Question

Suppose you have a spherical balloon filled with air at room temperature and 1.0 atm pressure; its radius is 17 cm. You take the balloon in an airplane, where the pressure is 0.87 atm. If the temperature is unchanged, what's the balloon's new radius?

Answer 1

alright here is what i'm thinking we are going to use Pv=nRT twice setting n and t to 1 and solve for v once at P=1 and another time at p=.87. after we have done so we are going to set up a porportion and solve for the unknown radius value. What do you think?

Answer 2

I started by rearranging P1*V1/T1= P2*V1/T2, but I don't get how to get the radius from that..am I looking at this problem the wrong way?

Answer 3

Yea I think you need to get the volume to go with your radius and then you could probably use the formula you posted above to get the 2nd volume.

Answer 4

ok, so the equation of volume of a sphere would be v=(4/3)pi*r^3. How do I incorporate that to the eqaution above?

Answer 5

\[v=\frac{(1)(8.314)(1)}{1}=8.314\]

Answer 6

I don't think you are going to need the sphere equation. If we have 2 volumes we should be able to set up a proportion and find the missing radius.

Answer 7

\[v_2=\frac{8.314}{.87}=9.56 L\]

Answer 8

ook i see

Answer 9

\[\frac{r_1}{v_2}=\frac{r_2}{v_2}\] Now I think we can just solve for r2

Answer 10

ok so I got 17cm, does that sound right?

Answer 11

well it should be bigger because we got a bigger volume.

Answer 12

I got 19.5 but lets see if we redo the volume equation

Answer 13

oh wait i recalculated and got 19.5cm as well, but its showing that its wrong

Answer 14

\[r=\sqrt[3]{\frac{9.56}{(\frac{4}{3})pi}}\]

Answer 15

ok, so I plugged it in and i'm getting small number like 1.3..so I don't think it's right

Answer 16

Yea this one is insteresting, I have never done a gas problem like this one before.

Answer 17

I got the answer, it's 0.178m..it's weird and confusing but it says its right. Thanks for your help :)

Answer 18

Well I'm glad it worked out for you how did you get that?

Answer 19

to be honest i really don't know..i just kinda converted the 17 cm i got earlier into meters and it was right

Answer 20

P1*V1=n*R*T
P2*V2=n*R*T
so P1*V1=P2*V2
V2=(P1/P2)*V1
4/3 π R2^3=(P1/P2)*4/3*π*R1^3
R2^3=(P1/P2)*R1^3
R2^3=(1/0.87)*17^3 (no need to change to m)
R2=17.8cm