Greg

If the kitchen begins at 0% relative humidity, a person will add moisture to it and make it feel hotter as time goes by. The evaporation will keep the person's temperature below that of the kitchen air. The person's body temperature will stay down at first but rise as the humidity of the room rises. A point will be reached when the body will not be able to stay below the temperature of the kitchen because to stay alive, the body must metabolize, producing its own heat. But that is already a deadly temperature for the person.

First of all, 105 F is such a high temp that man feels sick due to fever at this temp. Considering normal body temp around 95-97 F people present in the kitchen will absorbe heat and if the heat source is providing heat at constant rate, then temp will be maintained.

Ignoring the practical issues of people collapsing and so on, a human is not just an "ugly bag of mostly water" but a source of heat, albeit with a natural thermostatic regulation system set to 98.6. Since humans generate heat that must be exhausted at their boundary interface to the environment then they must be adding their heat to the environment. If the humidity of the environment is less than 100% then the body will use evaporative cooling to exhaust the heat by using heat from the environment to cause a phase change in the water in perspiration from liquid to vapor and that would not seem to raise the temperature. However, once the air can hold no more water vapor then thermodynamics require that the body temperature will rise to a temperature greater than the air in order to eliminate the approximately 800 btu per hour that a human generates. At this point the heat will increase until the body dies of hyperthermia and that's probably just as well because you will also have suffered brain damage by then. So eventually, if there is no circulation the humidity will reach saturation, the heat will rise until everyone dies and then it will go back down for a few days until the heat from bacterial action in the rotting corpses begins to heat it back up again. Meanwhile the customers will go hungry but will eventually call the authorities once the smell gets to be bad enough.

If you consider the kitchen as an adiabatic system, the introduction of some people at temperature lower that the kitchen would actually lower the system temperature, initially, by the reason:

The problem is a person cant be considered an adiabatic component. A human being need to radiate approximately 75 watts of power to maintain a core temperature of 37° C. There a whole host of mechanism that it uses to control the radiation of heat regardless of the temperature. It's not as simple as just looking at the temperature of each body you need to look at the enthalpy.

So even at an ambient temperature of 40.6° C (105° F) provided the humidity isn't 100% a human being will still radiate heat into the atmosphere. Having said that however the miniscule 75 W that each person radiates if insignificant compared to the kilo watt outputs of things like ovens and range tops. The end result would be that it is unlikely that and difference that the lack or presence people made could be detected.

105 deg. F is very warm indeed. If I were a waiter or someone who isn't assigned to the kitchen, I would avoid going in there. If I do have to go in, I'd get out as soon as possible. I don't think the manager needs to tell me to stay out.

As for the question, the more people there are in there, the hotter it will seem to get. In that heat, bodies will start to perspire and add to the humidity. Sweat evaporation will decline and the body will heat up. Heat it up sufficiently, and he may get heat exhaustion (or is it heat-stroke, the difference escapes me at the moment. I'll have to look that up).

Is this the correct thing to do, however? Certainly not! The OSHA website gives a recommendation of 77 deg. F for heavy work and 86 deg F for light work. Obviously, 105 deg F is way too hot already.

I don't believe so. They should absorb any heat above their body temperature. The misconception of being "hot" in an overly crowded room is due to the fact that your entire body will then be, roughly, 98.9. Your skin normally isn't as warm as it is inside the body, so it just feels hotter than it really is. Then add the humidity of the vapor found in the breath of these individuals - now it's muggy too.

You don't end up with a fever just because the atmospheric temperature is above 37°C do you so why would you in this instance?

Yes, as anyone whose sat in a crowed room, or rode on a crowded bus knows all too well. Now you might say, how can 98 to 99 "heat" up 105. The same way the appliances, and food, and refrigeration maintains the 105. Anyway, when he says "any hotter" he does not mean raise the temperature from 105. He means any hotter than it absolutely has to be, hence: not any less cooler than it is. So while his syntax might not be any better than an engineers, his logic is understandable and correct--for the safety of his employees.

Since you claim to know what the OP (Guest) means, then you must be the same.

I thought the question was silly/stupid and I think the answer you are providing fits the character of the question, and makes no sense at all.

Greg

Creg,

You are mistaken about who I am; but correct in interpreting my answer as reflecting a non-objective challenge. So you need to give yourself a slap for attitude. But thanks for agreeing succinctly.

Guest not the guest.

I am the Guest!!! Not for any reason you atribute words to me please!

Greg,

I am the poster of Greg's Challenge Question #1 and I find your comments inflamatory. Perhaps this question is silly as you suggest, and perhaps then you had no buisiness addressing it. Maybe you should have just moved on with your life instead of responding many many times to the silly/stupid question.

I think, however, that your critisism is misplaced evidenced by the plethora of different responses by other civilized people. The question was posed in the first place in order to spark a debate of ideas and brainstorming efforts among engineers which you took part in with your multiple responses. If you consider a question with a somewhat "obvious" answer to be "stupid/silly" then you shoud be labeled with such adjectives instead.

After all...it has been the questions with "obvious" answers throughout history that have been answered incorrectly and the people critisised for challenging those "obvious" answers are often proved correct.

Personally, I think you have no right to post such inflamatory things about someone's question. Just keep you big keyboard quiet next time and don't post comments at all!!

The people the boss is telling to stay out of the kitchen are obviously not employed in there, and so will be coming and going frequently - so as they begin to feel hot, will leave the kitchen taking some of the heat with them. By returning once they have cooled off, they will effectively be acting like the extractor fan the boss should have had installed.

While a human has access to water and the surrounding air is not saturated with water humans can maintain their body temperature at closet to 37° C. The main mechanism behind this is the vaporization of water and the latent heat of vaporization. Water vapor at 37° C contains more energy than water at 37° C therefore by vaporizing water you are adding energy to the water. This means that while the water being secreted by the pours in your skin can evaporate then the body can radiate energy to its environment and maintain its core at around 38° C and surface at around 37° C.

As for feeling hot or cold this has less to do with your body temperature than one would expect. A human feels comfortable when the atmosphere is at around 22° C with a relative humidity of around 55%. This is what you feel as normal and the rate of energy transfer at this temperature is what you feel comfortable with.

If the rate of energy loss to the atmosphere increases from the normal level you will feel cold and oppositely if it decreases you will feel hot. That is why you feel hot at 22° C with a relative humidity of 100% since you body will not be able to radiate the energy as readily. Conversely if your body temperature is actually above 37° C and you have a fever, you will feel cold at 22° C and start to shiver because you body is radiating energy into the environment faster than normal. You do not normally feel hot if you have a fever.

The upshot of all this is that in the given environment of the kitchen where the atmospheric temperature is 40.5° C any additional humans at 37° C will be radiating energy to the environment through water evaporating off their skin. The humans will not warm up to 40.5° C as some have stated. While the temperature in the room will not rise either the humidity will increase ant the enthalpy of the air in the room increases with the added moisture. Enthalpy is what humans actually detect as temperature as it is the enthalpy of the surrounding air that controls the rate of energy transfer not the temperature on its owne.

The old saying "To many cooks spoil the broth" seems to be true in this case.

Surely a more apt version would be "if you can't stand the heat..etc.etc

Human bodies generate heat while alive. As long as they live in the kitchen, they would heat it even more. After they expire, I expect decay is also exothermic. I don't think I want to eat there.