Linear expansion physics homework

[Jake4]

Homework Statement

A weather balloon is designed to expand to a maximum radius of 26m hen in flight at its working altitude where the air pressure is .026 atm and the temperature is 229K

If the balloon is filled at atmospheric pressure and 434K, what is its radius at lift off?

Homework Equations

The Attempt at a Solution

We learned linear expansion in class, and all about pressures and changes in pressure. However I don't think we ever went over anything of this sort.

Thanks for the help guys!

exam tomorrow!

 

[Jake4]

no one? :(

Even just help with the relevant equations?

 

[SteamKing]

It seems you need a gas equation which relates P, V, and T. Seen any good ones lately?

 

[Disconnected]

It seems you need a gas equation which relates P, V, and T. Seen any good ones lately?

Too funny!

 

[rwisz]

Hello there! As a fellow scientist, I would be happy to assist you with your linear expansion homework problem. The first thing we need to do is use the ideal gas law, PV = nRT, to find the initial volume of the balloon. We know the pressure (1 atm), temperature (434K), and the gas constant R, so we can solve for the initial volume (V1).

Once we have the initial volume, we can use the formula for linear expansion, ΔL = αLΔT, to find the change in length (ΔL) of the balloon. In this case, the change in length will be equal to the change in radius (ΔR) since we are dealing with a spherical balloon.

We know that at lift off, the balloon will be at its maximum radius of 26m. So we can set up the equation as follows:

26m = V1 + ΔR

Solving for ΔR, we get ΔR = 26m - V1

Now we can plug in the values we have and solve for the change in length (ΔL):

ΔL = αLΔT = α(26m - V1)

Next, we need to find the coefficient of linear expansion (α) for the material of the balloon. This can be found in a table or given in the problem. Once we have the value for α, we can plug it in and solve for ΔL.

Finally, we can use the formula for linear expansion again to find the final radius (R2) of the balloon at lift off:

R2 = R1 + ΔL

Where R1 is the initial radius of the balloon when it was filled at atmospheric pressure.

I hope this helps and good luck on your exam tomorrow! Remember to always double check your units and equations to make sure they are consistent. Happy studying!