GGRA03H3 Lecture 7: Lecture Seven

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aquamarineimpala638

17 Dec 2010

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Unsustainability, u see higher risks of healthy decline, and other declines. Giant cities are not a problem (theory), new york city most efficient in north america, generate less waste per capita. Large cities are often higher quality of life, attractive places to live, energy efficient, jobs created. Dystopia thought, there comes a point where a city becomes unliveable, in giant cities people don"t know each other, increase in crime, sci fi sees giant cities as problematic in future. There seems to be a distrust and fear of giant cities. Only 2 megacities, in 1950, tokyo and newyork. By 2007 there were 19 including 15 in developing countries. Has to be over 10 million population. In the past, it was 4 million, the number was lowered to provide more sample cities. Larger the city, higher land prices (more people competing for land) www. notesolution. com. At the centre, housing prices would be larger.

Related Questions

In this problem you are to consider an adiabatic expansion of anideal diatomic gas, which means that the gas expands with noaddition or subtraction of heat.

This applet shows the adiabatic compression and expansion of anideal monatomic gas with \gamma=5/3. It will help you to see thequalitative behavior of adiabatic expansions, though your actualcalculations will use a slightly different gamma.

Assume that the gas is initially at pressure p_0, volume V_0, andtemperature T_0. In addition, assume that the temperature of thegas is such that you can neglect vibrational degrees of freedom.Thus, the ratio of heat capacities is \gamma=C_p/C_V=7/5.

Note that, unless explicitly stated, the variable gamma should notappear in your answers--if needed use the fact that \gamma=7/5 foran ideal diatomic gas.

A. Find an analytic expression for p(V), the pressure as a functionof volume, during the adiabatic expansion.
Express the pressure in terms of V and any or all of the giveninitial values p_0, T_0, and V_0.

B. At the end of the adiabatic expansion, the gas fills a newvolume V_1, where V_1 > V_0. Find W, the work done by the gas onthe container during the expansion.
Express the work in terms of p_0, V_0, and V_1. Your answer shouldnot depend on temperature.

C. Find Delta U, the change of internal energy of the gas duringthe adiabatic expansion from volume V_0 to volume V_1.
Express the change of internal energy in terms of p_0, V_0, and/orV_1.

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

In certain cities, parking spaces are at a premium and anyavailable surface will be used for parking, even highly slopedroofs. Consider the SUV parked in the picture above. If you are thedriver, how can you be sure that your car wonât flip overbackwards?
The schematic diagram below gives a simplified model of thesituation with the SUV on the slope. We are approximating the SUVas a uniform cube three meters long and two meters high, mounted ontires a half-meter in diameter that are set in a half meter fromthe edges of the vehicle. The SUV has a mass of 1500 kg. Forsimplicity, we will ignore the mass of the tires. Assume that thecoefficient of static friction between the tires and the road is0.8. Using the principles of static equilibrium, letâs determinewhether the car will stay on the slope. In order to maintain staticrotational equilibrium, the magnitudes of the normal forces on theforward and rear wheels must adjust to create a situation of zeronet torque. In order to maintain static translational equilibrium,the static friction forces between the tires and the road mustadjust to create a situation of zero net force. If the angle Î¸ getstoo big, we will have a problem...
1. First, letâs assume that the angle Î¸ is 30 degrees (note thewheels are locked and donât roll) and the car is not moving. Whatis the magnitude of the normal force from the road on the frontwheels (top of incline)? On the back wheels (bottom of incline)?These normal force are unequal- why?
2. Now letâs take the situation to the extreme: what is the maximumvalue of the angle Î¸ which is possible, if the SUV is to remain instatic equilibrium? First, determine the maximum angle that the carwonât slide, and then determine the maximum angle that the carwonât rotate. What happens to the SUV first if the angle isexceeded? What is the normal force on the front (top of incline)wheels in this situation?
3. Assume that it rains, and the coefficient of static friction isreduced from 0.8 to 0.5. Now what is the maximum value of the angleÎ¸ for which the car can remain in static equilibrium? If the angleÎ¸ exceeds this value, what happens to the SUV?

GGRA03H3 Lecture 7: Lecture Seven

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