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## Aigneis Frey

on 28 March 2014

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Kinetic Molecular Theory (KMT)
Basic Concepts:
Gases are made up of a large number of small particles which travel in constant straight-line motion and obey Newton's Laws
The volume of the molecules in a gas is negligable compared to the overall volume of the container (therefore, gases are mostly empty space)
All collisions between molecules are completely elastic meaning that no energy is lost or gained during the collisions
No force of attractive forces exists between molecules or the walls of the container
The collisions of the particles and the walls of the container cause gas pressure
The kinetic energy of the gas particles is dependent on the temperature of the gas
Step #2: Prepare Flight Pattern
Mr. Fredricksen must carefully plan his flight pattern in order to avoid issues, such as balloons popping or expanding too much. As altitude increases, temperature and pressure decrease. The decrease in pressure will cause the volume of the balloons to increase due to the inverse relationship. If the volume of the balloons increases too much, then they will pop. If too many of the balloons pop, the house may begin to fall due to a lack of balloons lifting it.
Step #3: Factor in and Anticipate Risks
There are certain risks that Mr. Fredricksen must be vigilant for, one of which being the (extremely unlikely) possibility of the Helium liquefying. If the Helium were to liquefy, the density would become greater than that of air, causing the balloons and house to plummet from the sky. Although this is an extremely unlikely scenario due to the extremely low temperature at which Helium liquefies (around 4.2 K), Mr. Fredricksen must still be aware of this risk. Additionally, effusion poses a possible risk. Simply put, the particles in Helium effuse (move through a semi-permeable membrane like a balloon) more quickly than the particles in other gases such as Hydrogen and Methane. This effusion would cause the balloons lifting Mr. Fredricksen's house to not float as high or as easily. In order to combat effusion, Mr. Fredricksen should use balloons made of the polymer Mylar as opposed to latex or rubber ones, since Mylar is more impermeable.
Boyle's Law
Since Helium behaves as an ideal gas, it obviously abides by the Ideal Gas Law (PV=nRT). It also abides by Boyle's Law (which can be derived from the Ideal Gas Law. This law states that volume is inversely related to pressure when temperature remains constant. Therefore, when the house rises to a higher altitude and the pressure decreases, volume increases. This will cause a risk of popping balloons, as previously mentioned.

Help Mr. Fredrickson and Russell escape!
Step #1:
We already know that we need to fill the balloons with a gas, but let's review our final choice of gas.
Helium
The density of air (1.225 kg/m³) is greater than the density of Hydrogen (0.0899 kg/m³), Methane (0.66 kg/m³), and Helium (0.1785 kg/m³). This means that all of these gases float. Although Hydrogen has a lower density than Helium, Helium is the best choice of gas because:
It is not flammable
It does not react with any other element
Its liquefication point is extremely low, around 4.2 degrees K (-268.95 degrees C)
Since Mr. Fredricksen will not be anywhere with such a low temperature, the liquefication of the gas is not a concern
Helium behaves as an ideal gas
Since the Ideal Gas Law applies to all gases, James Maxwell and Rudolf Clasius developed the kinetic theory of gases, basing it on the idea that all gases behave similarly in terms of particle movement. These following concepts explain the experimental behavior of gases on a molecular level.
Mr. Frecricksen should plan ahead and compensate for this issue by overestimating the number of balloons needed to lift his house. However, if the number of balloons he attatches proves to be too great, lifting the house higher than it should go, then he should construct a simple way to cut the strings of extraneous balloons. Likewise, this contraption can be to cut off balloons in order to land the house in Indianapolis.
Kinetic Energy
Kinetic energy is energy possessd by a particle due to its motion. At a constant temperature, all ideal gases have equal kinetic energy. Temperature and kinetic energy have a direct relationship, so as temperature increases so does kinetic energy. The velocity of the particles will aslo increase with the kinetic energy.
KE=1/2(mass)(speed)^2
Calculations
PV=nRT
0.9958(V)=(3)(0.0821)(24+273)
0.9958V=75.1511
V=73.45.45963045
V~73.5 L

Havana Cuba
510mL x 1L/1000mL=0.51L
PV=nRT
P(0.51)=(3)(0.0821)(20.3+273)
0.51P=72.23979
P=141.6466471
P~141.6 atm

Indianapolis, Indiana
PV=nRT
0.872(1.202)=(3)(0.0821)T
1.048144=0.2463T
T=4.255558262
T~4.3 ºK
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