1. It is 37 °F outside, and an ice storm has left a solid sheet of ice on the ro
ID: 3307514 • Letter: 1
Question
1. It is 37 °F outside, and an ice storm has left a solid sheet of ice on the road. I estimate the sheet is ½ inch thick. It is raining right now, and the forecast states that 34 inches will fall today, and the temperature will remain around 37 °F. It is 8 AM and I am stuck inside.I wonder if it is enough rain to melt all the ice on the road so that I can leave by 2 PM for an appointment. Should I cancel my appointment? What do you think? Support your answers with a sketch of the system and with calculations. What assumptions do you need to make and how will they affect your answer? If there were ½ inch of snow rather than ice, do you think it would melt faster, slower, or the same? Explain. 2.Explanation / Answer
There is no need to cancel the appointment.
Density of water is greater than that of snow, moreover the forecast tell you that the amount of rain will be more than your estimated thickness of ice sheet. The latent heat of water will be greater than the heat of fusion of the ice-sheet, hence the ice-sheet would melt and it would clear up, by the aftenoon, provided the tempereture increases in the course of the dayand not decreases, also the of thickness of ice-sheet remains below the level of rainfall.
If either of the assumptions dont work, then the snow ice might not melt, the first assumeption is very well valid, however, the estimate if wrong, could affect the condition.
2. If it is 1/2 inch snow, then it is even better, because the density of snow is lesser than that of ice!
The density of snow is much lower than the density of ice - so the total heat of fusion needed to melt a volume of snow is much lower. That will mean the snow melts faster than the ice.
[The diagram could indicate the thickess of the layers of snow and ice and of rain over it, Q=MC*dt and the expression of enthalpy of fusion can be used to futher elaborate based on the level]
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