Results 1 to 11 of 11

Math Help - Two air pressure/density questions that I have little clue what to do with.

  1. #1
    Member MathBlaster47's Avatar
    Joined
    Jan 2010
    Posts
    93

    Two air pressure/density questions that I have little clue what to do with.

    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!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by MathBlaster47 View Post
    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!
    To #2:

    1. Google for Boyle-Mariotte.

    2. You are supposed to know the air pressure at sea level (at 20C). Then

    p_1 \cdot V_1 = p_2 \cdot V_2

    with p_1 = 70 kPA, V_1 = 1 dm, p_2 = you know that (101.3 kPa), V_2 = you calculate that!
    Last edited by earboth; June 21st 2010 at 04:44 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by MathBlaster47 View Post
    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 (<--- do you mean volume?) of the material making up the balloon is negligible.)

    I admit that I have no idea where to start 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 F_b = 1 kg \cdot 9.81 \frac{m}{s^2} = 9.81 N

    3. The densitiy of the surrounding air is d_a = 1.29 \frac{kg}{m^3}

    The force of buoyancy is calculated by: F_b = V_{air} \cdot d_a \cdot  9.81 \frac{m}{s^2}

    4. Solve for V_{air} which must be as large as the volume of the Helium gas.
    Spoiler:
    I've got 0.775 m
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    914
    Thanks
    27
    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
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member MathBlaster47's Avatar
    Joined
    Jan 2010
    Posts
    93
    Quote Originally Posted by earboth View Post
    To #2:

    1. Google for Boyle-Mariotte.

    2. You are supposed to know the air pressure at sea level (at 20C). Then

    p_1 \cdot V_1 = p_2 \cdot V_2

    with p_1 = 70 kPA, V_1 = 1 dm, p_2 = you know that (101.3 kPa), V_2 = you calculate that!
    Ok, I'm a little confused by "dm^3". Did you mean cm^3?
    Either way, am I getting it right that all I have to do is multiply the volume(1L, I think) by the pressure(70kPa) and then divide that number by the new pressure in order to find the new volume?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    914
    Thanks
    27
    Hi mathblaster47
    Yes this is true but you assume that the temperatures are the same.For a specific volume of gas at given conditions

    P1v1/T1= P2v2/T2

    bjh
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member MathBlaster47's Avatar
    Joined
    Jan 2010
    Posts
    93
    Quote Originally Posted by bjhopper View Post
    Hi mathblaster47
    Yes this is true but you assume that the temperatures are the same.For a specific volume of gas at given conditions

    P1v1/T1= P2v2/T2

    bjh
    The question did not give me any temperatures to work with, so I don't know what to do about that.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by MathBlaster47 View Post
    Ok, I'm a little confused by "dm^3". Did you mean cm^3?
    ...
    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.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    914
    Thanks
    27
    Hello mathblaster47,

    google-Engineering Toolbox

    Standard values of temperature and pressure above sea level

    Sea level 15 C 101.3kPa
    15000 ft -15 C 57 kPa


    bjh
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Member MathBlaster47's Avatar
    Joined
    Jan 2010
    Posts
    93
    Quote Originally Posted by earboth View Post
    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.....

    Quote Originally Posted by bjhopper View Post
    Hello mathblaster47,

    google-Engineering Toolbox

    Standard values of temperature and pressure above sea level

    Sea level 15 C 101.3kPa
    15000 ft -15 C 57 kPa


    bjh
    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.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Member MathBlaster47's Avatar
    Joined
    Jan 2010
    Posts
    93
    Quote Originally Posted by earboth View Post
    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 F_b = 1 kg \cdot 9.81 \frac{m}{s^2} = 9.81 N

    3. The densitiy of the surrounding air is d_a = 1.29 \frac{kg}{m^3}

    The force of buoyancy is calculated by: F_b = V_{air} \cdot d_a \cdot  9.81 \frac{m}{s^2}

    4. Solve for V_{air} which must be as large as the volume of the Helium gas.
    Spoiler:
    I've got 0.775 m
    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?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Joint Density Questions
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 18th 2009, 09:45 PM
  2. I hAVE No clue wat the questions askin
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: September 14th 2009, 05:30 AM
  3. Need help please have no clue
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 5th 2008, 06:11 PM
  4. Replies: 10
    Last Post: October 29th 2008, 05:31 PM
  5. Gas/Liquid pressure from temperature and density
    Posted in the Advanced Applied Math Forum
    Replies: 10
    Last Post: January 3rd 2007, 10:03 AM

Search Tags


/mathhelpforum @mathhelpforum