Ideal Gas Law - Real Life Question?

[Monday]

Hi Guys and Gals,

As I was pumping up a flat bike tyre, a weird thought occurred to me about the application of the ideal gas law.

Once the tyre essentially finds its physical dimension limitations (i.e. is shaped like a bike tyre and no longer changing shapes) and starts putting in reasonable volumes of air, let's say up to 60-70lbs/in^2, why doesn't the tube get stupidly hot - in essence, the pressure is going from say 1 atmosphere to 3-5 atmospheres of pressure, but the physical space is not changing. By extension, you could equally apply the same concept to scuba tanks that go even way higher in pressure than a bike tube (and there definitely isn't any change to vessel shape)!

The ideal gas law would suggest holding volume constant, by changing pressure, the only other variable is temperature. So yeah, the valve on the tube gets a little bit warm, but its hardly finger frying, 3rd degree burn territory.

Any thoughts would be appreciated!

Cheers,
M

 

[Let'sthink]

PV/T is constant law applies to a given amount of gas with same density. Not changing mass or density of gas. Think it as PV = nRT and think it over if P is increasing with V and T almost remaining constant then what is changing in the same proportion!?

 

[Monday]

Ok, so in a closed system (lets assume some sort of syringe device that is 100% closed - obviously theoretical only), if the volume of air is halved, but the pressure is doubled (so no change on T) is what youre getting at? Hence why I wouldn't see any temperature changes? 0.5 x V, but 2 x P = No change to the numerator?

For a practical application, can I ask then how would one dramatically increase T then simply by changing P or V, or is there no real ability to effect this in the 'real world'?

 

[mfig]

The temperature of the mass of air entering the tire at the end of each stroke of the pump is elevated, as you suspect. The higher the pumping pressure, the hotter the air. I have had the bottom section of a tire pump get nearly burning hot when quickly pumping a high pressure road bike tire (125 psi), so it can be significant. But that small amount of hot air then enters the tube and mixes with the larger body of colder air already inside the tire. Over the time it takes to pump up the tire the air inside the tube has had time to mix and cool. This is why the tire isn't anywhere near as hot as the bottom of the pump can get.