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To get started, we need to make a few assumptions:
- Let's look at 1 square meter of ground that is covered by 2 inches of wet snow. To determine the mass of this snow, use the conversion that 1 inch of wet snow is approximately 0.75 cm of rain. Furthermore, 1 cubic cm of rain has a mass of about 1 gram. What is the total mass of the snow on our 1 square meter of ground (give your answer in kg)?
- Assume the ambient temperature is exactly freezing (0° C). As the sun shines down on the snow, some of the energy is absorbed to melt the ice into water. You should recall from chemistry that the amount of energy required to melt one kilogram of a substance is called the heat of fusion. The heat of fusion of ice is approximately 334 kJ/kg. Using our answer to question 1, how much heat is required to melt all of the snow?
- The sun produces tremendous amounts of energy. Each second, approximately 1000 J of energy are delivered to each square meter of the Earth's surface. Assuming all of this energy works to melt the snow, how long will it take to completely melt all of the 2-inch-deep snow cover?
- Does the answer to question 3 seem reasonable?
In our calculations, we have made quite a few assumptions and also omitted a few important factors.
- Can you think of any assumptions or omissions we've made that might explain why our calculated value (problem 3) is higher than it should be? Explain!
- Can you think of any assumptions or omissions we've made that might explain why our calculated value (problem 3) is lower than it should be? Explain!
Post your answers to any of the above questions in the comments section. Please be sure to indicate which question you are addressing.
1) since there is 2inches of snow, there is 1.50 centimeters of rain. Since centimeters is a measure of length and cubic centimeters is one of volume, i multipled 1.5 by itself 3 times, my outcome was 3.375, then to convert to kgs i multiplied by .001 and my final answer was .00375 kg.
ReplyDelete2) It will take 1.25 joules to melt each kg.
3) Depending on the temperature outside, if the temperature is low then it will take longer to melt due to the conversion from snow to ice. I got 1252 seconds.
4) It seems like 20 minutes would be a little short for all the snow to melt, but that might be the wrong calculation.
1. I also found there were 1.5 cm of rain after converting the 2 in of snow, and I also cubed that answer to get 3.375 cubic cm. I was then able to recognize that value as being equivalent in grams, and I mutliplied it by .001 to find it was also equal to .003375 kg; my final answer.
ReplyDelete2. Since you provided the heat of fusion of ice is aprox. 334 kJ/kg, I used that value to set up a proportion and found melting .003375 kg of snow (all the snow in our 1m) would take 1.127525 kJ.
3. I converted that 1000 J to kJ by multipling by .001, and got 1 kJ. Since I found it takes about 1.28 kJ to melt 1 m of snow, I think it will take about 1.28 seconds.
4. The answer I found does not seem at all reasonable, but I also think it's reasonable to assume other factors would be involved that would prolong the time needed for the snow to melt.
The calculations above seem to be correct. I tried them as well and I got the same answers. I also think that 20 minutes to melt 2 inches of snow seems to be too short of a time period. The reason that I think the answer came out to be a lot shorter time than it actually would take is because we did not include the factor of wind. That will greatly affect our calculated answer.
ReplyDelete1. Since we are referring to a square meter of snow, that would mean (1 by 1 meter) Making both length and width one meter. However, the depth is .75 times 2 = 1.5 cm. So you cannot have different measurements. So you convert meters to centimeters because one meter is one hundred centimeters. So then to find the mass you multiply 100 x 100 x 1.5 = 15,000 cm which is roughly 11,250 when multiplied by the approximate mass. Then to convert grams to kilograms you simply divide by one thousand. That makes the mass 11.25 kg.
ReplyDelete2. If the mass were to be right than it would be 334KJ/11.25Kg, so it would take 29.69 joules
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1. 2 inches of snow = 1.5 cm of water.
ReplyDeleteVolume = l*w*h = (100 cm) * (100 cm) * (1.5 cm)
Volume = 15,000 cm^3
Mass = 15,000 g
1 kg = 1000 g, so
Mass = 15 kg
2. A proportion:
(334 kJ) / (1 kg) = H / (15 kg)
solving for H: H = 5,010 kJ = 5,010,000 J
3. The sun delivers 1,000 J per second, so it would take 5,010 seconds to provide necessary heat to melt all the snow.
In other words, it would take about 1.4 hours.
