Question

A space probe$\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{10}}\mathbf{}\mathbf{m}$ from a star measures the total intensity of electromagnetic radiation from the star to be $\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{}\mathbf{W}\mathbf{/}{\mathbf{m}}^{\mathbf{2}}$. If the starradiates uniformly in all directions, what is its total average power output?

Short answer

The total average power output is $2.5\times {10}^{25}\mathrm{W}$.

Step-by-step solution

Define the intensity ( I ).

The power transported per unit area is known as the intensity( I) .

The formula used to calculate the intensity( I) is:

$I=\frac{P}{A}$

Where, A is area measured in the direction perpendicular to the energy and P is the power in watts.

given values

Given that,

$$\begin{gathered} r=2\times {10}^{10}\mathrm{m} \\ I=5.0\times {10}^3\mathrm{W}/{\mathrm{m}}^2 \end{gathered}$$

calculation

Consider the path of the source to be a sphere.

Now, the average power output is

$$\begin{gathered} P=IA \\ =\left(5.0\times {10}^3\right)\left[4\pi \left(2\times {10}^{10}\right)\right] \\ =\left(5.0\times {10}^3\right)\left(5.02\times {10}^{21}\right) \\ =2.5\times {10}^{25}\mathrm{W} \end{gathered}$$

Hence, the average power output is equal to data-custom-editor="chemistry" $2.5\times {10}^{25}\mathrm{W}$.