Chapter 13 States OF Matter
13.1 Properties of Fluids
Fluids—liquids and gas
have the to flow
Pressure-- equals force divided by the surface area
Units pascals
Alternative expression:
Solid , liquid, gas, pressure
Caused by motion of particles.
SOILDS Or lack of range of motion of particles.
Caused by the force that holds the molecules in place
Liquids molecules slide past one another but moving molecules still apply forces on objects
When you deal with the pressure of a liquid at rest, the medium is treated as a continuous distribution of matter
Gas KMT collisions between the surface and object result in forces
Conservation of momentum and impulse can be applied to explain the pressures present.
But when you deal with a gas pressure, it must be approached as an average pressure from molecular collisions with the walls.
ATMOSPHERIC PRESSURE
APP 10N per cm2
STANDARD PRESSURE UNITS
1 atmosphere = 760 mmHg = 29.92 inHg = 14.7 lb/in2 = 101.3 KPa
Practice problems Page 344 1-5
Gauge Pressure
Does the flat tire on your automobile have zero air pressure? If it is completely flat, it still has the atmospheric pressure air in it. To be sure, it has zero useful pressure in it, and your tire gauge would read zero pounds per square inch. Most gauges read the excess of pressure over atmospheric pressure and this excess is called "gauge pressure". While a useful measurement for many practical purposes, it must be converted to absolute pressure for applications like the ideal gas law.
Since a partial vacuum will be below atmospheric pressure, the phrase "negative pressure" is often used. Certainly there is no such thing as a negative absolute pressure, but small decreases in pressure are commonly used to entrain fluids in sprayers, in carburetors for automobiles, and many other applications. In the case of respiration, we say that the lungs produce a negative pressure of about -4 mmHg to take in air, which of course means a 4 mmHg decrease from the surrounding atmospheric pressure.
THE GAS LAWS
COMBINED GAS EQUATION
where the subscripts i and f refer to the initial and final states of some process. If the temperature is constrained to be constant, this becomes:
BOYLES LAW
If the pressure is constant, then the ideal gas law takes the form
CHARLES LAW
TEMP IN KELVIN
· n = number of moles
· R = universal gas constant = 8.3145 J/mol K
· N = number of molecules
· k = Boltzmann constant = 1.38066 x 10-23 J/K = 8.617385 x 10-5 eV/K
· k = R/NA
· NA = Avogadro's number = 6.0221 x 1023 /mol
Avogadro's number
Standard Temperature and Pressure
STP is used widely as a standard reference point for expression of the properties and processes of ideal gases. The standard temperature is the freezing point of water and the standard pressure is one standard atmosphere. These can be quantified as follows:
Standard temperature: 0°C = 273.15 K
Standard pressure = 1 atmosphere = 760 mmHg = 101.3 kPa
Standard volume of 1 mole of an ideal gas at STP: 22.4 liters
WS IDEAL GAS LAW
13.2 Forces with Liquids
COHESION--Molecules liquid state experience strong intermolecular attractive forces. When those forces are between like molecules.
For example, the molecules of a water droplet are held together by cohesive forces, and the especially strong cohesive forces at the surface constitute surface tension.
SURFACE TENSION
Surface tension is typically measured in dynes/cm, the force in dynes required to break a film of length 1 cm. Equivalently, it can be stated as surface energy in ergs per square centimeter. Water at 20°C has a surface tension of 72.8 dynes/cm compared to 22.3 for ethyl alcohol and 465 for mercury.
Cohesion and Surface Tension
The cohesive forces between molecules down into a liquid are shared with all neighboring atoms. Those on the surface have no neighboring atoms above, and exhibit stronger attractive forces upon their nearest neighbors on the surface. This enhancement of the intermolecular attractive forces at the surface is called surface tension. /Surface Tension of Water
The surface tension of water is 72 dynes/cm at 25°C . It would take a force of 72 dynes to break a surface film of water 1 cm long. The surface tension of water decreases significantly with temperature as shown in the graph. The surface tension arises from the polar nature of the water molecule.
Hot water is a better cleaning agent because the lower surface tension makes it a better "wetting agent" to get into pores and fissures rather than bridging them with surface tension. Soaps and detergents further lower the surface tension. /Surface Tension Examples
Walking on water
Small insects such as the water strider can walk on water because their weight is not enough to penetrate the surface. /Floating a needle
If carefully placed on the surface, a small needle can be made to float on the surface of water even though it is several times as dense as water. If the surface is agitated to break up the surface tension, then needle will quickly sink.Don't touch the tent!
Common tent materials are somewhat rainproof in that the surface tension of water will bridge the pores in the finely woven material. But if you touch the tent material with your finger, you break the surface tension and the rain will drip through. /Soaps and detergents
help the cleaning of clothes by lowering the surface tension of the water so that it more readily soaks into pores and soiled areas.Clinical test for jaundice
Normal urine has a surface tension of about 66 dynes/cm but if bile is present (a test for jaundice), it drops to about 55. In the Hay test, powdered sulfur is sprinkled on the urine surface. It will float on normal urine, but sink if the S.T. is lowered by the bile. /Washing with cold water
The major reason for using hot water for washing is that its surface tension is lower and it is a better wetting agent. But if the detergent lowers the surface tension, the heating may be unneccessary.Surface tension disinfectants
Disinfectants are usually solutions of low surface tension. This allow them to spread out on the cell walls of bacteria and disrupt them. One such disinfectant, S.T.37, has a name which points to its low surface tension compared to the 72 dynes/cm for water. /Can you think of another
Surface Tension and the Water Strider
ADHESIVE--When the attractive forces are between unlike molecules,
The adhesive forces between water molecules and the walls of a glass tube are stronger than the cohesive forces lead to an upward turning meniscus at the walls of the vessel and contribute to capillary action.
