GGR252H1 : Ch 12.docx

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22 Apr 2012

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Traditionally chain stores have tended to dominate the planned shopping centres while independent have been restricted to unplanned central city or retail strip locations. Recent retail strips are typically located in the suburbs, geared towards auto-dependent suburban shopper, with parking a key consideration. Dominant business elements of centers and specialized areas are interpreted in terms of central place postulates. Davies: the retail pattern of the city center can be viewed in broad terms as a nucleation that is structured in a series of zonal belts of retail activity. Jones: provided a reworking of the berry model, dividing the urban retail system into two structural forms strips and centers, with each differentiated according to its location in either inner-city or suburban environments. Jones and simmons: classify retail types as either unplanned nodes, linear strips or planned shopping centers by the size of market they serve ranging from metropolitan to neighbourhood.

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Theory: Topics that you should be familiar with are: significantfigures, least count and estimated fraction, systematic and randomerrors, accuracy versus precision, percent difference and percenterror. These topics should have been covered in class already (orperhaps in an introduction to the lab manual or in a handout). Itis assumed that the instructor has discussed how to use the massbalance, etc.
Introduction: The goal of section I of this experiment is tomeasure (to the correct least count and estimated fraction) andcalculate (to the correct number of significant figures) thedensity of a metal ball and compare it to a table of accepteddensities (?=7.8x103 kg/m3).
To accomplish this goal keep in mind that: ? = m/V and Vsphere =(4/3) p r3
In the space below create a data table, show your calculations indetail, and compare your measured answer to accepted values givenabove. (Would you calculate a percent error or a percentdifference?)
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II. Is g (the acceleration due to gravity) a constant? If so, whatis it?
1) SetuptheFree-FallApparatusasdemonstratedbytheinstructor.
2)MeasurethetimeittakesforthemetalballtofallthroughthesuggesteddisplacementsshowninDataTable 1. Be sure to do 4 trials for each fall and take the averageof your time and displacement. For each trial measure thedisplacement and record your results as precisely as possible. Becareful how you measure the displacement!
Data Table 1
Displacement (meters) Time
Trial 1
___.40___ m .281 s
______.40_ m .284 s
___.40____ m .283 s
____.40___ m .285 s
Average Displacement =.40 m Average time .0285 s
Trial 2
____.60___ m .357 s
____.60___ m .358 s
_____.60__ m .347 s
____.60___ m .347 s
Time (seconds)
Average Displacement = .60 Average Time = .352
Trial3
_.80____ m .402 s
_.80____ m .401 s
_.80______ m .402 S
_.80___ m .401 s
Average Displacement = .80 m Average Time =.401 s

Trial4
__ 1.00____ m .454 s
___1.00____ m .453 s
___1.00____ m .463 s
___1.00____ m .453 s
Average Displacement = 1.00 m Average Time =.455 s
3)PlotDisplacement(usetheaveragedisplacement)asafunctionofTime(usetheaveragetime)usingacomputer software that you know the best. (Does Displacement orTime go on the âverticalâ (or y) axis? Make sure that you label theaxes of your graph properly and give the graph a descriptivetitle.), Please include (0,0) point.
4)UsetheCurveFitFunctiontotrytofindthecurvethatistheclosestfitforthegraph.Whichofthefollowing curve types gives the best fit? Try each to findout.
a) linear fit? b) quadratic (power 2)? c) exponential? d) Power?
The curve with the correlation coefficient (R) closest to 1 has theclosest fit. (e.g. 0.997 is better than 0.956)
5)Printthecurvewiththeclosestfit(oneforeachmemberofthelabgroup).Besureyourgraphincludesthe equation for your fit.
6)Canyoudeterminetheexperimentalaccelerationofgravityfromthisgraph?Explainhowandshowyourwork.
7)Ifalinearfunctionisnotthebestfitofyourplotfromstep3),howwouldyouplotdisplacementandtimeso that the resulting plot is linear? Explain. (Ask your instructorfor a hint if you are not sure of what to do, but be sure to thinkabout it for a while before you ask.)
3
8)Printacopyofthegraphforeachlabpartnershowingalinearfittoyourdataandproperlylabeledaxes.
9)Canyoudeterminetheexperimentalaccelerationduetogravityfromthisgraph?Explainandshowyourwork.
10) How do your experimental values of âgâ compare with theaccepted value (g = 9.80 m/s2) for the acceleration of gravity?Give a mathematical comparison using what you learned aboutmeasurements previously. (Show work)
4
Question and further procedures
1. What is the greatest source of error in performing theexperiment? Is this error random or systematic? Explain.
2. At this point you should have calculated g in two different ways(A quadratic graph, and a linear graph). Which technique do youthink is best? Do all two techniques give the same answer? If not,which technique do you think has the most error?
3. How might you modify your procedures to determine whether or notg depends on the mass of the falling object? Do the experiment andcalculate g using your favorite technique.

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

GGR252H1 : Ch 12.docx

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