How about some math

[robr]

Been a while since we've had a math problem. I cannot find the appropriate calculator online so here's my question.

Given that the air that we breathe contains about 20% oxygen, and that as air cools, it becomes more dense, thus contains more oxygen (good for runners and turbos).....

How much denser is air at say 32F than at 80F (ie how much more oxygen content is there)?

 

[Carguy!]

Been a while since we've had a math problem. I cannot find the appropriate calculator online so here's my question.

Given that the air that we breathe contains about 20% oxygen, and that as air cools, it becomes more dense, thus contains more oxygen (good for runners and turbos).....

How much denser is air at say 32F than at 80F (ie how much more oxygen content is there)?

Looks to be about 10% denser, here is a calculator that you can use to calculate the figures: http://www.webqc.org/ideal_gas_law.html

 

[bigbadberry]

PV=nRT

 

[robr]

Looks to be about 10% denser, here is a calculator that you can use to calculate the figures: http://www.webqc.org/ideal_gas_law.html

I can't even tell which one of those is density, nevermind which equation I should be using.

And doesn't it matter what sort of gas we are talking about? Ie, wouldn't temperature affect methane or helium differently than it would affect air?
ie, if air were 10% more dense by lowering temperature by 40 degrees, does that mean argon is also going to be 10% more dense?

I ask this because I find when running in colder weather, I do FAR better and get far less winded than when it's warm and I'm curious how much more oxygen I'm taking in. I ran 6 miles tonight (it was 35F) and I could NEVER do that if it were 70F out.

 

[Kyras]

I can't even tell which one of those is density, nevermind which equation I should be using.

And doesn't it matter what sort of gas we are talking about? Ie, wouldn't temperature affect methane or helium differently than it would affect air?
ie, if air were 10% more dense by lowering temperature by 40 degrees, does that mean argon is also going to be 10% more dense?

I ask this because I find when running in colder weather, I do FAR better and get far less winded than when it's warm and I'm curious how much more oxygen I'm taking in. I ran 6 miles tonight (it was 35F) and I could NEVER do that if it were 70F out.

I wonder if it's more to do with it being easier to run if you aren't overheating than to do with oxygen density. I know when I ride my ElliptiGO I do much better and ride faster when it's under 75*F than over. I just wilt when I'm hot.

^That's my ElliptiGO in case you've never heard of one.

 

[Carguy!]

I can't even tell which one of those is density, nevermind which equation I should be using.

And doesn't it matter what sort of gas we are talking about? Ie, wouldn't temperature affect methane or helium differently than it would affect air?
ie, if air were 10% more dense by lowering temperature by 40 degrees, does that mean argon is also going to be 10% more dense?

I ask this because I find when running in colder weather, I do FAR better and get far less winded than when it's warm and I'm curious how much more oxygen I'm taking in. I ran 6 miles tonight (it was 35F) and I could NEVER do that if it were 70F out.

http://en.wikipedia.org/wiki/Ideal_gas

Most gases behave like ideal gases, there are some that behave differently though. In the formula I mentioned before you are looking to solve for volume which in turn would provide the density.

 

[Vega$ NSX]

Carguy is right in that it is roughly 10% more dense. That's roughly equivalent of dropping about 3,000' in altitude to sea level.

Also keep in mind that you don't overheat as easily in the cooler weather so that certainly would help with your run times as well.

 

[Vega$ NSX]

http://en.wikipedia.org/wiki/Ideal_gas

Most gases behave like ideal gases, there are some that behave differently though. In the formula I mentioned before you are looking to solve for volume which in turn would provide the density.

There was one for density. It was the last equation (solving for q). Although it wouldn't have made a difference either way in calculating a % change.

 

[sahtt]

I can't even tell which one of those is density, nevermind which equation I should be using.

And doesn't it matter what sort of gas we are talking about? Ie, wouldn't temperature affect methane or helium differently than it would affect air?
ie, if air were 10% more dense by lowering temperature by 40 degrees, does that mean argon is also going to be 10% more dense?

I ask this because I find when running in colder weather, I do FAR better and get far less winded than when it's warm and I'm curious how much more oxygen I'm taking in. I ran 6 miles tonight (it was 35F) and I could NEVER do that if it were 70F out.

This is fun "math" compared to the CO2 enhanced oil recovery liquid rich nat gas estimations in the permian basin I'm working on (I know, TMI).

