Question

An astronomer is trying to estimate the surface temperature of a star with a radius of 5.0×108m by modeling it as an ideal blackbody. The astronomer has measured the intensity of radiation due to the star at a distance of 2.5×1013m and found it to be equal to 0.055W/m2. Given this information, what is the temperature of the surface of the star?

Answer 1

Answer:

3.944 x 10⁴ K.

Explanation:

Let the surface temperature of star be T in absolute scale.

Total thermal radiation from its surface can be calculated with the help of

stefan's formula as follows

E = σ A T⁴

σ is a constant called stefan's constant and is equal to 5.67x 10⁻⁸ W m⁻²K⁻⁴

A is area of surface of star  and T is the surface  temperature.

Putting  the given values

E = 5.67 X 10⁻⁸ X 4 X 3.14 X ( 5 X 10⁸ )² X T⁴

= 1780.38  X 10⁸ T⁴

At a distance of 2.5 x 10¹³ m intensity will be calculated by dividing E with area of sphere having radius equal to distance , so

Intensity at given point

= E / 4πd²

= $\frac{1780.38\times10^8T^4}{4\times3.14\times(2.5\times10^{13})^2}$

= 22.68 T⁴ X 10⁻¹⁸

Putting the value of given intensity at that point

.055 = 22.68 x 10⁻¹⁸ T⁴

T⁴ = 24.25 X 10¹⁷

= 242.5 X 10¹⁶

T = 3.944 x 10⁴ K.