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Consider a pond whose energy budget is dominated by radiation. The pond is disk-shaped, with a radius r and a depth H. The pond receives radiation in two forms: (i) sunlight, which has an average intensity of S [W/m²]; (ii) emission from the greenhouse gas layer with temperature Ta. Assume the pond absorbs all incoming radiation. Remember that the pond must also emit radiation. (a) Construct the energy budget for the pond. (b) If we assume S and Ta are constant, find an equation that relates temperature and time. Note that this equation is probably easier to express as t(T) rather than T(t) [weird but true]! (c) Let's imagine that the pond has just lost all its ice after the winter, and we want to know how long it will be until the pond is reasonable for swimming. Assuming S = 250 W/m², H is 3 m, and Ta is 255 K, and an appropriate swimming temperature is T =20°C. Make a spreadsheet with columns T and t. You might want to actually do the spreadsheet "backwards" of normal if it's easier to get numbers this way.

Consider a pond whose energy budget is dominated by radiation. The pond is disk-shaped, with a radius r and a depth H. The pond receives radiation in two forms: (i) sunlight, which has an average intensity of S [W/m²]; (ii) emission from the greenhouse gas layer with temperature Ta. Assume the pond absorbs all incoming radiation. Remember that the pond must also emit radiation. (a) Construct the energy budget for the pond. (b) If we assume S and Ta are constant, find an equation that relates temperature and time. Note that this equation is probably easier to express as t(T) rather than T(t) [weird but true]! (c) Let's imagine that the pond has just lost all its ice after the winter, and we want to know how long it will be until the pond is reasonable for swimming. Assuming S = 250 W/m², H is 3 m, and Ta is 255 K, and an appropriate swimming temperature is T =20°C. Make a spreadsheet with columns T and t. You might want to actually do the spreadsheet "backwards" of normal if it's easier to get numbers this way.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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I need help on this radiation problem,especially part A. Thank You. I know we need to use the Stef-bolt equation but I need help on setting it up. 

Consider a pond whose energy budget is dominated by radiation. The pond is disk-shaped, with a radius r and a depth H. The pond receives radiation in two forms: (i) sunlight, which has an average intensity of S [W/m²]; (ii) emission from the greenhouse gas layer with temperature T3. Assume the pond absorbs all incoming radiation. Remember that the pond must also emit radiation. (a) Construct the energy budget for the pond. (b) If we assume S and Ta are constant, find an equation that relates temperature and time. Note that this equation is probably easier to express as t(T) rather than T(t) [weird but true]! (c) Let's imagine that the pond has just lost all its ice after the winter, and we want to know how long it will be until the pond is reasonable for swimming. Assuming S = 250 W/m2, H is 3 m, and Ta is 255 K, and an appropriate swimming temperature is T =20°C. Make a spreadsheet with columns T and t. You might want to actually do the spreadsheet "backwards" of normal if it's easier to get numbers this way.
Transcribed Image Text:Consider a pond whose energy budget is dominated by radiation. The pond is disk-shaped, with a radius r and a depth H. The pond receives radiation in two forms: (i) sunlight, which has an average intensity of S [W/m²]; (ii) emission from the greenhouse gas layer with temperature T3. Assume the pond absorbs all incoming radiation. Remember that the pond must also emit radiation. (a) Construct the energy budget for the pond. (b) If we assume S and Ta are constant, find an equation that relates temperature and time. Note that this equation is probably easier to express as t(T) rather than T(t) [weird but true]! (c) Let's imagine that the pond has just lost all its ice after the winter, and we want to know how long it will be until the pond is reasonable for swimming. Assuming S = 250 W/m2, H is 3 m, and Ta is 255 K, and an appropriate swimming temperature is T =20°C. Make a spreadsheet with columns T and t. You might want to actually do the spreadsheet "backwards" of normal if it's easier to get numbers this way.
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