Chapter 27, Problem 49A

a.

To determine

To Find: The amount of energy from Sun that falls on one square meter each year.

Answer to Problem 49A

  $3.15\times {10}^{10}\text{J/yr}\cdot {\text{m}}^2$

Explanation of Solution

Given data:

Received energy $=1000\text{ J/s}$

Formula used:

  $\text{1year=365}\times 24\times 60\times 60\mathrm{s}$

Calculation:

In each year, energy falls on one square meter $=1000\times 1\text{year}$

  $\begin{array}{l}E=\text{1000}\times \text{365}\times 24\times 60\times 60\text{J/yr}\cdot {\text{m}}^2\\ E=315360\times {10}^5\text{J/yr}\cdot {\text{m}}^2\\ E=3.15\times {10}^{10}\text{J/yr}\cdot {\text{m}}^2\end{array}$

Conclusion:

In each year, $3.15\times {10}^{10}\text{J}$ energy falls on one square meter.

b.

To determine

To Find: The area of converter that would produce the energy needed by home from solar energy with 20 percent efficiency.

Answer to Problem 49A

  $63.5{\text{m}}^2$

Explanation of Solution

Given data:

Efficiency, $\eta =20\%$

In each year, $3.15\times {10}^{10}\text{J}$ energy falls on one square meter.

Energy used by home each year, $E_H=4\times {10}^{11}\text{J}$

Formula used:

Efficiency:

  $\eta =\frac{\text{useful energy}}{\text{energy fall on one square meter}}$

Required area of converter $=\frac{\text{Energy required by home per year}}{\text{Useful energy that falls per year per square meter}}$

Calculation:

  $\begin{array}{l}\eta =\frac{\text{useful energy}}{\text{energy fall on one square meter}}\\ \frac{20}{100}=\frac{E}{3.15\times {10}^{10}\text{J/yr}\cdot {\text{m}}^2}\\ E=\frac{1}{5}\times 3.15\times {10}^{10}\text{J/yr}\cdot {\text{m}}^2\\ E=0.63\times {10}^{10}\text{J/yr}\cdot {\text{m}}^2\end{array}$

  $E=6.3\times {10}^9\text{J/yr}\cdot {\text{m}}^2$

Required area of converter $=\frac{\text{Energy required by home per year}}{\text{Useful energy that falls per year per square meter}}$

  $A=\frac{4\times {10}^{11}\text{J/yr}}{\text{6}\text{.3}\times {\text{10}}^9\text{J/yr}\cdot {\text{m}}^2}=63.5{\text{m}}^{\text{2}}$

Conclusion:

The area of converter that would produce the energy needed by home $63.5{\text{m}}^2$ .