The goal in this problem is to find the growth of an ice layer as a function of time. Call the thickness of the ice layer L . (a) Derive an equation for dL/dt in terms of L , the temperature T above the ice, and the properties of ice (which can leave in symbolic form instead of substituting the numbers). (b) Solve this differential equation assuming that at t = 0 , you have L = 0 . If you have studied differential equations, you will know a technique for solving equations of this type: manipulate the equation to get dL/dt multiplied by a (very simple) function of L on one side, and integrate both sides with respect to time. Alternatively, you may be able to use your knowledge of the derivatives of various functions to guess the solution, which has a simple dependence on t . (c) Will the water eventually freeze to the bottom of the flask?
The goal in this problem is to find the growth of an ice layer as a function of time. Call the thickness of the ice layer L . (a) Derive an equation for dL/dt in terms of L , the temperature T above the ice, and the properties of ice (which can leave in symbolic form instead of substituting the numbers). (b) Solve this differential equation assuming that at t = 0 , you have L = 0 . If you have studied differential equations, you will know a technique for solving equations of this type: manipulate the equation to get dL/dt multiplied by a (very simple) function of L on one side, and integrate both sides with respect to time. Alternatively, you may be able to use your knowledge of the derivatives of various functions to guess the solution, which has a simple dependence on t . (c) Will the water eventually freeze to the bottom of the flask?
The goal in this problem is to find the growth of an ice layer as a function of time. Call the thickness of the ice layer L. (a) Derive an equation for dL/dt in terms of L , the temperature T above the ice, and the properties of ice (which can leave in symbolic form instead of substituting the numbers). (b) Solve this differential equation assuming that at
t
=
0
, you have
L
=
0
. If you have studied differential equations, you will know a technique for solving equations of this type: manipulate the equation to get dL/dt multiplied by a (very simple) function of L on one side, and integrate both sides with respect to time. Alternatively, you may be able to use your knowledge of the derivatives of various functions to guess the solution, which has a simple dependence on t. (c) Will the water eventually freeze to the bottom of the flask?
How can you tell which vowel is being produced here ( “ee,” “ah,” or “oo”)? Also, how would you be able to tell for the other vowels?
You want to fabricate a soft microfluidic chip like the one below. How would you go about
fabricating this chip knowing that you are targeting a channel with a square cross-sectional
profile of 200 μm by 200 μm. What materials and steps would you use and why? Disregard the
process to form the inlet and outlet.
Square Cross Section
1. What are the key steps involved in the fabrication of a semiconductor device.
2. You are hired by a chip manufacturing company, and you are asked to prepare a silicon wafer
with the pattern below. Describe the process you would use.
High Aspect
Ratio
Trenches
Undoped Si Wafer
P-doped Si
3. You would like to deposit material within a high aspect ratio trench. What approach would you
use and why?
4. A person is setting up a small clean room space to carry out an outreach activity to educate high
school students about patterning using photolithography. They obtained a positive photoresist, a
used spin coater, a high energy light lamp for exposure and ordered a plastic transparency mask
with a pattern on it to reduce cost. Upon trying this set up multiple times they find that the full
resist gets developed, and they are unable to transfer the pattern onto the resist. Help them
troubleshoot and find out why pattern of transfer has not been successful.
5. You are given a composite…
Human Biology: Concepts and Current Issues (8th Edition)
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