Mathematical challenge wrt diving

[Jonas Isaksen]

From the book Diving Science I got the following challenge, which I am not able to solve:

Application of the universal gas law

An explosion occurs in a hyperbaric chamber that is at a depth of 100 FSW. If the ambient temperature in the chamber before the explosion was 72 degrees F, and the pressure gauge on the outsideber shows that the chamber pressure immediately increased to 650 FSW. How high did the temperature rise in the chamber?

The book's only answer is:
Using the universal gas law, one can determine that the temperature rose to almost 750 degrees F.

If you are able to calculate this, please show me how you did it.

 

[brutus_scuba]

Well I can't get it and I'm at work so I dont have too much time to play with it if I get a chance at lunch I may come back to it, but I'll give ya what I tried...and see if that helps ya. Please note I haven't used the gas laws since I was in like 10th grade so I forget all the details...

so starting back at PV=nRT I decided to use pressure in atm (which I believe is okay as long as you use .08206 for your Gas constant and Liters for your volumne and Kelvin for temperature. First thing I did was conver the 72f to kelvin to get 295, and the 100 to atm to get 3.03. If you rearrange the equation you can get

3.03(V/nR)=295

and being that all the values for volumme, number of molecules and the gas constant stay the same you should be able to combine it into one constant value for the problem and

295/3.03=(v/nR)

that value comes out to be 97.3, but you should be able to use that constant then to assume

19.69atm = 650 fsw

19.69 * 97.3 should equal your answer but it does not. It's not even in the ball park. I hope that you can somehow learn by my mistakes though.

 

[Jonas Isaksen]

First of all I am unsure whether the pressure is 3,03 ATM or 4.03 ATM since 33 FSW is 2 ATA ?
Anyhow you had a new way to see it, however even though playing with the pressure I am stil far off as well.

 

[SmokinReefer]

Convert your pressure to kPa here:

http://www.gazza.co.nz/waterpressure.html

Convert your temps to Kelvin here:

http://www.onlineconversion.com/temperature.htm

Your volume will stay the same, so pick anything and plug the numbers into here:

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegasc.html#c1

Click on final temperature and you end up with 1507 K, which is 2253 F.

But since the final pressure is so high (over 20 atm), the ideal gas law isn't really ideal anymore. You may want to use the van der Waals equation of state since most gases differ significantly from the ideal gas law at high pressure.

Smokin

 

[ItsBruce]

Odd, I came up with 468 degrees. The universal gas law says that pressure is proportional to temperature. The pressure increased by a factor of 6.5, i.e. from 100 to 650, so the temperature must also increase by a factor of 6.5.

 

[ClayJar]

An explosion occurs in a hyperbaric chamber that is at a depth of 100 FSW. If the ambient temperature in the chamber before the explosion was 72 degrees F, and the pressure gauge on the outsideber shows that the chamber pressure immediately increased to 650 FSW. How high did the temperature rise in the chamber?

The book's only answer is:
Using the universal gas law, one can determine that the temperature rose to almost 750 degrees F.

Okay, there is a small problem here. If there was an "explosion" in the chamber, the amount (in moles, for example) of gas in the chamber is not a constant. Without any data about the explosion, however, I'm forced to assume it was, let's say, a sudden injection of a large amount of energy with no eveolved gases or change in volume of the chamber.

Okay, that said, the pre-"explosion" pressure was 100fsw, which I assume was a gauge pressure, and the post-"explosion" pressure was 650fsw (also gauge). To convert these to absolute pressures, we just add the 33fsw ambient pressure, yielding 133fsw and 683fsw, respectively. The pre-"explosion" internal temperature was 72°F, which we convert to absolute temperature by adding 460° to yield 532°R.

532°R * 683fsw / 133fsw = 2732°R = 2272°F

Either there is additional information that was not presented here, or the given answer is incorrect.

Odd, I came up with 468 degrees. The universal gas law says that pressure is proportional to temperature. The pressure increased by a factor of 6.5, i.e. from 100 to 650, so the temperature must also increase by a factor of 6.5.

You must use absolute values for pressure and temperature.

 

[knotical]

Concur with ClayJar, except I added 459 instead of 460 when converting to Rankine. So my end result is slightly different at 2268 F.

I agree that there is an error in the book.

 

[ClayJar]

0°F = 459.67°R (which rounds to 460.°R, given the temperature in the problem is specified as a nearest full degree.)

 

[knotical]

0°F = 459.67°R (which rounds to 460.°R, given the temperature in the problem is specified as a nearest full degree.)

You're right of course. Mainly I was trying to agree with your method, preserving units of the original question as much as possible. In any event, no one seems to have come up with an answer anywhere near the book's.

 

[ZzzKing]

From the book Diving Science I got the following challenge, which I am not able to solve:

Application of the universal gas law

An explosion occurs in a hyperbaric chamber that is at a depth of 100 FSW. If the ambient temperature in the chamber before the explosion was 72 degrees F, and the pressure gauge on the outsideber shows that the chamber pressure immediately increased to 650 FSW. How high did the temperature rise in the chamber?

The book's only answer is:
Using the universal gas law, one can determine that the temperature rose to almost 750 degrees F.

If you are able to calculate this, please show me how you did it.

My questions are:

1. "Can you calculate the area over which the guts are spread?"
and
2. "Do you like your meat rare, medium or well done?"