Calculating mass and Schwarzchild radius of Black Hole

[mattst88]

Homework Statement

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 Schwarzschild radius of a black hole at room temperature.

Homework Equations

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

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

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 Schwarzschild 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.

 

[Jhero]

I can confirm that your calculations are correct. The mass of a black hole at room temperature is indeed much smaller than our Sun, which is why they are so difficult to detect. The Schwarzschild radius also seems to be in the correct range for a black hole of this mass. Great job!