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
=
= 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.