Post on 26-Dec-2015
Chapter 13 Objectives
• Describe how fluids create pressure and relate Pascal's principle to some everyday occurrences
• Apply Archimedes' and Bernoulli's principles • Explain how forces within liquids cause
surface tension and capillary action, and relate the kinetic model to evaporation and condensation
Chapter 13 Objectives
• Compare solids, liquids, gases, and plasmas at a microscopic level, and relate their properties to their structures
• Explain why solids expand and contract when the temperature changes
• Calculate the expansion of solids and discuss the problems caused by expansion
Pressure
• Pressure is a result of gas molecules crashing into things.
• As the molecules collide with objects (such as walls of a container) they impart a force onto the object.
• Momentum is conserved as the objects bounce off and the force is directly related to the time of contact and change in momentum.
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Pressure: Temperature Influence
• Temperature is an indicator of the amount of random kinetic energy or molecules.
• As temperature goes up, so does the velocity of the molecules as they crash into the walls.
• Temperature up: Increase in pressure
Pressure: Volume Influence
• Pressure is also related to density (which is a combination of volume and mols).
• As density decreases, the molecules are more spread out and have less chance of colliding with the walls, which results in lower pressure.
• Density up: Pressure up
Pressure
• Pressure is measured in many things, but the SI unit is Pascals: Newtons per meters2
• Question: Estimate (to an order of magnitude) the pressure on your feet to the ground.
PV = NkT (Don’t Write))
This is the way physicists’ describe gas pressure and volume.
• This describes the Microscopic form of gas, where as PV=nRT describes the macroscopic form of gas
• N = number of molecules • k = Boltzmann’s constant = 1.38 E-23 J/K• V = Meters Cubed (not Liters)• P = Pascals
Other Gas Laws (know these)
• The PV = NkT is actually the combined gas law, and often not necessary to use, but always gets the right answer regardless
• Charles Law = • Gay-Lussac’s Law = • Boyle’s Law
• Avogadro’s =
TV TP
VP
1
NP
Question
• A certain jar is closed. The volume of the jar is 22.4 L and the temperature inside the jar is 273 K.
• What happens to the pressure if– Temp is raised?– More gas is added?– Volume decreases?
Question
• Before going on a trip, you check the tire pressure of your car wheels. The pressure reads 31.0 lb/in2 (214 kPa) at a temperature of 15.0 C. After driving for a few hours, you stop and take the pressure of the tires again. The pressure reads 35.0 lb/in2 (241 kPa). What is the temperature of the air in the tires now (assume no loss of air or change in volume)?
Follow up Question
• Suppose you then released some air, to keep the pressure between 28-32 psi. If you brought the psi down to 31 again, what will the gauge pressure read when the tires cool back down to 15.0 C?
Kinetic Energy and Temperature
• Temperature again, is average random kinetic energy. Rolling a ball down a bowling lane does increase the total amount of kinetic energy, but it does not increase the temperature (other than resistance).
Kinetic Energy (don’t write equation)
• The average kinetic energy of gas molecules is proportional to the absolute temperature of the gas.
• Total kinetic energy equals Boltzmann constant times Kelvin
kTKTr 2
3
Maxwell Boltzmann Graph
• A probability graph of what the average kinetic energy of each molecule is.
• If all molecules are the same, then the X-axis can become velocity.
Maxwell Boltzmann Graph
• Some water evaporates before 100 C because temp is an average with a huge range of motion
Maxwell Boltzmann Graph
• The area under the graph is a fraction of how many molecules are moving this fast at the given temperatures. Low Temperatures have a very high peak, but low average velocity.
• High temperatures are much more rounded but extend further on the X-axis.
Average* Speed (don’t write eq)
• The “average speed” of the gas molecules can be described by the following equation.
• m is mass of molecule (kg)• Vrms = not quite the same as average speed.
RMS refers to square root of the mean of the speed squared, and is generally higher than average
m
kTvrms
3
Average speed
• What has a larger average speed? Argon (molar mass 40) or Nitrogen (molar mass 28)?
• Which molecule would have a larger Maxwell Boltzmann range, Argon or Nitrogen?
Archimedes principle
• Mass of water displaced equals the buoyant force of the water– If 10 grams of water are displaced by a boat, the
boat is lifted with a bouyant force of 10 grams– If your density is less than 1, you can think of the
density being a percentage of what is under the water.• Density of 0.9 = 90% of volume under the water
– Mercury 13x more dense, 13 times the lift
Thermal Expansion of Liquids/Solids
• When molecules have more energy, they take up more room.
• The range of jiggling is much larger. As temperature goes up, objects increase in size due to the increase in temperature.
• Very noticeable for gases, less noticeable for solids and liquids, but still important for some projects.
Thermal Expansion
• Coefficient of Thermal Expansion – Alpha: A value which states: How much does the
material change with temperature? • Change in T is in Kelvin, Change in Length over
initial Length
TL
L
O
Relevance to Engineers
• Thermostats have two different metals connected to one another. (Bimetallic)
• As temperature changes, one expands faster than the other, causing it to bend (turn on and off switch)
Relevance to Engineers
• Important for Roads, as joints are left on bridges to expand during warm weather– But not so far apart
that when it gets cold they lose contact…
Relevance to those scared of the dark…
• House creaks during the night as thermal contraction takes place
Relevance to Engineers
• St. Louis Arch
Some Alpha Values (all E-6)
• Brick 1.0• Glass (Pyrex) 3.25• Granite 8.0• Glass (most types) 9.4• Iron/Steel/Cement 12.0• Copper 16.0• Brass 19• Lead 29
Questions
• A brass rod of length 10.0cm is at an intial temperature of 20 C. If the temperature increases to 50 C, by what length will the brass rod change?
• Two steel rods of length 70.0 m each are separated by 1.0cm at an initial temperature of 273 K. At what temperature do the two steel rods touch?
Question
• Two steel beams, one of length 10.0 m and the other of length 20.0 m are at the same temperature. Which beam, if either, will have the larger change in length if temperature changes?
• Molecularly, what are a few factors which influence the alpha value? How do they affect the expansion?
Area and Volume Expansion
• If length expands and contracts under temperature changes, then since area and volume are affected by length, they will also expand.
• Area Expansion
• Volume Expansion
TA
A
2
TV
V
Area and Volume Expansion
• Liquids and Gases do not have alpha values (for linear expansion)
• For Solids, their beta values are 3 times the size of their alpha values (due to 3 dimensional expansion)
Questions
• A 30cm by 30cm aluminum foil sheet is at an initial temperature of 300 K. What is the new area of the aluminum foil if the temperature decreases by 20 K?
• When is the best time to fill up your car with gasoline? Why?
Gasoline Question
• By what percentage does a change in 20 C (roughly 40 F) make in the volume of 1.0 gallons of fuel? Is filling up in the morning worth it? Beta value of Gasoline = 950 E-6
– (also think about temperature difference below surface of the earth)
Question
• Water has two beta values: – 0 Degrees C = - 68– 20 Degrees C = 207
• Explain the difference and what is going on.
Capillary Action
• The ability of a molecule to pull itself up (through electromagnetic interaction)
• Cohesion: Attractive force to oneself• Adhesion: Attractive force to others