Fluids Fluids are substances that can flow, such as liquids and gases, and even a few solids. Fluids...

FluidsFluids

Fluids are substances that can Fluids are substances that can flowflow, such as liquids and gases, , such as liquids and gases, and even a few solids.and even a few solids.

In Physics B, we will limit our In Physics B, we will limit our discussion of fluids to substances discussion of fluids to substances that can easily flow, such as liquids that can easily flow, such as liquids and gases.and gases.

Review: DensityReview: Density

= m/V= m/V: density (kg/m: density (kg/m33))m: mass (kg)m: mass (kg)V: volume (mV: volume (m33))

Units:Units:kg/mkg/m33

You should remember how to do density calculations from chemistry!

PressurePressure P = F/AP = F/A

P : pressure (Pa)P : pressure (Pa)F: force (N)F: force (N)A: area (mA: area (m22))

Pressure unit: Pressure unit: PascalPascal ( 1 Pa = 1 N/m ( 1 Pa = 1 N/m22)) The force on a surface caused by The force on a surface caused by

pressure is always normal (or pressure is always normal (or perpendicular) to the surface. This perpendicular) to the surface. This means that the pressure of a fluid is means that the pressure of a fluid is exerted in all directions, and is exerted in all directions, and is perpendicular to the surface at every perpendicular to the surface at every location.location.

balloon

Sample ProblemSample Problem Calculate the net force on an airplane window if cabin Calculate the net force on an airplane window if cabin

pressure is 90% of the pressure at sea level, and the pressure is 90% of the pressure at sea level, and the external pressure is only 50% of that at sea level. external pressure is only 50% of that at sea level. Assume the window is 0.43 m tall and 0.30 m wide.Assume the window is 0.43 m tall and 0.30 m wide.

Atmospheric PressureAtmospheric Pressure

Atmospheric pressure is Atmospheric pressure is normally about normally about 100,000 100,000 PascalsPascals..

Differences in Differences in atmospheric pressure atmospheric pressure cause winds to blow.cause winds to blow.

Low atmospheric pressure Low atmospheric pressure inside a hurricane’s eye inside a hurricane’s eye contributes to the severe contributes to the severe winds and the development of winds and the development of the the storm surgestorm surge..

Hurricane Katrina’s Storm SurgeHurricane Katrina’s Storm Surge

Mississippi River Gulf OutletMississippi River Gulf OutletNew Orleans East/St. Bernard ParishNew Orleans East/St. Bernard Parish

The Pressure of a LiquidThe Pressure of a Liquid P = P = gh gh

P: pressure (Pa)P: pressure (Pa) : density (kg/m: density (kg/m33)) g: acceleration constant (9.8 m/sg: acceleration constant (9.8 m/s22)) h: height of liquid column (m)h: height of liquid column (m)

This is often called This is often called hydrostatic pressurehydrostatic pressure if the if the liquid is water. It excludes atmospheric pressure.liquid is water. It excludes atmospheric pressure.

It is also sometimes called It is also sometimes called gauge pressuregauge pressure, since , since a diver’s pressure gauge will read hydrostatic a diver’s pressure gauge will read hydrostatic pressure. Gauge pressure readings never include pressure. Gauge pressure readings never include atmospheric pressure, but only the pressure of atmospheric pressure, but only the pressure of the fluid.the fluid.

Absolute pressureAbsolute pressure is obtained by adding the is obtained by adding the atmospheric pressure to the hydrostatic pressureatmospheric pressure to the hydrostatic pressure ppabsabs = p = patmatm + + ghgh

Sample ProblemSample ProblemCalculate for the bottom of a 3 meter (approx 10 feet) Calculate for the bottom of a 3 meter (approx 10 feet) deep swimming pool full of water:deep swimming pool full of water:

(a) hydrostatic pressure(a) hydrostatic pressure

(b) absolute pressure(b) absolute pressure

Which one of these represents the gauge pressure?Which one of these represents the gauge pressure?

Hydrostatic Pressure Hydrostatic Pressure in Dam Designin Dam Design

http://www.iit.edu/~karagian/smart00/physics.html

The depth of Lake Mead at the Hoover Dam is 600ft. What is the hydrostatic pressure at the base of the dam?

Hydrostatic Hydrostatic Pressure in Levee Pressure in Levee

DesignDesignHurricane Katrina, August 2005

A hurricane’s storm surge can overtop levees, but a bigger problem can be increasing the hydrostatic pressure at the base of the levee.

New Orleans Elevation MapNew Orleans Elevation MapNew Orleans is largely below sea level, New Orleans is largely below sea level, and relies upon a system of levees to keep and relies upon a system of levees to keep the lake and the river at baythe lake and the river at bay

Sample ProblemSample ProblemCalculate the increase in hydrostatic pressure Calculate the increase in hydrostatic pressure experienced by the levee base for an expected (SPH experienced by the levee base for an expected (SPH Design) storm surge. How does this compare to the Design) storm surge. How does this compare to the increase that occurred during Hurricane Katrina, where increase that occurred during Hurricane Katrina, where the water rose to the top of the levee?the water rose to the top of the levee?

