# Density of Hot Air Balloon Calculation

## What is the density of the air inside a hot air balloon heated to 120 C?

Given that the outside air temperature is 10.0C with a density of 1.25kg/m3.

## Answer:

The density of the air inside a hot air balloon, heated to 120 C, is approximately 1.746 kg/m3 when the outside air temperature is 10.0 C and has a density of 1.25 kg/m3, using Charles's Law.

To find the density of air inside a hot air balloon, we will use the principle of Charles's Law which states that the volume of a gas is directly proportional to its temperature, provided pressure and amount of gas remain constant. Hence, the ratio of temperatures (in absolute units, Kelvin) should be equal to the ratio of densities.

Firstly, convert both temperatures to Kelvin: 10.0C is 283.15K and 120.0C is 393.15K. Then, set up a proportion to solve for the new density: 1.25kg/m3 is to 283.15K as X is to 393.15K. Finally, solve for X: X = (1.25kg/m3 * 393.15K) / 283.15K. This gives a density of the air inside the hot air balloon of approximately 1.746 kg/m3.