Avalanche forecasters measure the temperature gradient dT/dh which is the rate a

Q: Avalanche forecasters measure the temperature gradient dT/dh which is the rate a

a) Using the mean value theorem dT/dh = [Temp(at ground) - Temp(at depth)]/[0-(-1.5)] => [3 -(-8)]/(1.5) => 7.333C/m (nearest tenth will be 7.3 C/m) Since dT/dh is less than 10C/m, hence the formation of weak layer is NOT likey, hence second answer will be NO b) dT/dh = [Temp(at ground) - Temp(at depth)]/[0-(-1.1)] => 12/1.1 => 10.9C /m YES, the formation of weak layer is likely

ID: 2891935 • Letter: A

Question

Avalanche forecasters measure the temperature gradient dT/dh which is the rate at which the temperature in a snowpack changes with respect to its depth. If the temperature gradient is large, it may lead to a weak layer of snow in the snowpack. When these weak layers collapse, avalanches occur. Avalanche forecasters use the following rule of thumb: If dT/dh exceeds 10 degree C/m anywhere in the snowpack, conditions are favorable for weak layer formation and the risk of avalanche increases dh Assume the temperature function is continuous and differentiable. Complete parts (a) through (d) below. a. An avalanche forecaster digs a snow pit and takes two temperature measurements. At the surface (h = 0) the temperature is -8 degree C. At a depth of 1.5 m, the temperature is 3degree C. Using the Mean Value Theorem, what can he conclude about the temperature gradient? dT/dh degree C m (Simplify your answer. Round to the nearest tenth as needed.) Is the formation of a weak layer likely? Select the correct answer below No Yes b. One mile away, a skier finds that the temperature at a depth of 1.1 m is 2 degree C, and at the surface, the temperature is -10 degree C. What can be concluded about the temperature gradient? dT/dh degree C/m (Simplify your answer. Round to the nearest tenth as needed.) Is the formation of a weak layer likely? Select the correct answer below. No Yes

Explanation / Answer

a) Using the mean value theorem

dT/dh = [Temp(at ground) - Temp(at depth)]/[0-(-1.5)]

=> [3 -(-8)]/(1.5)

=> 7.333C/m (nearest tenth will be 7.3 C/m)

Since dT/dh is less than 10C/m, hence the formation of weak layer is NOT likey, hence second answer will be NO

dT/dh = [Temp(at ground) - Temp(at depth)]/[0-(-1.1)]

=> 12/1.1

=> 10.9C /m

YES, the formation of weak layer is likely

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Avalanche forecasters measure the temperature gr which is the rate at which the

Avalanche forecasters measure the temperature gradient dT/dh, which is the rate

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Avalanche forecasters measure the temperature gradient dT/dh which is the rate a

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