Air temperature in soda bottle pumped to 8 atm

[SMD1990]

In theory, it should be about 2400 K, no? Yet, the bottle does not show any melting. I cannot even get a little piece of solder inside to melt. Is the heat loss during the thirty to sixty seconds of pumping that extreme? Or, is my understanding of the relationship between temperature and pressure incorrect?

 

[gsal]

2400K?
What are your initial conditions?
what are the conditions during the process?
what relationship between temperature and pressure do you have in mind?

 

[Vanadium 50]

First, what you are doing is very, very dangerous. You should stop immediately.

What the heck were you thinking? If things worked as you expected, you'd have an explosion with blobs of red-hot molten glass everywhere?

Second, why do you think increasing the pressure will increase the temperature?

 

[kmarinas86]

In theory, it should be about 2400 K, no? Yet, the bottle does not show any melting. I cannot even get a little piece of solder inside to melt. Is the heat loss during the thirty to sixty seconds of pumping that extreme?

Absolutely no way.

Or, is my understanding of the relationship between temperature and pressure incorrect?

You are adding air right? If you have more mass in a volume to generate a certain amount of pressure, the less the temperature has to be to generate a certain amount of pressure. So your pressure goes up without a linear increase of temperature.

 

[SMD1990]

I have read that soda bottles (plastic) can withstand 150 psi or more. I am not certain, but I think about 14 psi is around atmospheric pressure (101.325 kPa).

I thought:

increased pressure = increased temperature
decreased volume = increased pressure (and therefore, increased temperature)
decreased pressure = decreased temperature
increased volume = decreased pressure (and therefore, decreased temperature)​

http://easycalculation.com/chemistry/combined-gas-law.php" online calculator affirms what I thought.

And, since I was octupling the pressure of room temperature air, I was expecting 298.15 * 8 = 2385.2 K. Or perhaps, the average of the temperature increases of each downward stroke of the bike pump.

 

[Vanadium 50]

If the bottle behaved as you thought it would, you'd have an explosion of molten glass (or burning plastic). It was an exceptionally stupid thing that you did, and the fact that you are defending it concerns me deeply.

The reason the calculator gives you the wrong answer is because you are plugging the wrong numbers into it. What is your final volume? What is your initial volume?

 

[SMD1990]

Considering the bottle remains basically unchanged, the initial and final volumes are the same, no? Or, does "volume" refer to the amount of air, irrespective of its confinement within a fixed "volume"?

Ever heard of a water rocket? They typically use pressures of 75 to 150 psi, and bottles similar to what I have been using. (I have also been trying with a clogged syringe, but that is besides the point.)

I am not after extremely high temperatures. However, since doubling or tripling the pressure did not do the same to the temperature, I opted for higher pressures.

The bottle feels warmer after pumping. And, if I quickly release the pressure, it gets quite cool. Some drops of liquid can even be seen. Cool enough to liquify one of more of the gases in the air?

 

[kmarinas86]

Considering the bottle remains basically unchanged, the initial and final volumes are the same, no? Or, does "volume" refer to the amount of air, irrespective of its confinement within a fixed "volume"?

The volume refers to space occupied by a fixed amount of substance. When you pressurized the air, you added more air, so the original amount of air occupies less space. If your volume and pressure are inversely-related, then the temperature does not change. However, if your temperature slightly increases, that means that pressure increased by a factor greater than the factor by which the volume decreased. So if you increase pressure by a factor of 6 and decrease volume by a factor of 2, then your temperature would triple. You won't be able to achieve that without heating the air though. You can't just compress it with air at the same temperature. It won't work like that.

 

[SMD1990]

Oh, okay. Now I understand. Thank you for explaining!

 

[Fernbauer]

PV = nRT.

V is essentially constant.

The bike pump may increase pressure by 8 times. This means that n * T is 8 times greater. You can see T is warmer than when you started, but not by that much... mostly what the pump does is put more air molecules into the bottle.

Your analysis was treating the pump like a heater. You would indeed need to heat the bottle's air to around 2400K to get that pressure, assuming you put no more air molecules inside, and were just heating the ones that were in there to start with.