Energy emitted per second per unit area by Rigal star in Constellation Orion is 17000 times that emited by the sun. What is the surface temperature of that star if that of the sun is `6000K`?

Answer

To find the surface temperature of the Rigal star in the constellation Orion, we will use Stefan-Boltzmann's law, which states that the energy emitted per second per unit area (E) is proportional to the fourth power of the absolute temperature (T) of the black body. The relationship can be expressed as:

\[ E \propto T^4 \]

Given that the energy emitted by the Rigal star (E1) is 17,000 times that emitted by the Sun (E2), we can write:

\[ E1 = 17000 \times E2 \]

Let the surface temperature of the Rigal star be T1 and the surface temperature of the Sun be T2. We know that:

\[ T2 = 6000 \, K \]

Using the ratio of the energy emitted, we can express the temperatures as follows:

\[ \frac{E1}{E2} = \left(\frac{T1}{T2}\right)^4 \]

Substituting the known values:

\[ \frac{17000 \times E2}{E2} = \left(\frac{T1}{6000}\right)^4 \]

This simplifies to:

\[ 17000 = \left(\frac{T1}{6000}\right)^4 \]

Taking the fourth root of both sides gives:

\[ \frac{T1}{6000} = 17000^{1/4} \]

Now, we calculate \(17000^{1/4}\):

\[ 17000^{1/4} \approx 11.42 \]

Now, we can find T1:

\[ T1 = 11.42 \times 6000 \]

Calculating this gives:

\[ T1 \approx 68520 \, K \]

Thus, the surface temperature of the Rigal star is approximately **68520 K**.