# Volume change inside a balloon upon decreasing the the outer pressure

A balloon is filled with hydrogen at room temperature. It will burst if pressure exceeds 0.2 bar. If at 1 bar pressure the gas occupies 2.27 L volume, upto what volume can the balloon be expanded?

Now i can easily figure out that the pressure is 0.2bar at a volume of 11.35L. However, when i check the answer in my book, it says that the volume of the balloon should be less than 11.35L.

However, if you decrease the volume from 11.35L, wouldn't the pressure become greater than 0.2bar, hence bursting the balloon?

• Is this the REAL problem - exactly as stated? The problem doesn't make sense to me. – MaxW Mar 23 '16 at 14:11
• @MaxW I copy pasted the problem from a pdf of the excercise book (Although the book itself doesn't make sense. Before teaching any chemistry it dives into Quantum Mechanics (The physics companion is still on units/measurements and classical mechanics..) and starts randomly pointing out facts from QM without deriving or explaining them. That's India for you) – Aayush Agrawal Mar 23 '16 at 14:55

The relationship between pressure and volume is given by Boyle's Law. $$\mathrm{P}_1\mathrm{V}_1 = \mathrm{P}_2\mathrm{V}_2$$

      P       V
0.199    11.41
0.20     11.35
0.201    11.29

1.0      2.27


So yes, you're right. Using Boyle's Law, the volume should be more than 11.35L so the pressure stays below 0.20 bar.

However this doesn't make real world sense. When you blow up a balloon, as the pressure increases the volume increases.

Edit - Thanks @Mithoron here is a version of the problem that works...

A balloon is filled with hydrogen at room temperature (25 C) and pressure (1.00 bar) to a volume of 2.27 L in a chamber. The pressure in the chamber is then reduced isothermally. The balloon will burst when the pressure in the chamber is reduced to 0.200 bar. What will the volume of the balloon be just as it explodes?

• It does make sense: if you gradually lower pressure around ballon it will burst. – Mithoron Mar 23 '16 at 22:27
• @Mithoron - Ok, let's assume that the balloon starts at 1 bar. If it pops at 0.2 bar then you're already 0.8 bar over bursting strength. // I tried to think of relative pressure vs absolute pressure, but that just doesn't seem to work either. – MaxW Mar 23 '16 at 22:47
• No, no, it's the upper bound! The lower the pressure, the bigger balloon. When it's too big, it breaks. – Mithoron Mar 23 '16 at 22:54
• @Mithoron - ah... So the pressure in the room is 1 bar when the balloon has a volume 2.27 L, then you evacuate the air pressure in the room. That does work better. Not sure how you work the 0.2 bar pressure into that. It seems the statement should be "if the pressure is lower than 0.2 bar." – MaxW Mar 24 '16 at 1:47
• And that's where authors made mistake... – Mithoron Mar 24 '16 at 19:57

When you will decrease the volume, surely the pressure will increase. But this pressure will not act on the balloon's body. The picture shows two types of pressure, one is inside the balloon and another is outside the balloon. Now imagine, if the volume increases, the size will also increase and as the size increases the area will also increase. We also know that pressure is directly proportional to force. Therefore the increase in pressure will result the balloon to explode. I hope this will help .

• If you consider the pressure as force per unit area, the force will also decrease when increasing the volume.. – Aayush Agrawal Mar 23 '16 at 14:56
• Sorry for the mistake in my last answer. Now, I want to say that this anomalous answer is coming because the Boyle's law is only applicable on ideal gases. But in reality gases don't show ideal gas behavior and thus this this unexpected thing occurs. – R banik Mar 23 '16 at 16:28