Floating is a type of Floating is a type of equilibriumequilibrium

An upward force An upward force counteracts the force of counteracts the force of gravity for these objects. gravity for these objects. This upward force is This upward force is called the called the buoyant forcebuoyant force..

Fbuoy

mg

The Buoyant ForceThe Buoyant Force Archimedes’ Principle: a body immersed in a Archimedes’ Principle: a body immersed in a

fluid is fluid is buoyedbuoyed up by a up by a forceforce that is equal to the that is equal to the weight of the fluid displaced.weight of the fluid displaced.

FFbuoybuoy = = VgVg FFbuoybuoy: the buoyant force exerted on a submerged or : the buoyant force exerted on a submerged or

partially submerged object.partially submerged object. V: the volume of displaced liquid.V: the volume of displaced liquid. : the density of the displaced liquid.: the density of the displaced liquid.

When an object floats, the upward buoyant When an object floats, the upward buoyant force equals the downward pull of gravity.force equals the downward pull of gravity.

The buoyant force can float very heavy objects, The buoyant force can float very heavy objects, and acts upon objects in the water whether and acts upon objects in the water whether they are floating, submerged, or even sitting on they are floating, submerged, or even sitting on the bottom.the bottom.

Buoyant force on Buoyant force on submerged objectsubmerged object

mg

Fbuoy = Vg

A sharks body is not neutrally buoyant, and so a shark must swim continuously or he will sink deeper.


mg

VgSCUBA divers use a buoyancy control system to maintain neutral buoyancy (equilibrium!).


mg

Vg

If the diver wants to rise, he inflates his vest, which increases the amount of water he displaces, and he accelerates upward.

Buoyant force on floating Buoyant force on floating objectobject

mg

Vg

If the object floats on the surface, we know for a fact Fbuoy = mg! The volume of displaced water equals the volume of the submerged portion of the ship.

Sample problemSample problemAssume a wooden raft has 80.0% of the density of water. The Assume a wooden raft has 80.0% of the density of water. The dimensions of the raft are 6.0 meters long by 3.0 meters wide by dimensions of the raft are 6.0 meters long by 3.0 meters wide by 0.10 meter tall. How much of the raft rises above the level of the 0.10 meter tall. How much of the raft rises above the level of the water when it floats?water when it floats?

Sample problemSample problem You want to transport a man and a horse across a still lake on a wooden You want to transport a man and a horse across a still lake on a wooden

raft. The mass of the horse is 700 kg, and the mass of the man is 75.0 raft. The mass of the horse is 700 kg, and the mass of the man is 75.0 kg. What must be the minimum volume of the raft, assuming that the kg. What must be the minimum volume of the raft, assuming that the density of the wood is 80% of the density of the water.density of the wood is 80% of the density of the water.

Parking in St. Bernard Parish Parking in St. Bernard Parish after Hurricane Katrinaafter Hurricane Katrina

““Mobile” Homes in St. Mobile” Homes in St. Bernard Parish after Bernard Parish after

Hurricane KatrinaHurricane Katrina

Estimation problemEstimation problem

Estimate the mass of this house in kg.Estimate the mass of this house in kg.

Buoyancy Buoyancy LabLab

Using the Using the equipment equipment provided, verify provided, verify that the density that the density of water is of water is 1,000 kg/m1,000 kg/m33. .

Report must Report must include:include: Free body Free body

diagrams.diagrams. All data.All data. Calculations.Calculations.

waterair

Note: established value for the density of pure water is 1,000 kg/m3.

Reading a Venier CaliperReading a Venier Caliper

Fluid Flow ContinuityFluid Flow Continuity

The volume per unit time of a liquid flowing The volume per unit time of a liquid flowing in a pipe is constant throughout the pipe.in a pipe is constant throughout the pipe.

V = AvtV = Avt V: volume of fluid (mV: volume of fluid (m33)) A: cross sectional areas at a point in the pipe (mA: cross sectional areas at a point in the pipe (m22)) v: speed of fluid flow at a point in the pipe (m/s)v: speed of fluid flow at a point in the pipe (m/s) t: time (s)t: time (s)

AA11vv11 = A = A22vv22 AA11, A, A22: cross sectional areas at points 1 and 2: cross sectional areas at points 1 and 2 vv11, v, v22: speed of fluid flow at points 1 and 2: speed of fluid flow at points 1 and 2

http://library.thinkquest.org/27948/bernoulli.html

Sample problemSample problem A pipe of diameter 6.0 cm has fluid flowing through it at A pipe of diameter 6.0 cm has fluid flowing through it at

1.6 m/s. How fast is the fluid flowing in an area of the pipe 1.6 m/s. How fast is the fluid flowing in an area of the pipe in which the diameter is 3.0 cm? How much water per in which the diameter is 3.0 cm? How much water per second flows through the pipe?second flows through the pipe?

