Question

Boyles Law P1V1 = P2V2

An arrangement of helium balloons in the back of a delivery truck travels from a town at the base of a mountain up the mountain where the air pressure is half the amount. What do you expect to happen to the balloons?

A.The balloons will increase to twice their original volume.
B. The balloons will decease to one fourth their original size.
.C.The balloons will increase to four times their original size.
D.The balloons will decrease to half their original size.

Answer 1

A. The balloons will increase to twice their original volume.

Step-by-step explanation:

Boyle's law states that the pressure exerted on a gas is inversely proportional to the volume occupied by the gas at constant temperature. That is:

P ∝ 1/V

P = k/V

PV = k (constant)

P = pressure, V = volume.

`P_1V_1=P_2V_2`

Let the initial pressure of the balloon be P, i.e.
`P_1=P`, initial volume be V, i.e.
`V_1=V`. The pressure is then halved, i.e.
`P_2=(P)/(2)`

`P_1V_1=P_2V_2\\\\P*V=(P)/(2) *V_2\\\\V_2=(2*P*V)/(P)\\\\V_2=2V`

Therefore the balloon volume will increase to twice their original volume.