The intensity of electromagnetic waves from the sun is 1.4 kW/m² ...

Question

The intensity of electromagnetic waves from the sun is 1.4 kW/m² just above the earth's atmosphere. Eighty percent of this reaches the surface at noon on a clear summer day. Suppose you think of your back as a 30 cm x 50 cm rectangle. How many joules of solar energy fall on your back as you work on your tan for 1.0 h?

Accepted Answer

Hey everyone in this problem, a square solar collector with a side of 30 centimeters is used to charge batteries on Mars above Mars atmosphere. Solar electromagnetic radiation has an intensity of approximately 590 watts per square meter. Only 65% of the initial intensity reaches the solar collector. And we're asked to calculate the amount of solar energy hitting the solar collector during six hours. We're given four answer choices all in rules. Option A 2.1 times 10 to the exponent two. Option B 1.3 times 10 to the exponent five. Option C 7.5 times 10 to the exponent five and option D 2.5 times 10 to the exponent six. Now, we're asked to find an amount of energy. Ok. So let's recall that the energy E can be written as the power P multiplied by the time T and we were given the amount of time that we want to find this energy for. So we have our time but we need to find this power in order to calculate our energy. Now, the other information we were given was about intensity. Ok. So let's recall that the intensity I is equal to the power P divided by the area. All right. So we know the intensity and we're told that this is square and we have the side length so we can calculate the area that will allow us to find the power P. Then we can get back to our energy equation and use that power. And the time we were given in the problem to calculate the energy. All right. So let's start with the area. OK? Now, the area, this is the square. So it's just gonna be the side length squared. Now the side is 30 centimeters. We wanna use our standard units because the answer choices are in jewels. OK? So we're gonna convert 30 centimeters into meters. We divide by 100 we get 0.3 m and we're squaring this to find our area. And this is gonna give us an area of 0.09 m squared. All right. So we have our area, we have the intensity we were given in the problem. So let's use our intensity equation. So we have intensity is equal to the power divided by the area. Now, when we put our power or sorry, our intensity into our equation, 590 watts per meter squared, you have to be a little bit careful. OK. Remember that the question is telling us only 65% of the initial intensity reaches the solar click. OK. So when we're talking about the energy and the power associated with this, we want to consider that 65%. OK. So our initial intensity is 590 but only 65% actually makes it. So we're gonna multiply this by 0. and this is gonna be equal to our power divided by the area. We just found 0.09 m squared. Solving for the power, we're gonna multiply both sides by 0.09 m squared. Fear that the power is equal to 590 watts per meter squared, multiplied by 0.65 multiplied by 0.09 m squared. The units of meters square will divide out and we're gonna be left with the power of 34 0. watts. All right. Now let's go back to the top and remind ourselves what we're actually calculating here. We want to find the amount of energy E OK? We said that that was gonna be equal to the power multiplied by the time we found the power, the time is given in the problem. Let's get back to our energy equation. So the energy E is gonna be equal to the power multiplied by the time. Now, the time we were given is in hours. OK? We were given six hours again, we want this in our standard unit of seconds. So we get that final unit of jewel that we're looking for. So we're gonna take our six hours, we're gonna multiply it by 60 minutes per hour. And then we're gonna multiply again by 60 seconds per minute. When we do that, the unit of hours will divide out, the unit of minutes will divide out. We're gonna be left with six, multiplied by 60 multiplied by 60 seconds. And so we get 21,600 seconds and that's our time to you. So our energy now we have E is equal to 0.515 watts. The time is 21,600 seconds. We multiply these two together and we are gonna get an energy of 7. times 10 to the exponent five jules, ok? And that is the amount of energy delivered and we had 65% of that initial intensity and this is the energy that that delivers in six hours if we go to our answer choices and we can compare what we found. Ok? We're gonna round to two significant digits and we can see that the correct answer is gonna be option C 7.5 times 10 to the exponent five tools. Thanks everyone for watching. I hope this video helped see you in the next one.

Key Concepts

Intensity of Electromagnetic Waves

Energy Calculation

Area of Exposure

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