Natural WaterwaysNatural Waterways

Flash flooding can be explained by fluid flow Flash flooding can be explained by fluid flow continuity.continuity.

Sample problemSample problemThe water in a canal flows 0.10 m/s where the canal is 12 The water in a canal flows 0.10 m/s where the canal is 12 meters deep and 10 meters across. If the depth of the canal meters deep and 10 meters across. If the depth of the canal is reduced to 6.5 meters at an area where the canal narrows is reduced to 6.5 meters at an area where the canal narrows to 5.0 meters, how fast will the water be moving through this to 5.0 meters, how fast will the water be moving through this narrower region? What will happen to the water if something narrower region? What will happen to the water if something prevents it from flowing faster in the narrower region?prevents it from flowing faster in the narrower region?

Artificial WaterwaysArtificial Waterways

Flooding from the Mississippi River Gulf Outlet was responsible for catastrophic flooding in eastern New Orleans and St. Bernard during Hurricane Katrina.

Fluid Flow Fluid Flow Continuity in Continuity in WaterwaysWaterways

A hurricane’s storm surge can be “amplified” by waterways that become narrower or shallower as they move inland.

Mississippi River Gulf Outlet levees are overtopped by Katrina’s storm surge.

Bernoulli’s TheoremBernoulli’s Theorem

The sum of the pressure, the potential The sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume, and the kinetic energy per unit volume at any one location energy per unit volume at any one location in the fluid is equal to the sum of the in the fluid is equal to the sum of the pressure, the potential energy per unit pressure, the potential energy per unit volume, and the kinetic energy per unit volume, and the kinetic energy per unit volume at any other location in the fluid for a volume at any other location in the fluid for a non-viscous incompressible fluid in non-viscous incompressible fluid in streamline flow.streamline flow.

All other considerations being equal, when All other considerations being equal, when fluid moves faster, the pressure drops.fluid moves faster, the pressure drops.

Bernoulli’s TheoremBernoulli’s Theorem

P + P + g h + ½ g h + ½ vv22 = Constant = ConstantP : pressure (Pa)P : pressure (Pa) : density of fluid (kg/m: density of fluid (kg/m33))g: gravitational acceleration constant g: gravitational acceleration constant

(9.8 m/s(9.8 m/s22))h: height above lowest point (m)h: height above lowest point (m)v: speed of fluid flow at a point in the v: speed of fluid flow at a point in the

pipe (m/s)pipe (m/s)

Sample ProblemSample Problem Knowing what you know about Bernouilli’s principle, Knowing what you know about Bernouilli’s principle,

design an airplane wing that you think will keep an design an airplane wing that you think will keep an airplane aloft. Draw a cross section of the wing.airplane aloft. Draw a cross section of the wing.

Bernoulli’s Principle and Bernoulli’s Principle and HurricanesHurricanes

In a hurricane or tornado, the high In a hurricane or tornado, the high winds traveling across the roof of a winds traveling across the roof of a building can actually lift the roof building can actually lift the roof off the building.off the building.

http://video.google.com/videoplay?docid=6649024923387081294&q=Hurricane+Roof&hl=en

Big City EvacuationBig City Evacuation

These URLs, some of which are disputed, These URLs, some of which are disputed, are provided for the Big City Evacuation are provided for the Big City Evacuation projectprojecthttp://www.mvn.usace.army.mil/ChannelSurveys/

survey.asp?prj_id=15http://en.wikipedia.org/wiki/Mississippi_River_Gulf

_Outlethttp://www.cclockwood.com/stockimages/hurrican

ekatrina_MississippiGulfOutlet.htmhttp://www.washingtonpost.com/wp-dyn/content/a

rticle/2005/09/13/AR2005091302196.html

Storm Surges in Storm Surges in HurricanesHurricanes

http://www.nhc.noaa.gov/aboutsshs.shtml

http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/hurr/home.rxml

http://science.howstuffworks.com/http://science.howstuffworks.com/hurricane.htmhurricane.htm

http://www.nd.edu/~adcirc/katrina.htmhttp://www.nd.edu/~adcirc/katrina.htm

Bernoulli Effect in DesignBernoulli Effect in Design

http://en.wikipedia.org/wiki/Lift_(force)http://en.wikipedia.org/wiki/Lift_(force) http://scienceworld.wolfram.com/http://scienceworld.wolfram.com/

physics/topics/Aerodynamics.htmlphysics/topics/Aerodynamics.html http://user.uni-frankfurt.de/~weltner/http://user.uni-frankfurt.de/~weltner/

Flight/PHYSIC4.htmFlight/PHYSIC4.htm http://www.bbc.co.uk/dna/h2g2/http://www.bbc.co.uk/dna/h2g2/

A517169A517169 http://www-history.mcs.st-http://www-history.mcs.st-

andrews.ac.uk/Mathematicians/andrews.ac.uk/Mathematicians/Bernoulli_Daniel.htmlBernoulli_Daniel.html

