How to Calculate the Volume of a Helium-filled Weather Balloon at Different Altitudes

Calculating the volume of a helium-filled weather balloon at different altitudes involves applying the principles of gas laws, specifically Gay-Lussac's Law and the combined gas law. These laws allow us to determine the relationship between pressure, volume, and temperature under changing conditions.

Gay-Lussac's Law states that the pressure of a gas is directly proportional to its absolute temperature when the volume is held constant. The combined gas law combines the principles of Boyle's Law, Charles's Law, and Gay-Lussac's Law and is expressed as (P1V1)/T1 = (P2V2)/T2, where P represents pressure, V is volume, and T is temperature.

Before performing calculations, it is crucial to convert all temperature values to Kelvin by adding 273.15, as temperature must be in Kelvin for gas law problems. In this case, we have data for the initial conditions at sea level (21.9°C and 754 mmHg) and the conditions at 4.24 km altitude (-6.1°C and 523 mmHg).

By substituting the given values into the combined gas law equation and solving for the volume at the new altitude, we find that the volume of the helium-filled weather balloon at 4.24 km altitude would be approximately 978 Liters.

Understanding and applying gas laws in scenarios like this allow scientists and researchers to predict and analyze the behavior of gases under varying environmental conditions. It is a fundamental concept in the field of physics and plays a crucial role in numerous practical applications.