GGR100H1 Final: finals study guide part 1

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erinsalmon243

21 Apr 2011

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Midterm exam questions and answers: this treaty initially drawn up in 1493, then revised in 1494, decreed that most of south. 107 under mexico: at the time of spanish conquest in the 16th century the valley of mexico (the current location of mexico city) was home to about 300,000 people from what indigenous group, aztec

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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

GGR100H1 Final: finals study guide part 1

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