Building for HurricanesBuilding for Hurricanes

http://www.campcastaway.com/http://www.campcastaway.com/ http://www.bbc.co.uk/dna/h2g2/http://www.bbc.co.uk/dna/h2g2/

A517169A517169

Building in the WetlandsBuilding in the Wetlands

http://www.campcastaway.com/http://www.campcastaway.com/ http://www.bbc.co.uk/dna/h2g2/http://www.bbc.co.uk/dna/h2g2/

A517169A517169

Hydrostatic Pressure: Hydrostatic Pressure: DamsDams

http://www.pbs.org/wgbh/http://www.pbs.org/wgbh/buildingbig/dam/basics.htmlbuildingbig/dam/basics.html

http://en.wikipedia.org/wiki/Damhttp://en.wikipedia.org/wiki/Dam(This has information on failed dams at (This has information on failed dams at

end of article).end of article). http://http://

www.hooverdamtourcompany.com/www.hooverdamtourcompany.com/build.htmlbuild.html

http://www.dur.ac.uk/~des0www4/http://www.dur.ac.uk/~des0www4/cal/dams/foun/press.htmcal/dams/foun/press.htm

Hydrostatic Pressure: LeveesHydrostatic Pressure: Levees http://www.innovtg.com/http://www.innovtg.com/

Levees.htmLevees.htm http://www.wired.com/news/http://www.wired.com/news/

technology/0,68746-0.htmltechnology/0,68746-0.html

ThermodynamicsThermodynamics

Thermodynamics is the study of Thermodynamics is the study of heat and thermal energy.heat and thermal energy.

Thermal properties (heat and Thermal properties (heat and temperature) are based on the temperature) are based on the motion of individual molecules, so motion of individual molecules, so thermodynamics is a lot like thermodynamics is a lot like chemistry.chemistry.

Total energyTotal energy

E = U + K + EE = U + K + Eintint

U: potential energyU: potential energyK: kinetic energyK: kinetic energyEEintint: internal or thermal energy: internal or thermal energy

Potential and kinetic energies are Potential and kinetic energies are specifically for “specifically for “bigbig” objects, and ” objects, and represent represent mechanical energymechanical energy..

Thermal energy is related to the kinetic Thermal energy is related to the kinetic energy of the energy of the moleculesmolecules of a substance. of a substance.

Temperature and HeatTemperature and Heat

TemperatureTemperature is a measure of the average is a measure of the average kinetic energy of the molecules of a kinetic energy of the molecules of a substance. Think o it as a measure of how substance. Think o it as a measure of how fast the molecules are moving. The unit is fast the molecules are moving. The unit is OOC or K.C or K.

Temperature is NOT heat!Temperature is NOT heat! HeatHeat is the internal energy that is is the internal energy that is

transferred between bodies in contact. The transferred between bodies in contact. The unit is Joules (J), or sometimes calories unit is Joules (J), or sometimes calories (cal).(cal).

A difference in temperature will cause heat A difference in temperature will cause heat energy to be exchanged between bodies in energy to be exchanged between bodies in contact. When two bodies are at the same contact. When two bodies are at the same temperature, no heat is transferred. This is temperature, no heat is transferred. This is called called Thermal EquilibriumThermal Equilibrium..

Ideal Gas LawIdeal Gas Law

PP1 1 VV1 1 / T/ T11 = P = P2 2 VV2 2 / T/ T22 PP11, P, P22: initial and final pressure (any : initial and final pressure (any

unit)unit)VV11, V, V22: initial and final volume (any : initial and final volume (any

unit)unit)TT11, T, T22: initial and final temperature (in : initial and final temperature (in

Kelvin!)Kelvin!) Temperature in K is obtained from Temperature in K is obtained from

temperature in temperature in ooC by adding 273.C by adding 273.

Sample problemSample problem Suppose an ideal gas occupies 4.0 liters at 23Suppose an ideal gas occupies 4.0 liters at 23ooC and C and

2.3 atm. What will be the volume of the gas if the 2.3 atm. What will be the volume of the gas if the temperature is lowered to 0temperature is lowered to 0ooC and the pressure is C and the pressure is increased to 3.1 atm.increased to 3.1 atm.

Ideal Gas EquationIdeal Gas Equation

P V = n R T P V = n R T P: pressure (in Pa)P: pressure (in Pa)V: volume (in mV: volume (in m33))n: number of molesn: number of molesR: gas law constantR: gas law constant

8.31 J/(mol K)8.31 J/(mol K)

T: temperature (in K)T: temperature (in K)

Sample problemSample problem Determine the number of moles of an ideal Determine the number of moles of an ideal

gas that occupy 10.0 mgas that occupy 10.0 m33 at atmospheric at atmospheric pressure and 25pressure and 25ooC.C.

