Hello again MHF!
I have a some questions that I need a little help with concerning air density and buoyancy.
(1):
The density of air near the earth's surface is 1.29 kg/m^3. If a helium balloon with a mass of 1kg floats in air with out rising or falling, what is the minimum volume of the helium in the balloon? Show your calculations.(presume that the mass of the material making up the balloon is negligible.)
I admit that I have no idea where to start with this one.....
(2):
A balloon filled with one liter of air is tied to a brick and dropped from a height of 4600m above sea level. If the atmosphere 4600m above sea level has a pressure of 70kPa, what will the volume of the balloon be when it reaches sea level? Show your calculations.
Same story sadly, I have no idea what to do with this one.
Thanks in advance for your help!
1. A solid surrounded by a gas experiences a force of buoyancy(?) which has the opposite direction of the weight of the solid and has the absolute value of the weight of the displaced gas. (Principle of Archimedes)
2. Since the body looses all it's weight you get as force of buoyancy
3. The densitiy of the surrounding air is
The force of buoyancy is calculated by:
4. Solve for which must be as large as the volume of the Helium gas.
Spoiler:
Problem 1. 1 kg of helium = 1/4 kg mol STP volume =.25x 22.4 cume=5.6cume
correct only for a temp of 293 deg K 20+273 5.6x293/273=6.0 cu me
Problem 2. Molal volume of air @ the 4600m elevation 70 kPa and temp not given can be calculated by specifying temp.
Use gr mols here 29 grs 0f air = 1mol or 22.4 liters STP 1 liter is what percent of the actual volume calculated.This percent is the fraction of 1gr mol put into balloon.Calculate the volume of this weight at the conditions @ sea level
Sorry for the confusion....
You wrote: "A balloon filled with one liter of air ...". 1 l is the volume of a cube with the side-length = 10 cm = 1 dm (<--- that's 1 deci-meter)
In Germany liter is mostly used for liquids. Therefore I used the mathematically correct unit of a volume.
No problem, I thought that might be the case, just had to make sure!
I wish America would switch over to the metric system already.....
The thing is, the book that I got this question from says nothing about that part of the formula, and the question doesn't ask me to take that into consideration, I will do the working for my own benefit though.
I'm just not sure if I'll get the question right or wrong if I include that in my answer.
Let me make sure I have this straight:
Because the balloon has a weight of 9.81N the force of buoyancy is also 9.81N.
Since the density of the air is 1.29kg/m^3 it displaces that much air for 1kg of mass.
So, all I have to do is(ignoring the unit symbols): (9.81/9.81)/1.29, to get my answer.
Am I correct on the principle?