# Calculating mass and Schwarzchild radius of Black Hole

1. Oct 14, 2008

### mattst88

1. The problem statement, all variables and given/known data

The temperature of a black hole is given by
$$T = \frac{\hbar c^3}{8 \pi k G M}$$
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,
$$M = \frac{\hbar c^3}{8 \pi k G T}$$

$$r_s = \frac{2 G M}{c^2}$$

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.