Ideal Gas EquationIdeal Gas Equation

PV = n R T (using moles)PV = n R T (using moles) P V = N kP V = N kBB T (using molecules) T (using molecules)

P: pressure (Pa)P: pressure (Pa)V: volume (mV: volume (m33))N: number of moleculesN: number of moleculeskkBB: Boltzman’s constant: Boltzman’s constant

1.38 x 101.38 x 10-23-23 J/K J/K

T: temperature (K)T: temperature (K)

Sample problemSample problem Suppose a near vacuum contains 25,000 molecules of Suppose a near vacuum contains 25,000 molecules of

helium in one cubic meter at 0helium in one cubic meter at 0ooC. What is the pressure?C. What is the pressure?

Sample problemSample problem Can you find a relationship between the Universal Can you find a relationship between the Universal

Gas Law constant R (8.31 J/mol K) and Boltzman’s Gas Law constant R (8.31 J/mol K) and Boltzman’s constant kconstant kBB (1.38 x 10 (1.38 x 10-23-23 J/K) ? J/K) ?

Kinetic Theory of GasesKinetic Theory of Gases

1.1. Gases consist of a large number of Gases consist of a large number of molecules that make elastic collisions molecules that make elastic collisions with each other and the walls of the with each other and the walls of the container.container.

2.2. Molecules are separated, on average, Molecules are separated, on average, by large distances and exert no forces by large distances and exert no forces on each other except when they collide.on each other except when they collide.

3.3. There is no preferred position for a There is no preferred position for a molecule in the container, and no molecule in the container, and no preferred direction for the velocity.preferred direction for the velocity.

SimulationsSimulations

http://comp.uark.edu/~jgeabana/http://comp.uark.edu/~jgeabana/mol_dyn/KinThI.htmlmol_dyn/KinThI.html

http://intro.chem.okstate.edu/http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm1314F00/Laboratory/GLP.htm

Average Kinetic EnergyAverage Kinetic Energyof a Gasof a Gas

KKaveave = 3/2 k = 3/2 kBBTTKKaveave: average kinetic energy (J): average kinetic energy (J)

kkBB: Boltzmann’s Constant (1.38 x 10: Boltzmann’s Constant (1.38 x 10-23-23 J/K) J/K)T: Temperature (K)T: Temperature (K)

The molecules have a range of kinetic The molecules have a range of kinetic energies; Kenergies; Kaveave is just the average of is just the average of that range.that range.

Sample ProblemSample Problem What is the average kinetic energy and the What is the average kinetic energy and the

average speed of oxygen molecules in a gas average speed of oxygen molecules in a gas sample at 0sample at 0ooC?C?

Sample ProblemSample Problem Suppose nitrogen and oxygen are in a sample of gas Suppose nitrogen and oxygen are in a sample of gas

at 100at 100ooC. C. A) What is the ratio of the average kinetic energies A) What is the ratio of the average kinetic energies

for the two molecules?for the two molecules? B) What is the ratio of their average speeds?B) What is the ratio of their average speeds?

SystemSystem

Boundary

For our purposes, the system will almost always be an ideal gas.

System BoundarySystem Boundary

The system boundary controls how The system boundary controls how the environment affects the system.the environment affects the system.

If the boundary is “closed to mass”, If the boundary is “closed to mass”, that means that mass can’t get in that means that mass can’t get in or out.or out.

If the boundary is “closed to If the boundary is “closed to energy”, that means energy can’t energy”, that means energy can’t get in or out.get in or out.

DiscussionDiscussion

Consider the earth as a system. Consider the earth as a system. What type of boundary does it What type of boundary does it have?have?

First Law of ThermodynamicsFirst Law of Thermodynamics

U(Eint)

WQ

Awkward notation WARNING!Awkward notation WARNING!

We all know that U is potential energy in We all know that U is potential energy in mechanics. However…mechanics. However…

U is EU is Eintint (thermal energy) in thermodynamics! (thermal energy) in thermodynamics! Yuk.Yuk. This means when we are in thermo, U is This means when we are in thermo, U is

thermal energy, which is related to thermal energy, which is related to temperature. When we are in mechanics, it is temperature. When we are in mechanics, it is potential energy, which is related to potential energy, which is related to configuration or position.configuration or position.

More about UMore about U

U is the sum of the kinetic energies of U is the sum of the kinetic energies of all molecules in a system (or gas).all molecules in a system (or gas).

U = N KU = N Kave ave

U = N (3/2 kU = N (3/2 kBBT)T) U = n (3/2 R T)U = n (3/2 R T)

Since kSince kBB = R /N = R /NAA

First Law of ThermodynamicsFirst Law of Thermodynamics

U = Q + WU = Q + WU: change in internal energy of system (J)U: change in internal energy of system (J)Q: heat added to the system (J). This heat Q: heat added to the system (J). This heat

exchange is driven by temperature exchange is driven by temperature difference. It occurs only if the boundary difference. It occurs only if the boundary allows energy transfer.allows energy transfer.

