#212 When spring finally arrives in the mountains
When spring finally arrives in the mountains - Physics
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When spring finally arrives in the mountains, the snow pack may be two meters deep, composed of 50% ice and 50% air. Direct sunlight provides about. 1000 watts/m2 to earth’s surface, but the snow might reflect 90% of this energy. Estimate how many weeks the snow pack should last, if direct solar radiation is the only source of energy.
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During fusion of ice, the heat released by water and absorbed by the air is given by the following formula;
Here, m is the mass of ice and is the latent heat of fusion of ice.
The snow will melt because of the heat energy coming from the sunlight.
Since of energy reflects back hence only of energy is only being used to melt the snow.
Then, the amount of heat generated by the sunlight is used in melting of snow can be calculated as,
The depth of the snow pack would be,
The time for which the snow pack will exist would be,
Here, is the time, is the rate of heat transfer, is the area of heat transfer and is the solar energy flux
The amount of heat transfer during the melting of snow per unit area can be calculated as follows,
Here, is the mass of the snow pack, is the volume of the snow pack, is the density of the ice, is the depth of the snow pack and is the latent heat of fusion of ice.
So, the time can also be written as follows,
Substitute, for, for, for and for in the above expression to get the time required as follows,
Convert the required time from seconds to week.
Thus, the snow pack will last.
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