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Chapter 1: Problem 28

The intensity of the Sun's radiation that reaches Earth's atmosphere is $1.4 \mathrm{kW} / \mathrm{m}^{2}(\mathrm{kW}=\text { kilowatt } ; \mathrm{W}=\text { watt })\( Convert this to \)\mathrm{W} / \mathrm{cm}^{2}$.

Short Answer

Expert verified
Question: Convert the intensity of the Sun's radiation from 1.4 kW/m² to W/cm². Answer: The intensity of the Sun's radiation that reaches Earth's atmosphere is 0.14 W/cm².

Step by step solution

01

Convert kilowatts to watts

To convert kilowatts to watts, we know that \(1\text{kW} = 1000 \text{W}\). Therefore, we can multiply the given intensity value by 1000 to obtain the intensity in watts per square meter. $$1.4 \text{ kW/m}^2 \times (1000 \frac{\text{W}}{\text{kW}}) = 1400 \text{ W/m}^2$$ Now, let's convert square meters to square centimeters:
02

Convert square meters to square centimeters

To convert from square meters to square centimeters, we need to know the relationship between the two units. 1 meter is equal to 100 centimeters, so we have: $$1 \text{ m}^2 = (1 \text{ m} \times 100 \frac{\text{cm}}{\text{m}})^2 = 10000 \text{ cm}^2$$ Now we can convert the intensity from watts per square meter to watts per square centimeter by dividing the intensity value by 10000: $$1400 \frac{\text{W}}{\text{m}^2} \times \frac{1}{10000 \frac{\text{m}^2}{\text{cm}^2}} = 0.14 \frac{\text{W}}{\text{cm}^2}$$ Thus, the intensity of the Sun's radiation that reaches Earth's atmosphere is \(0.14\ \text{W/cm}^2\).

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