W: work done on the system (J). Work will W: work done on the system (J). Work will be related to the change in the system’s be related to the change in the system’s volume. It occurs only if the boundary can volume. It occurs only if the boundary can change shape in some way.change shape in some way.

This law is sometimes paraphrased as This law is sometimes paraphrased as “you can’t win”.“you can’t win”.

ProblemProblem A system absorbs 200 J of A system absorbs 200 J of heatheat energy from energy from

the environment and does 100 J of work on the environment and does 100 J of work on the environment. What is its change in the environment. What is its change in internal energy?internal energy?

ProblemProblem

How much work does the environment How much work does the environment do on a system if its internal energy do on a system if its internal energy changes from 40,000 J to 45,000 J changes from 40,000 J to 45,000 J without the addition of heat?without the addition of heat?

Walker, 18.5Walker, 18.5

A B

B C

C A

Q W U

-53 J a) b)

-280 J -130 J c)

d)150 Je)

Walker, 18.6Walker, 18.6

One mole of an ideal monatomic gas is initially a a One mole of an ideal monatomic gas is initially a a temperature of 323 K. Find the temperature of the temperature of 323 K. Find the temperature of the gas if 2250 J of heat are added and it does 834 J of gas if 2250 J of heat are added and it does 834 J of work.work.

Gas ProcessGas Process

The The thermodynamic statethermodynamic state of a gas of a gas is defined by pressure, volume, is defined by pressure, volume, and temperature.and temperature.

A “gas process” describes how gas A “gas process” describes how gas gets from one state to another gets from one state to another state.state.

Processes depend on the behavior Processes depend on the behavior of the boundary and the of the boundary and the environment more than they environment more than they depend on the behavior of the gas.depend on the behavior of the gas.

T1T2 T3

Gas “isotherms”

Isothermal ProcessIsothermal Process(constant temperature)(constant temperature)

P

V

PV = nRT

T = 0 (constant T)

Initial State of Gas

Final State of Gas

Isothermal Process

Isobaric ProcessIsobaric Process(constant pressure)(constant pressure)

P

V

T1T2 T3 PV = nRT

P = 0 (constant P)

Isobaric Expansion

Isobaric Contraction

Isometric ProcessIsometric Process(constant volume)(constant volume)

P

V

T1T2 T3

V = 0 (constant V)

PV = nRT

Adiabatic processAdiabatic process(insulated)(insulated)

P

V

T

isotherm

adiabat

Q = 0 (no heat enters or leaves)

Temperature, pressure, Temperature, pressure, and volume all change and volume all change in an adiabatic process.in an adiabatic process.

PV = nRT

WorkWork

Calculation of work done on a Calculation of work done on a system (or by a system) is an system (or by a system) is an important part of thermodynamic important part of thermodynamic calculations.calculations.

Work depends upon volume Work depends upon volume change.change.

Work also depends upon the Work also depends upon the pressure at which the volume pressure at which the volume change occurs.change occurs.

p

Work done BY gasWork done BY gas

V

p Wgas = pV

Wenv = -pV

Positive work

Negative work

p

Work done ON gasWork done ON gas

V p

Wgas = pV

Wext = -pV

Negative since V is negative

Positive since V is negative

Sample problemSample problem Calculate the work done by a gas that expands from Calculate the work done by a gas that expands from

0.020 m0.020 m33 to 0.80 m to 0.80 m33 at constant atmospheric pressure. at constant atmospheric pressure. How much work is done by the environment when the How much work is done by the environment when the

gas expands this much?gas expands this much?

Sample problemSample problem What is the change in volume of a cylinder What is the change in volume of a cylinder

operating at atmospheric pressure if its internal operating at atmospheric pressure if its internal energy decreases by 230 J when 120 J of heat are energy decreases by 230 J when 120 J of heat are removed from it?removed from it?

WCD = p1V

Work (isobaric)Work (isobaric)

P

V

P2

V1

A

V2

B

P1C D

WAB > WCD

Where we are

considering work done BY the gas

WAB = p2V

WACD

Work is path dependentWork is path dependent

P

V

P2

V1

A

V2

B

P1C D

WABD > WACD

Where we are considering work done BY the gas

WABD

ProblemProblem

One mole of a gas goes from state A (200 kPa One mole of a gas goes from state A (200 kPa and 0.5 mand 0.5 m33) to state B (150 kPa and 1.5 m) to state B (150 kPa and 1.5 m33). ). A) What is the change in temperature of the gas A) What is the change in temperature of the gas

during this process?during this process?

ProblemProblem

One mole of a gas goes from state A One mole of a gas goes from state A (200 kPa and 0.5 m(200 kPa and 0.5 m33) to state B (150 ) to state B (150 kPa and 1.5 mkPa and 1.5 m33). ). B) Draw this process, assuming the B) Draw this process, assuming the

smoothest possible transition (straight line) smoothest possible transition (straight line) for the process.for the process.

