GGRB28H3 Lecture 2: Lecture 2 notes

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14 Apr 2011

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Globalization" is a very prominent word in today"s world. It has been used especially since the 1980s to capture a series of economic, political, and social changes. It is also widely used to discuss health. For instance global health" is a term that is very common when talking about health issues that cross a number of boundaries. The bill and melinda gates foundation has a global health program. So does the us aid (which is the program through which the us channels foreign aid) and cida (canadian. There are organizations that take the name, such as the global health council. It is difficult to believe that this way of looking at health is actually quite new. Is there anything particularly unique about the present period, for instance in comparison with the colonial period which connected peoples in new ways or the expansion of europe into the so-called new world .

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DUE DATE: 12 00 noon Monday. Dec 6. 2010. The problems on this assignment are quite word because strong direction is being given to Students in how to proceed. Two problems will be selected at random for marking. Percentage polarization. It is useful to characterize partially polarized light in terms of its "percentage polarization". A light beam of constant intensity Io. is allowed to fall at normal incidence on an "ideal linear polarizer" (a linear polarizer is "ideal" if it panes all light polarized parallel to the polarizer's axis, and stops all light polarized perpendicular to that axis.) As the ideal polarizer is rotated continuously (see Figure 8.1; about an axis perpendicular to its plane, the transmitted intensity I passes through successive maximum and minimum values (denoted by I max and I min). The percentage polarization of the incident light is denned to be Find the percentage polarization measured in this way for the following light beams: "Unpolarized natural light" tor which I max = I min = Io/2. A beam of light. Initially unpolarixed. that has been passed through an ideal linear polarizer before being measured for percentage polarization. A beam of light, initially unpolarizcd, that has been passed through a non-ideal polarizer that (in terms of light intensity) transmits 70% of light polarized parallel to its polarizing axis and 20% of light polarized perpendicular to its polarizing axis. Circularly polarized light. (Circular polarization means that at any given fixed observation point In the beam, the E-vector has constant magnitude but rotates at the frequency of the electric field oscillations so that the tip of the vector describes a circle in the zy plane (perpendicular to the light ray at the point in question). Elliptically polarized light for which the tip of the E-vector moves on an ellipse in the x y plane, defined by where Ax and Ay are the amplitudes of the oscillating Ex and E y components of the electric field vector, and is the phase difference between those oscillations. NOTE: Do your calculation for the special case Ax = 2Ay and e =pi / 2. [(8.2) taxes a particularly simple form when e = pi / 2.]

An important question to consider when thinking about globalwarming is, "If the ice sheets near the poles melt, how much willthe sea level rise?" This seems like a difficult question, giventhe odd shapes of both the ice sheets and the oceans. But there aresome accurate approximations that allow the answer to be estimatedfairly accurately with reasonably simple calculations.

The critical idea is that both the thickness of the ice sheets andthe amounts of the sea-level rise are extremely small compared tothe radius of the earth. The radius of the earth is about 2/p x 107m -- more than 6000 kilometers. The ice sheet thicknesses we willbe concerned with are single digit miles and the sea level riseswill be in dozens of feet. As a result, in thinking about them, wecan essentially ignore the curvature of the earth. We can imaginepeeling the map of the earth off a globe and flattening it out (bymaking cuts, not by stretching it, so that we preserve the area).Then, both the ice and the sea level rise can be treated as right(not tilted) cylinders (though with funny shaped bases and tops).Since we know that the volume of a right cylinder is the area ofthe base times the height, we can easily estimate all the volumeswe need. A schematic picture of this approximation (with the heightof the ice mass greatly exaggerated -- you couldn't see it if Ididn't) is shown below. The error in these approximations is on theorder of the height of the cylinder considered divided by theradius of the earth; a very small number.
a. Assume that (after flattening the surface of the earth in ourimaginations) the ice sheet to be considered covers an area, A, andhas a thickness, d. The oceans currently cover about 75% of theearth's surface, and note that the surface area of a sphere is 4pr2where r is the radius of the sphere.

