1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Unit problem with calculating the mass concentration of a particle

  1. Nov 11, 2011 #1
    1. The problem statement, all variables and given/known data

    We have to calculate the mass concentration for a particle size distribution. I'm just doing the first size range here, since once I get that the rest is just repetition.

    FYI, the particles are spherical.

    Size range (diameter) = 0.005-0.5 μm
    Average particle size (diameter) = 0.25 μm
    Number concentration = 1 cm[itex]^{-3}[/itex]
    Particle density = 1800 kg m[itex]^{-3}[/itex]

    The answer is supposed to be in units μg m[itex]^{-3}[/itex] μm[itex]^{-1}[/itex]

    2. Relevant equations

    [itex]m=\rho _{p}\frac{\pi }{6}D_{p}^{3}n_{n}(D_{p})[/itex]

    3. The attempt at a solution

    First thing I did was convert the density from kg m[itex]^{-3}[/itex] to μg m[itex]^{-3}[/itex]:

    [itex]\frac{1800 \: kg}{m^{3}} * \frac{1\: \mu g}{1*10^{9\: }kg}=\frac{1.8*10^{12}\: \mu g}{m^{3}}[/itex]

    Then I plugged into the mass concentration formula:

    [itex](1.8*10^{12}\mu g\: m^{-3})(\frac{\pi }{6})(0.25\: \mu m)^{3}(1\: cm^{-3})=1.473*10^{10}\mu g\: m^{-3\: }\mu m^{3}\: cm^{-3}[/itex]

    So now, since there's no cm in the units we're supposed to have, I figured I'd get rid of that:

    [itex](1.473*10^{10}\: \frac{\mu g\: \mu m^{3}}{m^{3}\: cm^{3}})*(\frac{100\: cm}{1\: m})^{3}=1.473*10^{16}\: \frac{\mu g\: \mu m^{3}}{m^{6}}[/itex]

    So now we have this mess, and at this point I give up, because idk how the heck to get this in μg m[itex]^{-3}[/itex] μm[itex]^{-1}[/itex]... Not to mention the number I'm getting seems way too large...
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Unit problem with calculating the mass concentration of a particle
Loading...