C) Estimate the work done by the gas C) Estimate the work done by the gas during the process.during the process.

D) Estimate the work done by the D) Estimate the work done by the environment during the process.environment during the process.

Sample ProblemSample ProblemDraw the gas process from state A (200 kPa and 0.5 m3) to state B (150 kPa and 1.5 m3).

Work done by a cycleWork done by a cycle

When a gas undergoes a complete When a gas undergoes a complete cycle, it starts and ends in the cycle, it starts and ends in the same state. The gas is identical same state. The gas is identical before and after the cycle, so there before and after the cycle, so there is no identifiable change in the is no identifiable change in the gas.gas.

U = 0 for a complete cycle.U = 0 for a complete cycle. The environment, however, has The environment, however, has

been changed.been changed.

Work done by cycleWork done by cycle

P

V

P2

V1

A

V2

B

P1C D

Work done by the gas is equal to the area circumscribed by the cycle.

WABCD

Work done by gas is positive for

clockwise cycles, negative for

counterclockwise cycles.

Work done by environment is

negative of work done by gas.

Sample ProblemSample Problem

Consider the cycle ABCDA, whereConsider the cycle ABCDA, where State A: 200 kPa, 1.0 mState A: 200 kPa, 1.0 m33

State B: 200 kPa, 1.5 mState B: 200 kPa, 1.5 m33

State C: 100 kPa, 1.5 mState C: 100 kPa, 1.5 m33

State D: 100 kPa, 1.0 mState D: 100 kPa, 1.0 m33

A) Sketch the cycle.A) Sketch the cycle. B) Graphically estimate the work done B) Graphically estimate the work done

by the gas in one cycle.by the gas in one cycle. C) Estimate the work done by the C) Estimate the work done by the

environment in one cycle.environment in one cycle.

A: 200 kPa, 1.0 mA: 200 kPa, 1.0 m3 3 B: 200 kPa, 1.5 mB: 200 kPa, 1.5 m33

C: 100 kPa, 1.5 mC: 100 kPa, 1.5 m3 3 D: 100 kPa, 1.0 mD: 100 kPa, 1.0 m33

ProblemProblem Calculate the heat necessary to change the Calculate the heat necessary to change the

temperature of one mole of an ideal gas from 300K to temperature of one mole of an ideal gas from 300K to 500K 500K

A) at constant volume.A) at constant volume.

B) at constant pressure (assume 1 atmosphere).B) at constant pressure (assume 1 atmosphere).

Second Law of Second Law of ThermodynamicsThermodynamics

No process is possible whose sole No process is possible whose sole result is the complete conversion result is the complete conversion of heat from a hot reservoir into of heat from a hot reservoir into mechanical work. (Kelvin-Planck mechanical work. (Kelvin-Planck statement.)statement.)

No process is possible whose sole No process is possible whose sole result is the transfer of heat from a result is the transfer of heat from a cooler to a hotter body. (Clausius cooler to a hotter body. (Clausius statement.)statement.)

Efficiency Lab – part 1Efficiency Lab – part 1

Efficiency is defined as the fraction of work or Efficiency is defined as the fraction of work or energy put into a system is actually useful.energy put into a system is actually useful.

At your disposal are T-shirts, water, plastic At your disposal are T-shirts, water, plastic baskets, mass balances, and an 1800 Watt baskets, mass balances, and an 1800 Watt hair drier. Develop a procedure to determine hair drier. Develop a procedure to determine the efficiency of the hair drier.the efficiency of the hair drier.

Hint: You must use the fact that it takes 2260 J Hint: You must use the fact that it takes 2260 J of heat energy to vaporize one gram of water.of heat energy to vaporize one gram of water.

Write a procedure to figure out the efficiency Write a procedure to figure out the efficiency of a hair drier in your “mega group”. of a hair drier in your “mega group”. Each Each person in the group must perform one person in the group must perform one and only one step in the procedure.and only one step in the procedure.

Heat EnginesHeat Engines

Heat engines can convert heat into Heat engines can convert heat into useful work.useful work.

According to the 2According to the 2ndnd Law of Law of Thermodynamics. Heat engines always Thermodynamics. Heat engines always produce some waste heat.produce some waste heat.

Efficiency can be used to tell how much Efficiency can be used to tell how much heat is needed to produce a given heat is needed to produce a given amount of work.amount of work.

NOTE: A heat engine is not something NOTE: A heat engine is not something that produces heat. A heat engine that produces heat. A heat engine transfers heat from hot to cold, and transfers heat from hot to cold, and does mechanical work in the process.does mechanical work in the process.

Heat TransferHeat Transfer

Heat Source (High Temperature)

Heat Sink (Low Temperature)

QH

QC

QH = QC

Heat EnginesHeat Engines

Engine



QH

QC

W

QH = QC + W

Carnot CycleCarnot Cycle

P

V

Isothermal expansion

Adiabatic expansion

Isothermal compression

Adiabatic compression

QH = QC + WEfficiency = W/QH

Work and Heat EnginesWork and Heat Engines

QQHH = W + Q = W + QCC

QQHH: Heat that is put : Heat that is put into the system and into the system and comes from the hot comes from the hot reservoir in the reservoir in the environment.environment.

