# Hot Air Balloon Science Exploration

## Why do hot air balloons float?

Hot air is less dense than cold air, which is why hot air balloons float. But how does temperature affect the volume of a gas in a hot air balloon?

## What temperature must the gas be in celsius in order to float?

According to the data, the hot air balloon must be inflated to a volume of approximately 2.80x10^6L to float. So, what temperature does the gas need to be in celsius to achieve this volume?

## Explanation:

The question requires us to determine the final temperature of the air in order for a hot air balloon to float, considering the initial temperature, volume, and the volume necessary for the balloon to float.

## Answer:

The temperature of the gas must be at 117.93°C in order for the hot air balloon to float.

To understand why hot air balloons float, we need to delve into the science behind gas behavior at different temperatures. Hot air is less dense than cold air, which means it has more energy and its molecules are more spread out, causing it to rise above colder, denser air.

In the case of a hot air balloon, when the air inside the balloon is heated, it expands and becomes less dense than the surrounding air. This density difference creates an upward force, allowing the balloon to float and rise into the sky.

When it comes to calculating the temperature at which the gas must be in Celsius in order to float, we can use Charles's Law, which relates the temperature and volume of a gas at constant pressure.

Charles's Law is represented by the formula: V1/T1 = V2/T2, where V is the volume and T is the temperature of the gas at different states. Rearranging the equation to solve for the final temperature, we get: T2 = (V2 * T1) / V1.

Given the initial volume of 2.60x10^6 L at an initial temperature of 90°C, and the final volume required for the balloon to float of 2.80x10^6 L, we can calculate the final temperature using the formula.

By plugging in the values and converting the temperature to Kelvin for the calculations, we find that the gas must be at 117.93°C in order for the hot air balloon to float.