Can a Fan Increase Temperature in a Closed Room?

[bassplayer142]

Heat is the vibration of atoms. According to this theory if you shook something then it would heat up on a microscopic level. Now imagine a closed system. Say a room that is in a closed system. If there is a fan spinning in the middle, then wouldn't the fan heat up the room. Disregard the heat released from the fan motor and other electronic things. Just concentrate on the movement of the air.

 

[ekrim]

yea, in the E=Q-W equation, that's work done on the system, which means an increase in internal energy

of course, the circulation of air would cool down any occupants. which is why fans are not a huge hoax

 

[AbedeuS]

The concept is correct, you are in effect speeding up the translational energy of the molecules in the gas, but the initial speed of most gas molecules is massive.

Using the two following equations, we can find the average speed of a gas molecule, in a room, the volume and pressure do not matter in this case, as a gases velocity is purely decided by it's temperature in ideal gas situations:

PV = nRT (Your standard ideal gas equation used very commonly)
PV = 1/3 Nmc^2 (Equation from the basic Kinetic theory of gases, works in ideal gas situations)

The Variables
P = Pressure (not necessary when we combine)
V = Volume (not necessary when we combine)
n = Moles of gas in the enclosed system (Not necessary either)
R = Ideal gas constant (8.31 Roughly)
T = Temperature (In kelvin)
N = Number of molecules, will change to n*Na to make it clearer later
m = Mass of molecule in question (In grams)
c = Speed of that molecule
Na = Avagadros constant (6.02*10^23)

Make Kinetic theory equation molar, to match up with the ideal gas equation (and make it easier to work with)

PV = 1/3*n*Na*m*c^2​

Combine equations

1/3*n*Na*m*c^2 = n*R*T​

Make gas speed the subject:

c = Sqrt( (3*n*R*T)/(n*Na*m) )[/CENTER]

Cancel anything possible:

c = Sqrt( (3*R*T)/(Na*m)​

Na*m == Molar mass of a molecule, for Oxygen this is 16 Per atom for example), molar mass is usually symbolised by a big M, so we get this as our final molar mass based equation.

c = Sqrt( (3RT/M) )​

Lets use an oxygen molecule (M=32) as an example, at 298K (25Degrees, room temperature) and find its speed using this equation.

c = Sqrt( (3*8.31*298)/(32) ) = 15.24 Meters per second​

In more everyday european speeds or whatever even 15.24 Meters per second is equal too 54.86 Kilometers per hour average speed of an oxygen molecule, an average desk or room fan will not increase the speed of air by a lot in comparison to its average speed anyway I guess (couldnt find any hard numbers for any name brands of fan)

What must also be taken into account that the relative amount of air being compressed and decompressed by a deskfan is still small in comparison to the amount of air in the room, meaning that the average temperature of the room will not change much, the faster moving molecules generated by the fan will slow down as their kinetic energy is transferred to other molecules in air (by collisions), resulting in a net "dilution" of kinetic energy generally uniformly across the whole room. The cool feeling that the fast moving air makes is i would think either from the higher air flow causing heat to move away from your body, giving the apparent feeling of coldness, or the faster higher pressure air produced by the fan expanding in a somewhat pseudo-isothermal style, and getting thermal energy from the other air, but that's a silly suggestion.

The only reason I gave such a massive reply however is because I'd like too see an explanation from the real masters on this forum, as I'm quite interested myself as too why air from a fan is colder, and why the net speed increase doesn't heat up the room noticably.​

 

[TVP45]

The room does heat up. You are adding energy to the room from the electric system.
The air from the fan is not colder. It feels colder, primarily due to 2 effects: (1) moving air evaporates sweat from a person and that heat of evaporation comes primarily from the skin of the person; and (2) there will be a stagnant layer of heated air around the person's body which will be dissipated by the fan circulation.
When the air is hot enough and humid enough, a fan does absolutely no good.

 

[russ_watters]

Fans fight air resistance and take energy to do it. That energy heats up the room.

