Aweather balloon is designed to expand to a maximum radius of 22 m at its working altitude, where the air pressure is 0.030 atm and the temperature is 200 k. if the balloon is filled at atmospheric pressure and 280 k, what is its radius at lift-off?

R_2 = 7.647 m

Explanation:

HI!

Let us consider that the aballon is filled with a gas that follows the ideal gas equation. Since the amount (number of moles) of the gas is constant we should have:

Therefore, we can have the following relationship between two differnet states given their Volume, Pressure and Tempreature:

Since the volume of a sphere is

The relathionship will be:

Solving for R_2:

Where the index 2 is the state at the lift-off and the index 1 denotes the state at its maximum radius. Replacing all the values given we find that:

R_2 = 7.647 m