weather balloon is designed to expand to a maximum radius of 20 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 300 k, what is its radius at liftoff?

A theoretical gas called an ideal gas is one that has lots of point particles flying around arbitrarily and not being affected by other particles.
The ideal gas law, also known as the perfect gas law, is a relationship between a gas's pressure P, volume V, and temperature T in the range of low pressures and high temperatures where the gas's molecules move virtually independently of one another.
In this situation, the ideal gas law, a state equation for all gases, holds true:

PV = nRT

The universal gas constant, R = 8.31446261815324 joules per kelvin per mole, and the number of moles of the gas, n,

Given in the question the following informations:

P1 = Initial pressure = 0.03 atm

P2 = Final pressure = 1 atm

r1 = Inital radius = 20 m

V1 = Intial volume of gas = 4/3 x 3.14 x r1^3

V2 = Final volume of gas = 4/3 x 3.14 x r2^3

T1 = Initial temperature = 200 K

T2 = Final temperature = 300 K

Let the radius at the liftoff be r2

From ideal gas law we have

P1V1/T1 = P2V2/T2

P1V1T2 = P2V2T1

P1 x 4/3 x 3.14 x r1^3 x T2 = P2 x 4/3 x 3.14 x r2^3 x T1

P1 x r1^3 x T2 = P2 x r2^3 x T1

r2^3 = P1 x r1^3 x T2 / P2 x T2

= 0.03 x 20 x 20 x 20 x 300/ 1 x 200

= 360 m

r2 = 6.83 m

Hence, The radius at liftoff is 6.83 m

To learn more about ideal gas from the given link

https://brainly.com/question/27870704

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