Here is a simplified but actual example of the "math" -

Problem using .850 ATM, 1 mole of O2 in 1 liter of water, 25 degree Celsius which is about 77 degrees F (the 298 in the equation is 273+25 since the formula uses degrees kelvin not celsius, much less Fahrenheit)

PV=nRT

.850(v) = 1.00(.0821)298
v = 28.8 L O2

Moles × molecular mass = grams
1.00 moles O2 × 32.0 = 32.0 grams O2
Finally, we take the mass and divide it by volume to find density:
32.0 grams ÷ 28.8 L = 1.11 g/L

Now substituting 0 degrees Celsius (freezing point of water, 32 F) -

.850(v) = 1.00(.0821)273
v = 26.4 L O2
32.0 grams ÷ 26.4 L = 1.21 g/L

Everything else held constant, the density of oxygen in the one liter of water keeping everything else constant was 9.2% higher when the temperature was 32 degrees F versus 77 degrees F.

*Disclaimer - I don't do these sorts of problems on a regular basis.

I will throw another problem at you that is just as interesting. How many calories are required to run x miles at your age/weight/pace in 77 degree ambient temps vs 32 degrees? :smile:

I'll give you a clue, very high temps and very low temps (especially) require your body to consume massive quantities of energy!

*Edit - Vegas needs to hire me after I graduate.

 

[Vega$ NSX]

*Edit - Vegas needs to hire me after I graduate.

Lol, I would, but my field would bore and be way too beneath you. That's why I jump on these math and engineering questions here on Prime so I can actually have something fun and challenging to do! :smile:

 

[robr]

thanks, im surprised it's only 10% so it must be the overheating thing that makes the bigger difference. my lungs give out before everything else when it's warm. today it was my lower back. did a 5mi run a few days ago and it was my leg that fell asleep at mile 3 and never woke up until I took off my sneakers. If not for those, I could have kept right on going.

 

[sahtt]

thanks, im surprised it's only 10% so it must be the overheating thing that makes the bigger difference. my lungs give out before everything else when it's warm. today it was my lower back. did a 5mi run a few days ago and it was my leg that fell asleep at mile 3 and never woke up until I took off my sneakers. If not for those, I could have kept right on going.

FWIW, please don't over do it Rob. I am 27 and have ran a total of 25-50 miles since I had knee surgery 3 or 4 years ago. There is no "need" to run many miles on concrete on a regular basis. I used to and paid a heavy price. I can still ski double diamonds and daily ride sport bikes, but my knee's durability is permanently reduced. I do circuit style training and a lot of low impact cardio, think 4mph on the tread mill with a good incline.

I jump off every 5 minutes and do 15-25 push ups. My heart rate stays up and I don't damage joints in the process. I do sets of 20 pull ups/chin ups (just finished a set of 5 actually), 50+ push ups, rock climb like a champ, extreme ski, etc. and I really think the average healthy person way over does it with the running to be in good shape. There is no need! I am no doctor but limbs going numb while working out is not a good thing. I went from healthy eating to 99% vegetarian (not religious about it) and I think changes to diet go a lot farther than most exercise.

 

[Kyras]

http://www.elliptigo.com/injured-former-runner.html
^Check out the ElliptiGO. It really is a great way to get the runner's high without the impact.

 

[robr]

Holy crap! Those things start at $1800 and go up from there quickly. I'd rather have a real elliptical machine for that. I think I just saw them making fun of the on modern family

I'll stick to running, it's free... Well almost. Just ordered new sneakers. I'll be fine once I drop some weight.

 

[robr]

Hmmm. Don't see how to edit with Tapatalk. Anyway you're right sahtt. Dieting does go further however it's not something I'm good at. I like very few things that are healthy. Once my wife's ankle is healed ill be giving crossfit a try. Sounds like your work out is similar.

 

[Kyras]

Holy crap! Those things start at $1800 and go up from there quickly. I'd rather have a real elliptical machine for that. I think I just saw them making fun of the on modern family

I'll stick to running, it's free... Well almost. Just ordered new sneakers. I'll be fine once I drop some weight.

Yeah, if I could still run I'd do that instead! My back is fried though. I was using the ellipticals in the gym and hate the gym. BORING. My ElliptiGO 11R cost $3,500, the same price as the carbon fiber bicycle I bought just 5 months before discovering the ElliptiGO. You get what you pay for. I want to be outside exercising. I love it. It's like flying.