The attractive forces between molecules in a liquid can be viewed as residual electrostatic forces and are sometimes called van der Waals forces or van der Waals bonds.
Capillary Action
Capillary action is the result of adhesion and surface tension. Adhesion of water to the walls of a vessel will cause an upward force on the liquid at the edges and result in a meniscus which turns upward. The surface tension acts to hold the surface intact, so instead of just the edges moving upward, the whole liquid surface is dragged upward./
Capillary Action
Capillary action occurs when the adhesion to the walls is stronger than the cohesive forces between the liquid molecules. The height to which capillary action will take water in a uniform circular tube is limited by surface tension. Acting around the circumference, the upward force is/ / The height h to which capillary action will lift water depends upon the weight of water which the surface tension will lift:
The height to which the liquid can be lifted is given by
Capillary Action Calculation
/ / The height h to which Capillary action will lift water depends upon the weight of water which the surface tension will lift:The height to which the liquid can be lifted is given by
ViSCOSITY
Laminar Flow
The resistance to flow in a liquid can be characterized in terms of the viscosity of the fluid if the flow is smooth. In the case of a moving plate in a liquid, it is found that there is a layer or lamina which moves with the plate, and a layer which is essentially stationary if it is next to a stationary plate.
There is a gradient of velocity as you move from the stationary to the moving plate, and the liquid tends to move in layers with successively higher speed. This is called laminar flow, or sometimes "streamlined" flow. Viscous resistance to flow can be modeled for laminar flow, but if the lamina break up into turbulence, it is very difficult to characterize the fluid flow.
/ The common application of laminar flow would be in the smooth flow of a viscous liquid through a tube or pipe. In that case, the velocity of flow varies from zero at the walls to a maximum along the centerline of the vessel. The flow profile of laminar flow in a tube can be calculated by dividing the flow into thin cylindrical elements and applying the viscous force to them.Viscosity
The resistance to flow of a fluid and the resistance to the movement of an object through a fluid are usually stated in terms of the viscosity of the fluid. Experimentally, under conditions of laminar flow, the force required to move a plate at constant speed against the resistance of a fluid is proportional to the area of the plate and to the velocity gradient perpendicular to the plate. The constant of proportionality is called the viscosity .
Viscosity of Liquids and Gases
Liquids / Viscosity(Poise)
Acetone / 0.0032
Alcohol(ethyl) / 0.012
Blood (whole) / 0.04
Blood plasma / 0.015
Gasoline / 0.006
Glycerine / 14.9
Mercury / 0.016
Oil (light) / 1.1
Oil (heavy) / 6.6
Water / 0.01
/ Gases / Viscosity
(Poise)
Air / 0.00018
Helium / 0.00019
Methane / 0.00020
Nitrogen / 0.00018
Oxygen / 0.00020
Water vapor
(steam) / 0.00013
/ Viscosity has the SI units Pascal seconds (Pa s) which is called the Poiseuille. More commonly used is the dyne sec/cm2 which is called Poise. One Pa s is 10 Poise. The Poise is used in the table because of its more common usage. Data from Gustafson. These viscosities are at 20°C except for the blood and blood plasma which are at body temperature, 37°C, and for steam which is at 100°C.
13.3 Fluids at rest and in Motion
Pascal’s Principle
The force exerted on the second piston is equal to the force exerted on the first piston multiplied by the ratio of the second area divided by the 1st area.
Pressure is transmitted undiminished in an enclosed static fluid.
Hydraulic Press
A multiplication of force can be achieved by the application of fluid pressure according to Pascal's principle, which for the two pistons impliesP1 = P2
This allows the lifting of a heavy load with a small force, as in an auto hydraulic lift, but of course there can be no multiplication of work, so in an ideal case with no frictional loss:
Winput = Woutput
/
Example: Automobile Hydraulic Lift
For example, if the lift cylinder were 25 cm in diameter and the small cylinder were 1.25 cm in diameter, then the ratio of the areas is 400, so the hydraulic press arrangement gives a multiplication of 400 times the force. To lift a 6000 newton car, you would have to exert only 6000 N/400 = 15 N on the fluid in the small cylinder to lift the car. However, to lift the car 10 cm, you would have to move the oil 400 x 10cm = 40 meters. This is practical by pumping oil into this small cylinder with a small compressor.
Hydraulic Brakes
Static Fluid Pressure
The pressure exerted by a static fluid depends only upon the depth of the fluid, the density of the fluid, and the acceleration of gravity.
The pressure in a static fluid arises from the weight of the fluid and is given by the expression
Pstatic fluid = ρgh where / ρ = m/V = fluid densityg = acceleration of gravity
h = depth of fluid
The pressure from the weight of a column of liquid of area A and height h is
The most remarkable thing about this expression is what it does not include. The fluid pressure at a given depth does not depend upon the total mass or total volume of the liquid. The above pressure expression is easy to see for the straight, unobstructed column, but not obvious for the cases of different geometry which are shown.
Buoyancy
Buoyancy
Buoyancy arises from the fact that fluid pressure increases with depth and from the fact that the increased pressure is exerted in all directions (Pascal's principle) so that there is an unbalanced upward force on the bottom of a submerged object.
/ Since the "water ball" at left is exactly supported by the difference in pressure and the solid object at right experiences exactly the same pressure environment, it follows that the buoyant force on the solid object is equal to the weight of the water displaced (Archimedes' principle).Objects of equal volume experience equal buoyant forces.
Archimedes' Principle