Lab 4_Heating the Earth and the Atmosphere 2

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METO 1010 Online Lab 4. Heating the Earth and the Atmosphere 2 Instructions: 1) Type your answers in this Microsoft Word file and save your completed lab on your computer. 2) Upload your lab on CANVAS by the due date. To upload the file, go to the course homepage and click on “assignments”. Click on the assignment that you want to submit, and on “submit assignment”. In the “file upload” box, click on “choose file” and select the appropriate file. Finally, click on “submit assignment”. Only .doc, .docx, and .pdf files are accepted. 3) In questions that require calculations, you are required to show every step of your work. 4) Proper units and terminology are always necessary. Lab Overview: The main goal of this fourth lab is for you to learn how to apply the laws of radiation, particularly Stefan-Boltzmann’s and Wien’s laws. Understanding these laws and their applications is critical to understand the greenhouse effect, which is the process that keeps our planet at a temperature that is suitable for the survival of life. Learning Objectives: At the end of this lab, you are expected to be able to:  Apply Stefan Boltzmann’s law to calculate the power per unit area of the radiation released by an object given its temperature  Apply Wien’s law to calculate the wavelength of maximum emission of the radiation released by an object given its temperature  Compare and contrast the radiative properties of the Sun with those of the Earth 1

1 ) The Sun has an average surface temperature of approximately 6000 K. Calculate the power per unit area released by the surface of the Sun using Stefan-Boltzmann Law and report the value below. Units are a must . (2 points) Power per unit area released by the Sun= 73,483,200 W/m^2 OR 7.34 x 10^7 W/m^2 E=5.67 x 10^-8 x 6000k^4 = 73,483,200 W/m^2 (cancel out k) 2) The radius of the Sun is 7·10 8 m. Calculate the total power released by the surface of the Sun and report the value below. Write the number is scientific notation and keep two decimal figures. Units are a must . (3 points) Hint: the surface area of a sphere is equal to 4πr 2 , where r is the radius Total power released by the Sun= 4.52 x 10^26 W 4π(7*10^8) 2 = 6.16 x 10^18 m^2 (Surface Area) Total power=7.34 x 10^7 W/m^2 x 6.16 x 10^18 m^2 = 4.52 x 10^26 W (m^2 cancels out) 3) The Earth has an average surface temperature of approximately 300 K. Calculate the power per unit area released by the surface of the Earth and report the value below. Keep two decimal figures. Units are a must . (2 points) Power per unit area released by the Earth= 459.27 W/m^2 E=5.67 x 10^-8 x 300k^4 = 459.27 W/m^2 (cancel out k) 4) How many times warmer is the Sun than the Earth? (1 point) 6000/300 = 20 times warmer 5) How many times more power per unit area does the Sun release relative to the Earth? (1 point) 160,000 W (73,483,200 / 459.27) 6) Calculate the wavelength of maximum emission for the Earth using Wien’s Law and report the value below. Keep two decimal figures. Units are a must . (2 points) λ max Earth= 9.66um (micrometers) 2898um x k / 300k = 9.66um 2

7) Calculate the wavelength of maximum emission for the Sun using Wien’s Law and report the value below. Keep two decimal figures. Units are a must . (2 points) λ max Sun= 0.48um (micrometers) 2898um x k / 6000k =0.48um 8) In what portion of the electromagnetic spectrum (i.e., what type of radiation) is the maximum emission from the Sun? (1 point) Visible band 9) In what portion of the electromagnetic spectrum (i.e., what type of radiation) is the maximum emission from the Earth? (1 point) Infrared 10) Your body has an average surface temperature of approximately 99°F. Calculate the power per unit area released by your body using Stefan-Boltzmann Law and report the value below. Keep two decimal figures in the final result and in all your intermediate calculations. Units are a must . (2 points) Power per unit area released by your body= 525.12 W/m^2 C= (99-32)/1.8 = 37.22 C K=273+37.22 = 310.2 K E= 5.67 x 10^-8 x 310.2^4 = 525.12 W/m^2 11) Calculate the wavelength of maximum emission for your body using Wien’s Law and report the value below. Keep two decimal figures. Units are a must . (2 points) λ max your body= 9.34um (micrometers) 2898um x k / 310.2K = 9.34um (micrometers) (cancel out k) 3

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12) In what portion of the electromagnetic spectrum (i.e., what type of radiation) is the maximum emission from your body? (1 point) Infrared 4

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