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Homework Help: Calculating mass and Schwarzchild radius of Black Hole

  1. Oct 14, 2008 #1
    1. The problem statement, all variables and given/known data

    The temperature of a black hole is given by
    [tex]T = \frac{\hbar c^3}{8 \pi k G M}[/tex]
    where h is Planck's constant, k is Boltzmann constant, G is the universal gravitation constant, and M is mass.

    Calculate (A) the mass, and (B) the Schwarzchild radius of a black hole at room temperature.

    2. Relevant equations

    Rearranging the above equation for M,
    [tex]M = \frac{\hbar c^3}{8 \pi k G T}[/tex]

    Schwarzchild radius
    [tex]r_s = \frac{2 G M}{c^2}[/tex]

    3. The attempt at a solution

    I assume 'room temperature' to be 25 C or 298.15 K.

    Solving for M, I get 2.59 E21. Solving for the Schwarzchild radius, I get 3.84 E-6.

    Do these numbers look correct? The mass is _much_ smaller than our Sun (actually smaller than the Earth), which makes me question it.
  2. jcsd
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