How Much Air Does a 600W Hair Dryer Circulate Per Second?

In summary, a hair dryer uses a coil to generate thermal energy at 600 W and a fan to blow the warm air out. The density of air is assumed to be 1.25 Kg/m^3 with a specific heat capacity of 990J/Kgk. The dryer takes in room temperature air at 20C and outputs it at 40C. The volume of air flowing per second is calculated by dividing the mass per unit time by the density, but the answer key multiplies the two values instead. For the second part of the problem, the answer key divides the energy needed to evaporate 180g of water at 40C by the power rating of the dryer, while the student uses cross-multiplication
  • #1
YarnJunior
7
0

Homework Statement



A hair dryer consists of a coil that warms air and a fan that blows the warm air out. The coil generates thermal energy at a rate of 600 W. Take the density of the air to be 1.25 Kg/m^3 and its specific heat capacity to be 990J/Kgk. The dryer takes air from a room at 20C and delivers it at a temperature of 40 C. What volume of air flows per second? The warm air makes water in the hair evaporate. If the mass of water in the air is 180g, calculate how long it will take to dry the hair if the HEAT required to evaporate 1g of water at 40C is 2200J.

Homework Equations



Density = M/v
Q = Mc(Change T)
P = Q/t

The Attempt at a Solution



I think this is a simple problem, however the answer sheet seems to disagree with me. The volume per second I calculated by simply finding the m/t which is basically P = mcT/t and assuming m/t = M; so I concluded that P = McT and, since i have the change in T and the specific heat capacity as well as P, I managed to calculate M. With this, I used Volume = Mass/Density and concluded that Volume/t = Mass/(Density x Time), where that equals the M I calculated beforehand. Supposedly, I should get 0.03/1.25 (where 0.03 = M). However, the answer key solves it by multiplying 1.25 x 0.03 or something? As for the second part, I don't think I have much trouble with it barring one little part. Basically I use cross-multiplication to find that 2200 x 180 = Energy needed to evaporated 180g of water, then divided that over the power rating of the dryer, so I should get something like 11 minutes. The answer key, however, solves it by dividing over 750. 750 is the product of 1.25 and 600. Why we chose to multiply those two numbers is beyond me. Anyways, I basically have no idea what to do to get that result. I tried thinking from the logic that 600 W releases 1.25 kg/m3 of air, but then I remembered that this 600W is the rate of ENERGY. So it's already Q/t. I'd appreciate any help, thanks!
 
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  • #2
You're missing a volume flow rate for the fan, or at least omitted it for us.
 
  • #3
Bystander said:
You're missing a volume flow rate for the fan, or at least omitted it for us.

That's exactly the givens for the question. You're meant to calculate the volume per unit time of the dryer. The answer sheet just says Density x (Change in Volume / Change in Time) and multiplies density with the mass per unit time for some reason? Is this an error or am I missing something?

Math-wise it makes little sense. Density = m/v, so v = m/Density. Therefore, (m/t) / density = V/t. Why do we have to multiply volume/t x density or even mass/t x density? They still won't give you the v/t.
 
  • #4
Okay, my bad. "Dividing by 750?" Does sound like a "re-written" problem that failed to rewrite the answer key.
 
  • #5
Bystander said:
Okay, my bad. "Dividing by 750?" Does sound like a "re-written" problem that failed to rewrite the answer key.

The answer key is directly from the book, so supposedly it has some merit. It's quite confusing to say the least. Is there any way to justify this answer? It seems like a very simple question, but it became needlessly complicated.
 
  • #6
If it's an "nth" edition, n > 1, someone can decide to swap 600 for 750, and the graduate student slave labor fail to carry the value completely through the new answer key. There are no corrections for raising water temperature in the hair from body temperature of 37 C to 40, or allowing for heat input from the scalp, so the simplest interpretation is that the heater size in the dryer was changed from a previous edition.
 
  • #7
It seems to me the book did the volume flow rate wrong, and you did it right. They should have divided by the density, not multiplied.

Chet
 

1. How does a hair dryer produce thermal energy?

A hair dryer produces thermal energy through the conversion of electrical energy into heat energy. The hair dryer contains a heating element, usually made of nichrome wire, which heats up when an electric current passes through it. The hot air produced by the heating element is blown out of the dryer, providing the thermal energy needed to dry the hair.

2. What is the maximum temperature that a hair dryer can reach?

The maximum temperature that a hair dryer can reach varies depending on the type and model of the hair dryer. However, most hair dryers have a maximum temperature range of 120-150 degrees Fahrenheit. Some high-end hair dryers may have a higher maximum temperature, but it is important to use caution and avoid using the hair dryer at its highest setting for extended periods of time to prevent damage to the hair.

3. Can using a hair dryer at high temperatures damage my hair?

Yes, using a hair dryer at high temperatures can damage your hair. The high heat can cause the hair to become dry, brittle, and prone to breakage. It can also strip the hair of its natural oils, leading to frizz and damage. It is recommended to use a hair dryer at a lower temperature setting or to use a heat protectant product to minimize damage to the hair.

4. How does the wattage of a hair dryer affect its thermal energy output?

The wattage of a hair dryer directly affects its thermal energy output. A higher wattage hair dryer will produce more thermal energy and therefore dry the hair faster. However, using a hair dryer with a higher wattage may also increase the risk of damage to the hair. It is important to find a balance between wattage and temperature to achieve the desired results without causing harm to the hair.

5. Can a hair dryer's thermal energy cause burns or damage to the scalp?

Yes, if a hair dryer is used at a high temperature and held too close to the scalp, it can cause burns or damage to the scalp. It is important to use a hair dryer at a safe distance from the scalp and to avoid using it at its highest temperature setting. It is also recommended to use a heat protectant product and to take breaks while using a hair dryer to prevent overheating the scalp.

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