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

Question

Avalanche forecasters measure the temperature gradient dT/dh, which is the rate at which the temperature in a snowpack T changes with respect to its depth h. 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 degrees C/m anywhere in the snowpack, conditions are favorable for weak layer formation and the risk of avalanche increases. Assume the temperature function is continuous and differentiable. a. An avalanche forecaster digs a snow pit and takes two temperature measurements. At the surface (h=0) the temperature is -12 degees C . At a depth of 1.1 m the temperature is 2 degees C. Using the mean value Theorem, what can he conclude about the temperature gradient? Is the information of a weak layer likely? b. One mile away, a skier finds that the temperature at a depth of 1.4m is -1 degrees C, and at the surface it is -12 degees C. What can be concluded about the temperature gradient? Is the information of a weak layer in her location likely?

Explanation / Answer

Fractional distillation will have the more volatile compound evaporate first as the temperature rises to a point. So the highest concentration in your example would be compound B. However, all volatile compounds will have a particles that have evaporated out so you will see a small portion of compound A in there potentially. An example of real world fractional distillation I will pull from my organic chemistry lab example. A mixture of ethanol and water is mixed. Ethanol has a boiling point of 78.4 Celsius and water at 100 Celsius. The mixture is unique in the fact that their combined solution actually boils at a lower temperature (76 Celsius or so). As the vapor rises through the temperature gradient of the column, the vapor condenses. This will distill the solution as it trickles back down. The lower BP of the ethanol allows it to reach the cooler top of the column and distill out, leaving the water to trickle back down to the original container to revaporize. Now in more complex fractional distillations like in oil refining there are multiple steps. At each stage of the distillation column a different product is made. Everything from methane, ethane, propane, and pentane could all come from the same source as they have varying boiling points. Short answer: The more volatile liquid ends up in the receiving flask for a simple fractional distillation set up as the less volatile liquid will mostly not reach the top of the distillation column.

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