W: Work that is W: Work that is done by the system done by the system on the environment.on the environment.

QQCC: Waste heat that : Waste heat that is dumped into the is dumped into the cold reservoir in the cold reservoir in the environment.environment.

Engine



QH

QC

W


A piston absorbs 3600 J of heat and dumps A piston absorbs 3600 J of heat and dumps 1500 J of heat during a complete cycle. How 1500 J of heat during a complete cycle. How much work does it do during the cycle?much work does it do during the cycle?

Efficiency of Heat EngineEfficiency of Heat Engine

In general, efficiency is related what In general, efficiency is related what fraction of the energy put into a system fraction of the energy put into a system is converted to useful work.is converted to useful work.

In the case of a heat engine, the energy In the case of a heat engine, the energy that is put in is the heat that flows into that is put in is the heat that flows into the system from the hot reservoir.the system from the hot reservoir.

Only some of the heat that flows in is Only some of the heat that flows in is converted to work. The rest is waste converted to work. The rest is waste heat that is dumped into the cold heat that is dumped into the cold reservoir.reservoir.

Efficiency of Heat EngineEfficiency of Heat Engine

Efficiency = W/QEfficiency = W/QH H = (Q= (QHH - Q - QCC)/Q)/QHH

W: Work done by engine on W: Work done by engine on environmentenvironment

QQHH: Heat absorbed from hot reservoir: Heat absorbed from hot reservoir

QQCC: Waste heat dumped to cold : Waste heat dumped to cold reservoirreservoir

Efficiency is often given as percent Efficiency is often given as percent efficiency.efficiency.

Sample problemSample problem

A certain coal-fired steam plant is operating A certain coal-fired steam plant is operating with 33% thermodynamic efficiency. If this is a with 33% thermodynamic efficiency. If this is a 120 MW plant, at what rate is heat energy 120 MW plant, at what rate is heat energy used?used?

Efficiency of Carnot CycleEfficiency of Carnot Cycle

For a Carnot engine, the efficiency For a Carnot engine, the efficiency can be calculated from the can be calculated from the temperatures of the hot and cold temperatures of the hot and cold reservoirs.reservoirs.

Carnot Efficiency = (TCarnot Efficiency = (THH - T - TCC)/T)/THH

TTHH: Temperature of hot reservoir (K): Temperature of hot reservoir (K)

TTCC: Temperature of cold reservoir (K): Temperature of cold reservoir (K)


Calculate the Carnot efficiency of a heat Calculate the Carnot efficiency of a heat engine operating between the temperatures of engine operating between the temperatures of 60 and 1500 60 and 1500 ooC.C.


For the problem described in the previous For the problem described in the previous example, how much work is produced when 15 example, how much work is produced when 15 kJ of waste heat is generated.kJ of waste heat is generated.

Entropy…Entropy…

Entropy is disorder, or randomness.Entropy is disorder, or randomness. The entropy of the universe is The entropy of the universe is

increasing. Ultimately, this will lead increasing. Ultimately, this will lead to what is affectionately known as to what is affectionately known as “Heat Death of the Universe”.“Heat Death of the Universe”.

Does the entropy in your room tend Does the entropy in your room tend to increase or decrease?to increase or decrease?

EntropyEntropy

S = Q/TS = Q/T S: Change in entropy (J/K)S: Change in entropy (J/K) Q: Heat going into system (J)Q: Heat going into system (J) T: Kelvin temperature (K)T: Kelvin temperature (K)

If change in entropy is positive, If change in entropy is positive, randomness or disorder has increased.randomness or disorder has increased.

Spontaneous changes involve an Spontaneous changes involve an increase in entropy.increase in entropy.

Generally, entropy can go down only Generally, entropy can go down only when energy is put into the system.when energy is put into the system.

Sample problemSample problem

You vaporize 8 kg of liquid water at its You vaporize 8 kg of liquid water at its boiling point. What is the entropy boiling point. What is the entropy change?change?

Efficiency Lab – part 2Efficiency Lab – part 2

Determine the % efficiency of your Determine the % efficiency of your hair drier using the procedure from hair drier using the procedure from the previous day.the previous day.

Keep a record of all data collected.Keep a record of all data collected. Calculate the % efficiency.Calculate the % efficiency. Turn in your mega-group report, with Turn in your mega-group report, with

all calculations clearly illustrated.all calculations clearly illustrated. Heat of vaporization of water is 2260 Heat of vaporization of water is 2260

J/g.J/g.

Fluids Fluids are substances that can flow, such as liquids and gases, and even a few solids. Fluids...

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Transcript of Fluids Fluids are substances that can flow, such as liquids and gases, and even a few solids. Fluids...