Physics problem dealing with Ideal Gas Laws?

Question

Balloon pressure when full = P1
Balloon Volume when full = V1

Cylinder pressure = P2
Cylinder Volume = V2

Everything else is negligable. How many balloons can I fill?

I can't figure out what I am supposed to solve for...

Answer 1

Imagine filling all the balloons at once. When you are done, the final volume of the gas will be n*V1 + V2 (n is the number of balloons), and the final pressure is P1. Before you started, all the gas was in the cylinder at pressure P2 and volume V2. According to the gas law, the product of volume and pressure before and after will be the same (assuming the same temperature). Therefore

(n*V1 + V2)*P1 = V2*P2

n*P1*V1 = V2*P2 - V2*P1

n = V2*(P2 - P1) / V1*P1

Answer 2

Let the number of balloons be N.

Imagine all the balloons are enclosed in a single envelope,
The volume of this big balloon is NV1
But pressure remains the same as P1.


P1* NV1 = P2 V2.

N = P2 V2/ P1V1.

Answer 3

(P1) (V1)=(P2) (V2)

without seeing any numbers, I am assuming they are giving you P1 & P2 and then V2. So you would need to solve for V1. If this is the case, find out how much volume there is and divide it by the volumn that fits into one balloon. this should tell you how many ballons it will fill.

Answer 4

PV = MRT
M1 = P1V1/RT: subscript 1 being balloon Mass
M2 = P2V2/RT: total mass available in cylinders

You can fill M2/M1 balloons = P2V2/(P1V1)