Chapter 14, Problem 49GP

(a)

To determine

The total power radiated by the sun into space.

Answer to Problem 49GP

The total power radiated by the sun into space is $3.19\times {10}^{26}\text{W}$ .

Explanation of Solution

Given info:

The temperature for the power is, $T=5500\text{K}$ .

The radius of the sun is, $r=7\times {10}^8\text{m}$ .

Formula Used:

The expression to calculate the total power radiated by the sun into space is,

  $P=4\pi \sigma r^2{T}^4$

Here, $\sigma$ is Stefan’s constant.

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}P=4\pi \left(5.67\times {10}^{-8}\text{W}/{\text{m}}^2\cdot {\text{K}}^4\right){\left(7\times {10}^8\text{m}\right)}^2{\left(5500\text{K}\right)}^4\\ =3.19\times {10}^{26}\text{W}\end{array}$

Conclusion:

Thus, the total power radiated by the sun into space is $3.19\times {10}^{26}\text{W}$ .

(b)

To determine

The power per unit area arriving to earth.

Answer to Problem 49GP

The power per unit area arriving to earth is $1128.24\text{W}$ .

Explanation of Solution

Given info:

The distance between the sun and earth is, $d=1.5\times {10}^{11}\text{m}$ .

Formula Used:

The expression to calculate the power per unit area arriving to earth is,

  $P_e=\frac{P}{4\pi d^2}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}{P}_e=\frac{3.19\times {10}^{26}\text{W}}{4\pi {\left(1.5\times {10}^{11}\text{m}\right)}^2}\\ =1128.24\text{W}\end{array}$

Conclusion:

Thus, the power per unit area arriving to earth is $1128.24\text{W}$ .