Change in Volume in Relation to Pressure

[kevin2400]

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I'm kind of confused about this. Can anyone offer a reasonable answer/correct explanation? Thanks.

42. What happens to a balloon as it descends into the water at a uniform rate?


A. The volume of the balloon decreases linearly.
B. The volume of the balloon does not change.
C. The volume of the balloon changes a little at first, then gradually more as it descends.
D. The volume of the balloon changes considerably at first, then gradually less as it descends.

 

[gtbROX]

I would say "A" because gauge pressure is directly proportional to depth so pressure increases linearly as depth increases, but as pressure increases, volume decreases (volume is inversely proportional to pressure). So as a balloon descends at a uniform rate, its volume decreases linearly.
Formulas/Info:
-Uniform rate - suggests constant speed (v)
-gauge pressure = density*g*depth
-Gas Law - P1V1=P2V2

Edit: D - see below.

 

[LianaStan]

If the water is ideal and non-compressible, the volume of the balloon will decrease Edit: non linearly.

 

[cheesier]

Pressure increases linearly as rho g h, but PV=nRT, so V=nRT/P. You can see that the volume doesn't decrease linearly, but decreases less and less as the pressure gets greater, so D.

 

[LianaStan]

Ah of course. Forgot it was an inverse relationship. Thanks for the correction.

 

[kevin2400]

Sorry I just had a massive brain fart about inverse relationships. How would the volume change be (linear or inverse?) if pressure was decreased instead?

 

[circulus vitios]

edit: Wow, I'm dumb.

 

[circulus vitios]

Sorry I just had a massive brain fart about inverse relationships. How would the volume change be (linear or inverse?) if pressure was decreased instead?

The relationship is always the same:

V=(nRT)/P
V ∝ 1/P
V is inversely proportional to P

Changing V would do the inverse to P, or vice versa.

Increase V ⇔ Decrease P
Decrease V ⇔ Increase P

 

[gtbROX]

Sorry I just had a massive brain fart about inverse relationships. How would the volume change be (linear or inverse?) if pressure was decreased instead?

Same here, I totally forgot what an inverse graph looks like.

It only becomes a line if you plot 1/V, but it's the above graph if you plot V. I'm glad to get it wrong now versus getting it wrong on my mcat...thank God.