Power output of a star

Stars emit massive amounts of energy per second and so the power of a star is enormous. We assume that a star behaves as a perfectly 'black body' in other words it is a perfect radiator of radiation at its surface temperature.

The Stefan- Boltzmann law states that the power emitted by a black body of surface area A and with a surface temperature T (K) is given by the equation:

Power = sAT⁴ where s is a constant (5.7x10^-8 Wm^-2K^-4).

(Note: we are assuming here that the temperature of the surroundings (deep space) has a temperature of 0 K)

If we assume that a star is roughly spherical then A = 4pr² for a star of radius r.

The power of a star is therefore 4psr²T⁴ = 7.16x10^-7r²T⁴.

Consider our Sun. It is a star of surface temperature 6000 K, and a radius 6.96x10⁸ m. Using the preceding equation we can calculate its power output:

Power output of the Sun = 7.16x10^-7r²T⁴ = 7.16x10^-7x[6.96x10⁸]2x[6000⁴] = 7.16x10^-7x 4.84x10¹⁷x1.296x10¹⁵
= 4.5x10²⁶ W

An alternative way of finding out the power output of the Sun is to use the solar constant.

(See: 16-19/Thermal physics/Transfer of heat/Text/Solar constant)

It is interesting to compare this power output with that of Canopus (a Carinae). Canopus has a surface temperature of 7500 K and a radius of 2x10¹¹ m. Using these figures it is possible to calculate its power output as being in the region of 9x10³¹ W, about 200 000 times greater than that of the Sun!