Question

A helium balloon containing 5m³ of gas at a pressure of 30kPa is released into the air. Assuming that the temperature is constant calculate the volume the balloon would have when the pressure inside the balloon has fallen to 5kPa. Answer in m³.

Answer 1

30 m³

Step-by-step explanation:

Parameters given:

Initial volume of helium, V1 = 5 m³

Initial pressure in balloon, P1 = 30 kPa

Final pressure, P2 = 5 kPa

To find the volume of the balloon at that volume, we apply Boyle's law.

It states that at constant temperature, the pressure of a gas is inversely proportional to the volume of the gas.

Mathematically:

P = k / V

Where k = constant of proportionality

This implies that:

P * V = k

This means that if the pressure or volume of the gas changes at the same temperature, the product of the pressure and volume would be the same:

Hence:

P1 * V1 = P2 * V2

Hence, to find the final volume:

30 * 5 = 5 * V2

=> V2 = (30 * 5) / 5

V2 = 30 m³

The volume of the gas when the pressure is 5 kPa is 30 m³.