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

• chantalprince
In summary, the conversation discussed finding the percentage change in volume of a helium filled balloon released from sea level to an altitude of several thousand meters, where the temperature and pressure changed. The person proposed using the ideal gas law to solve for volume and then calculating the percentage change using a formula. They also expressed uncertainty about the units in the volume equation. The expert confirmed that the proposed method was correct and explained that the units in the volume equation cancel out when calculating percent change. They also clarified that when using the ideal gas law, the units of nR (or Nk) must be included.
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.

Looks good to me.

Units? Try working them out.

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?

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

Thank you BF.

## What is the formula for calculating % change in a balloon's volume at different altitudes and temperatures?

The formula for calculating % change in a balloon's volume is: ((V2 - V1) / V1) * 100, where V2 is the volume at a different altitude or temperature and V1 is the initial volume.

## What units should be used for altitude and temperature in the calculation?

Altitude should be measured in meters (m) and temperature should be measured in degrees Celsius (°C) for accurate calculations.

## Can this calculation be applied to any type of balloon?

Yes, this calculation can be applied to any type of balloon as long as the volume can be accurately measured at different altitudes and temperatures.

## How does altitude and temperature affect the volume of a balloon?

As altitude increases, the air pressure decreases, causing the volume of the balloon to expand. Similarly, as temperature increases, the molecules inside the balloon have more energy and move faster, also causing the volume to expand.

## Are there any limitations to this calculation?

One limitation of this calculation is that it assumes the balloon is in a closed system and there are no external forces affecting the volume. Additionally, other factors such as humidity and air density can also affect the volume of the balloon and may need to be considered in the calculation.

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