Question

At a festival, spherical balloons with a radius of 170.cm are to be inflated with hot air and released. The air at the festival will have a temperature of 25°C and must be heated to 100°C to make the balloons float. 1.00kg of butane C4H10 fuel are available to be burned to heat the air. Calculate the maximum number of balloons that can be inflated with hot air.

Answer 1

To calculate the maximum number of balloons that can be inflated with hot air, we need to consider the amount of fuel available and the energy required to heat the air inside the balloons.

Step-by-step explanation:

To calculate the maximum number of balloons that can be inflated with hot air, we need to consider the amount of fuel available and the energy required to heat the air inside the balloons.

First, we need to calculate the energy required to heat the air from 25°C to 100°C.

The specific heat capacity of air is approximately 1 J/(g °C), so the energy required can be calculated as:

Energy = mass * specific heat capacity * temperature change

Next, we need to calculate the mass of air inside each balloon.

The volume of a sphere can be calculated using the formula:

Volume = (4/3) * π * radius^3

Finally, we can calculate the maximum number of balloons that can be inflated by dividing the available fuel mass by the mass of air inside each balloon.