4. It seems reasonable to me that it might take about 1.4 hours for the snow to melt on a cold, but sunny day.
Thanks for the comments this week. Now, with provided answers to the first four questions, let's work to come up with some better answers for the final two questions. (The extra-credit window for this post has been extended until next week.)
ReplyDeleteQUESTIONS 1 AND 2
ReplyDeleteThe factors that could affect the outcome of the time it takes to melt two inches of snow could possibly depend on the temperature, if it's warmer than the snow could melt faster but if it's colder it could take longer for the snow to melt completely. Also it could depend on how windy it is outside, the more wind there is the more colder it could become, making it harder for the snow to melt. Another factor could be whether or not the sun is shining directly on the snow or if the snow is shaded by a tree or a building. If the snow is being shaded it would take longer for the sun to reach that area and melt that section.
The answer we got might be higher than it should be since we did not take into consideration how cold it is outside, how windy it is outside, how cloudy it is, whether or not our spot of snow is covered by shade, what time of the day it is, or how damp the ground beneath the snow is. The answer we got got might be lower than it should be, for example, it might be warm outside, with no wind, no clouds(just sun), out in the open with no shade, in the afternoon, with warm damp ground underneath. All these factors would cause the snow to melt faster than if the opposite were true.
ReplyDelete-Hannah Zwiernik
I agree with the last two comments completely if we took inconsideration the temperature and wind, along with shade, dampness of the ground and also humidity along with direct sunlight all these factors can determine whether or not the snow melts faster or slower. Yes, if the conditions were just right the snow could melt in the 1.4 hr allotted time but this is usually not the case. If i had to give my best guess i would say that it would take a lot more time to melt the snow in our weather conditions this week because its been a lot colder and windier.
ReplyDeleteI agree with what useful_idiot said as well. I believe that it would take way longer than 1.4 hours to completly melt the snow. In order for it all to melt the weather conditions would have to be exact. Most of the time the weather changes through out the day, even through out the hour. If its not exact then the snow will not melt in 1.4 hours due to all of the factors that could make it harder for the snow to melt.
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ReplyDelete1. The sun would not be directly overhead, especially close to the winter solstice, so you need a factor of cos (theta), which is about 0.4 for sun near 24 degrees above horizon (zenith angle of 66 deg)(reasonable late morning in December)
ReplyDelete2. Fresh snow only absorbs about 20% of energy hitting it (10% of visible and 30% of near
infrared), but this would probably go up to maybe 40% since some light gets through to be absorbed by dark ground underneath.
Putting in those factors, 1.4 hours / (0.4 * 0.4) = 8 hours (It would take all day) if air temp is at freezing. Of course it would be faster for south-facing slopes such as south hillsides or rooftops, or if air temp is above freezing. I think these results are entirely reasonable.
I also agree with what everyone has been saying, in that there are many things that could change the answer and make it take a longer or shorter period of time for the snow to melt. The factors that have been stated above are the exact ones I was thinking of. And because the earth is always moving and many things are constantly changing, it is hard to predict exactly the amount of time it will take to melt all of the snow.
ReplyDeletei believe that it would take longer then 1.4 hours to melt the snow on the ground. depending on where the snow is, humidity, and how much sunlight shines on that snow can determine how long it will take for the snow to melt. lately it has been pretty cold so i think that it would take longer for the snow to melt. if it was warmer the snow could melt in that time but it depends on the temperature a lot.
ReplyDeletemason smeznik
The calculations could be slightly higher or lower for a number of reasons. The rate at which the snow melts could depend on whether or not the snow is in direct sunlight, the temperature outside, whether or not it is windy, or whether or not the sun is in the shade. These factors all have the potential to change the time it takes for the snow to melt. A warmer day with little or no wind would cause the snow to melt faster; while a cold, windy day with no sun would cause the snow to melt much slower.
ReplyDeleteI agree with what other people have said as well. The amount of time it takes for the snow to melt that we calculated could be a little different because it would depend on multiple factors. For example the wind would play a factor in the amount of time it took for the snow to melt. As well as if our square meter of snow is in the shade or not would play a role as well. If it was in the shade for a period of time it would take longer for the snow to melt then if the sun was on it for the whole time.
ReplyDeleteThanks for the comments this week!
ReplyDelete