Generate an equation that will allow you to calculate h, the heightthe ocean levels will rise due to the melting of a an ice sheet interms of A, d, and r

b. As shown in the combined satellite photo on the right (fromGoogle Earth), Greenland is covered by a sheet of ice. This ice hasbeen measured to have a mean thickness of about 2 km. Recentobservations indicate that this ice sheet is beginning to retreat-- that it is melting at an accelerating rate.

Using the depth of the ice sheet and the scale given on thepicture, estimate how much sea level rise would be produced by themelting of the entire ice sheet lying on Greenland. (Note: You caneasily look this information up on the web. But the goal of thisproblem is in part to develop your estimation skills for thepurpose of building your ability to decide for yourself whether anygiven piece of information you find on the web is reasonable orbogus.)

Vapor cycles
5EM - Thermodynamics
September 2010
1 The T-S diagram
The temperature-entropy diagram is an alternative to the well knownpressure-
volume diagram. Before using it to analyze different vapor cycles,we need
to understand it properly.
1. Plot the following transformations for ideal gases in a T-Sdiagram
(a) Isothermal expansion
(b) Isobaric expansion
(c) Isometric heating
(d) Reversible adiabatic expansion
(e) Irreversible adiabatic expansion
2. Repeat the last question, but this time do it for a realsubstance,
starting in the compressed liquid1 region and ending in thesuperheated
region, when possible. Indicate the boundaries of eachregion.
3. We know that under certain circumstances the area under theplot
in a P-V diagram represents the work performed during theprocess.
What does it represent in this case? Under what assumptions isyour
answer true? Compare examples 6.1 and 6.2.
2 Thermal machines
We understand by thermal machine a device capable of transformingther-
mal energy (heat) into mechanical energy (work). We already knowthat
these machines have a limited efficiency which, in the two-sourcesmodel, is
obtained by Carnotâs cycle.
(Compressed liquid is sometimes also called subcooled liquid)
2.1 Carnot cycle
This cycle, although efficient, is impractical. To begin with, theextreme
temperatures of the cycle should be within the sources temperaturesfor a
finite heat flow to exist.
1. Given the temperature of the sources, draw the cycle accordingto the
named limitation.
2. Show that this leads to lower efficiency than the theoreticallimit.
3. Assume that heat flow from/to the sources is proportional to thetem-
perature difference between them and the working fluid, anddemon-
strate that a higher power output is related to a decreasedefficiency.
2.2 Rankine cycle
Out of the several practical possibilities, Rankine cycle and itsvariations is
widely used, especially for electric power generation.
1. Draw the basic cycle in a T-S diagram and explain it.
2. What does the efficiency of the cycle depend on? Comparewith
Carnotâs.
3. What are the differences between the ideal cycle and the realone?
4. Describe how it is modified by superheating and/or reheating.Explain
te benefits.
2.3 Problems
After answering the previous questions solve the followingexercises from the
book: 8.2, 8.4, 8.5, 8.13, 8.19, 8.20
3 Frigorific machines
3.1 Reverse Carnot cycle
We have already studied Carnot cycle in detail as the ideal thermalmachine.
Now we will take is as the starting point to understand thecharacteristics
of frigorific machines.
1. Draw the ideal cycle in a T-S diagram and explain it.
2. Show that this cycle has a theoretical efficiency Ã =Tcold/Thot-Tcold
3. What are the difficulties in implementing such cycle in actualdevices?
3.2 Actual refrigerators
1. Why is the turbine replaced by an expansion valve in mostcases?
2. Plot the actual cycle and explain the differences with the idealcase.
3. How do cascade and multistage systems improve the performanceof
the refrigerator?
4. What aspects are important in the choice of a refrigerant fluid?Justify
3.3 Problems
After answering the previous questions solve the followingexercises from the
book: 10.2 10.7, 10.8, 10.9, 10.22, 10.23 10.1D

GGRB28H3 Lecture 2: Lecture 2 notes

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