I'm studying for the GRE and I'm happy with Charles', Boyle's and Gay-Lussac's laws. I'm doing some questions on the ideal gas law. Please hear me out. This may come across as a homework style question but I have done all of the working and would just like scientific clarification so that I can go on in my studies.

I'm looking at a question that is about the pumping up of a tyre. A pump cylinder of volume $2.6 \times 10^{-4}$ m$^3$ is allowed to be forced through a valve into a tyre that is currently at a pressure of $1.11 \times 10^{-3}$ atm. The tyre has a volume of $10.0 \times 10^{-4}$ m$^3$. Assume the pressure of the gas before pumping is $1$ atm and that the temperature of the tyre, pump and their surroundings is $15$ celcius.

I have already calculated how many moles of gas are in the pump before it is compressed, how many moles are in the tyre before the additional air is added and how many moles there will be in total in the tyre when the pump is empty.

I calculated these using the ideal gas laws. Manipulation of $PV=nRT$

In the pump before compression are $0.00001099$ moles

In the tyre before the additional air is added are $0.0000469$ moles

In the tyre once the pump is empty, there are $0.0423$ moles.

Now I'm trying to figure out what the final pressure inside the tyre will be.

All I would like to know is how to manipulate the ideal gas law one last time in order to establish this.


closed as off-topic by knzhou, user36790, John Rennie, CuriousOne, Qmechanic Jun 23 '16 at 11:42

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  • $\begingroup$ You have V, n, R, and T, correct? So you want to solve for P? $\endgroup$ – BowlOfRed Jun 22 '16 at 23:40
  • $\begingroup$ I have the initial V, but no final V. T is 15 celcius or 288.15 Kelvins throughout. Am trying to solve for P yes! $\endgroup$ – I come from a land down under Jun 22 '16 at 23:43
  • $\begingroup$ Why do you think the volume would change? $\endgroup$ – BowlOfRed Jun 23 '16 at 0:25
  • $\begingroup$ The pressure is changing, and the volume is inversely proportional to this. $\endgroup$ – I come from a land down under Jun 23 '16 at 0:25
  • 1
    $\begingroup$ That initial pressure is not reasonable unless it is gauge pressure. It would represent almost a perfect vacuum. How could the inside of the tire be under vacuum? No way!! But, if it were gauge pressure, then the initial absolute pressure in the tire would be 1.00111 atm. That would correspond to about 0 05 moles. $\endgroup$ – Chet Miller Jun 23 '16 at 1:03

Assuming that your preliminary calculations are correct, you now have everything that you need: n, R and T. And unless you have been given a modulus of elasticity for the tyre, you must assume that it is rigid, so you have V as well (as a commentator hinted above). Just plug them into the ideal gas equation.

If you know the modulus of elasticity of the tyre, you will need to calculate $\delta$V/$\delta$P.

  • $\begingroup$ The elasticity has been given as constant, I've read the question again. Ahh so I'm looking for the change in velocity/pressure. I'll do this when I get home from work today. Thanks for your help. $\endgroup$ – I come from a land down under Jun 23 '16 at 9:52

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