A power plant is "burning" fuel and radiating the power as black body radiation

Classical Mechanics Level 2

A power plant is fusing 0.600820757947 Pg per second of ${}^1H$ to ${}^4He$ . The atomic mass of ${}^1H$ is 1.00782503207 u. The atomic mass of ${}^4He$ is 4.00260325415 u. Four hydrogen atoms are consumed to produce one atom of helium. The power plant, for this problem, is considered spherical with a radius of 0.6957 Gm. The power plant is radiating all the power produced as black body radiation. The spectrum is at what peak temperature expressed in degrees Kelvin?

The answer is 5778.

1 solution

A Former Brilliant Member
Dec 22, 2018

The fraction of the original hydrogen converted to energy and not to helium is $\frac{1}{140.4787194}$ .

Therefore, the mass per second being converted to energy is 4.2769521288 Tg/s or 384.393287497 YW.

Since the power plant is spherical with a radius of 0.6957 Gm, that is 63.201 $\text{MW}/m^2$ .

The Stefan–Boltzmann law gives the power radiated, in the units being used as: $5.6704\times 10^-8 \frac{W}{m^2 K^4}$ . Solving for K gives 5778.

And this power plant is, of course, the Sun. Nice problem

Steven Chase - 2 years, 5 months ago

A power plant is "burning" fuel and radiating the power as black body radiation

The answer is 5778.

1 solution

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