 

[AbedeuS]

Their replies were better ^^ i thought the compression and decompression caused by the pressure differances a fan made could potentially cause a cold and hot sector, but the difference would be minor if it existed.

 

[TVP45]

Abedeus,
You got to built yourself a swamp cooler sometime. That will show you about 98% of the answer.

 

[AbedeuS]

Whats a swamp cooler? ^^

 

[bassplayer142]

Thanks for the replies. Those equations I could have worked out if I would have thought about it. Nice to see physics applied.

 

[AbedeuS]

Nah the equations are handy for other things, but they are a little out of context for this argument, i think i typed those equations last night and didnt have much of a straight mind, there's probably better equations for the job

 

[Loren Booda]

Fans make you feel cool by increasing evaporation and breaking up the region of warm air next to the skin. A fan heats up air from turbulence driving finite air molecules, their mutual friction and singularities preventing laminar flow. This heat is a small fraction of that generated by the motor.

 

[cesiumfrog]

and singularities preventing laminar flow.

What do you mean exactly?

 

[Loren Booda]

That smooth movement by molecules is impossible where and when two or more are expected in the same place at the same time by linear projection. Turbulent flow would involve an otherwise laminar flow with singularities (e. g., "sinks" or "sources").

 

[cesiumfrog]

smooth movement by molecules is impossible where and when two or more are expected in the same place at the same time by linear projection. Turbulent flow would involve an otherwise laminar flow with singularities (e. g., "sinks" or "sources").

Usually, when a flow is said to contain "sinks" or "sources", it is equivalent to saying that the continuity equation is not satisfied. Surely you're not claiming that to be the case for a simple air fan?

Are you instead claiming that an ideal fluid (not composed of discreet molecules) would behave in a qualitatively different manner?

As for your statement about impossibility of smooth movement, isn't that trivially disproved by every demonstration of laminar flow through pipes of decreasing radius?

 

[Loren Booda]

Since the edge of the fan is irregular at the atomic level, it can initiate turbulence and therefore disperse its nonlinearity (the butterfly effect). Also, the fan itself, deviating from an idealized continuous, symmetric air propeller, has implied at least one singularity between each of its blades. Both of these mechanisms would be significant causes of fan blades' mechanical energy converted to air's thermal energy (though not significant contributors to heat overall).

I guess that a fluid composed of infinitesimal atoms, being able to travel sinks and sources, would remove at least one dimension of potential turbulence with finite atoms.

The laminar flow in pipes of decreasing radius works until the pipe diameter approaches the scale of the finite molecules.

What turbulence is not initiated on the atomic level?

 

[cesiumfrog]

Loren: your comments frequently (as in this thread) contain strings of technical terms arranged in a manner that conveys no meaning to me. This suggests that either your knowledge far surpasses my own on these topics (in which case you've certainly overshot the OP here) or the other way around (in which case you're just making up "technobabble" like a script writer for TV sci-fi).

I'm criticising posts that I cannot reason, not you as an individual person.

 

[Loren Booda]

cesiumfrog,

Thank you for your honesty. I am both of those people you describe, so by default, I am the lesser of the two. With concerned feedback like yours I will eventually make middle ground. I tend to be too qualitative and abstract for most physicists, and have created my share of pseudoscience. Having a Masters degree in physics but not having studied in the field for 21 years, I feel like I know what I am writing but am not strict enough with my reasoning to justify it logically to the satisfaction of many. So you know that I have some expertise, see my straightforward proof, "The Booda Theorem," found on my website (below) among articles of much speculation. Please attribute my imperfections here to relearning physics. I hope it is my lack of critical thinking you do not like, not me.

 

[sepowens]

If you are willing to take an example of water instead of air, the cables that planes catch to slow them down when landing on aircraft carriers are attached to drums that are fixed to a set of paddles in tanks of water. As the plane lands the cable pays out and the paddles spin. The resistance of the water dissipates the aircrafts speed and heats the water, often to the boiling point.

 

[cesiumfrog]

That's a very interesting application of Joules experiment (which in turn was the reason why earlier assertions, that a fan necessarily causes insignificant heating itself compared to its motor, were incorrect).