What is the average energy contained in a 1.00-m 3 volume near the Earth’s surface due to radiant energy from the Sun? See Example 31–6.

Welcome back everyone in this problem. Suppose the star Vega emits radiation that reaches planet Nerea with an intensity of 1100 watts per square meter. Determine the average energy contained in a three cubic meter volume near the surface of Narea. Due to the radiant energy from Vega A says it's 1.1 multiplied by 10 to the negative fifth joules B 2.5 multiplied by 10 to the negative fifth joules C 1.1 multiplied by 10 to the negative fourth joules and D 2.5 multiplied by 10 to the negative fourth joules. Now how are we going to figure out the average energy contained in our three cubic meter volume? What do we know about energy and volume? Well, recall that the total energy is going to be equal to the energy density U multiplied by the volume V. In this case, we don't know the energy density, but we can find the energy density because the energy density of the radiant energy can be calculated by U being equal to the radiation intensity S divided by C the speed of light. Now, do we have this information? Well, so far. OK. We know that our radiation intensity is is 1100 watts per square meter. We also know that our volume is three cubic meters and we know that the speed of light C is three multiplied by 10 to the 8 m per second. So we have all we need to solve our problem because no, by substituting the formula for U into the formula for total energy, it equals S divided by C multiplied by V. Let's go ahead and substitute the solve. That's going to be 1100 watts per square meter multiplied by three cubic meters all divided by the speed of light, which is three multiplied by 10 to the 8 m per second. Now when we go ahead and solve, OK, then we should get our total energy to be equal to 1.10 multiplied by 10 to the negative 5th 5th joules or to two significant figures approximately 1.1 multiplied by 10 to the negative fifth joules. Thus, this is going to be the average energy contained in our volume due to the radiant energy from Vega A is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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32. Electromagnetic Waves

Intro to Electromagnetic (EM) Waves

Physics

32. Electromagnetic Waves

Intro to Electromagnetic (EM) Waves

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2:56 minutes

Problem 30

Textbook Question

What is the average energy contained in a 1.00-m³ volume near the Earth’s surface due to radiant energy from the Sun? See Example 31–6.

Verified step by step guidance

Determine the intensity of sunlight near the Earth's surface. The intensity (I) is the power per unit area received from the Sun. Near the Earth's surface, this value is approximately 1360 W/m² (known as the solar constant).

Recall the relationship between intensity and energy density. The energy density (u) of electromagnetic radiation is related to the intensity by the formula:

u = \frac{I}{c}

, where

c

is the speed of light in a vacuum (approximately

3.00 \times 10 ⁸ m / s

Substitute the known values into the formula for energy density. Use

I = 1360 W / m ²

and

c = 3.00 \times 10 ⁸ m / s

to calculate

u

Once the energy density

u

is determined, calculate the total energy in the given volume. The total energy (E) is given by the formula:

E = u \times V

, where

V

is the volume. Here,

V = 1.00 m ³

Substitute the calculated energy density and the given volume into the formula for total energy to find the average energy contained in the 1.00-m³ volume near the Earth's surface.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Radiant Energy

Radiant energy is the energy of electromagnetic waves, including visible light, infrared, and ultraviolet radiation. It is emitted by the Sun and travels through space, reaching the Earth. The amount of radiant energy received by a given area can be quantified in terms of power per unit area, typically measured in watts per square meter (W/m²). Understanding radiant energy is crucial for calculating the energy contained in a specific volume.

Energy Density

Energy density refers to the amount of energy stored in a given volume or mass. In the context of radiant energy, it can be expressed as the total energy contained in a specific volume of space, such as 1.00 m³. This concept is important for determining how much energy is available in a defined space, which is essential for answering the question about the average energy contained in the specified volume.

Solar Constant

The solar constant is the average amount of solar electromagnetic radiation per unit area that is received at the outer surface of Earth's atmosphere, approximately 1361 W/m². This value is crucial for calculating the total radiant energy available to a specific volume near the Earth's surface. By knowing the solar constant, one can estimate the energy input from the Sun to a given volume over time, which is necessary for answering the question posed.

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