Calculating % Change in Balloon's Volume at Different Altitude and Temp

[chantalprince]

Homework Statement

A child holding a helium filled balloon @ sea level (T= 20 C) let's go of the string. The balloon rises freely several thousand meters, where T = 5 C and P = 0.70 atm. Find the percentage change in the balloon's volume.

Homework Equations

PV = nRT

percentage change = amount of change (amt change = V2-V1)/ original amount (V1)

The Attempt at a Solution

Is my reasoning correct on this one? Since n and R don't change with altitude, temperature or volume, I solved for volume: V = P/T Then I solved for V1 and V2. Lastly used the above % change equation.

The only thing that is bothering me about my method is that I'm not sure how the units work out for the volume equation I posted. I guess I am figuring it jut works out (?) But, I really need to understand it for exams I see no other way to work this problem. Also- is the % change formula correct?

Thanks.

 

[Bill Foster]

Looks good to me.

Units? Try working them out.

 

[chantalprince]

V = P/T

m^3 or liters = Pa or (N/m^2) / (C)

I'm still don't understand how it works out. Do you mean work it out with the n and R included?

 

[Bill Foster]

When you are calculating percent change in volume, that is a ratio and there are no units; they cancel out.

However, when working out the units in the ideal gas law, you will need to include nR, (or Nk):

PV=NkT=nRT

 

[chantalprince]

Thank you BF.