FLUIDS & THERMODYNAMICS AP Physics. Fluids Fluids are substances that can flow, such as liquids and...
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Transcript of FLUIDS & THERMODYNAMICS AP Physics. Fluids Fluids are substances that can flow, such as liquids and...
Fluids
Fluids are substances that can flow, such as liquids and gases, and even some solids We’ll just talk about the liquids & gases
Review of Density (remember this from chem?) ρ = m/V
ρ = density m = mass (kg) V = volume (m3) density units: kg/m3
Pressure
P = F/A P = pressure (Pa) F = force (N) A = area (m2)
Units for pressure: Pascals 1 Pa = 1 N/m2
Pressure is always applied as a normal force on a surface. Fluid pressure is exerted in all directions and is perpendicular to every surface at every location.
Pressure Practice 1
Calculate the net force on an airplane window if cabin pressure is 90% of the pressure at sea level and the external pressure is only 50 % of the pressure at sea level. Assume the window is 0.43 m tall and 0.30 m wide.
Atmospheric pressure
Atmospheric pressure is normally about 100,000 Pascals.
Differences in atmospheric pressure cause winds to blow
Pressure of a Liquid
The pressure of a liquid is sometimes called gauge pressure
If the liquid is water, it is called hydrostatic pressure
P = ρgh P = pressure (Pa) ρ = density (kg/m3) g = 9.81 m/s2
h = height of liquid column (m)
Absolute Pressure
Absolute pressure is obtained by adding the atmospheric pressure to the hydrostatic pressure
Patm + ρgh = Pabs
2. The depth of Lake Mead at the Hoover Dam is 600 ft. What is the hydrostatic pressure at the base of the dam?What is the absolute pressure at the base of the dam?
Buoyancy Force
Floating is a type of equilibrium: An upward force counteracts the force of gravity for floating objects
The upward force is called the buoyant forceArchimedes’ Principle: a body immersed in a
fluid is buoyed up by a force that is equal to the weight of the fluid it displaces
Calculating Buoyant Force
Fbuoy = ρVg Fbuoy: buoyant force exerted on a submerged or
partially submerged object V: volume of displaced fluid ρ: density of displaced fluid
When an object floats, the upward buoyant force equals the downward pull of gravity
The buoyant force can float very heavy objects, and acts upon objects in the fluid whether they are floating, submerged, or even resting on the bottom
Buoyant force on submerged objects
A shark’s body is not neutrally buoyant, so a shark must swim continuously or it will sink deeper
Scuba divers use a buoyancy control system to maintain neutral buoyancy (equilibrium)
If the diver wants to rise, he inflates his vest, which increases his volume, or the water he displaces, and he accelerates upward
Buoyant Force on Floating Objects
If the object floats on the surface, we know that Fbuoy = Fg! The volume of displaced water equals the volume of the submerged portion of the object
#3
Assume a wooden raft has 80.0 % of the density of water. The dimensions of the raft are 6.0 m long by 3.0 m wide by 0.10 m tall. How much of the raft rises above the level of the water when it floats?
Buoyant Force Labs
1. Determine the density of water by using the buoyant force.
Equipment: BeakersStringPulleysWeights/MassesGraduated cylinder(NO BALANCES!)
2. Balloon Race:Determine the buoyant force on your balloon with the balloon, masses & a balanceWithout using the balloon, design an apparatus so that when released, your balloon will hit the ceiling LAST.
Moving Fluids
When a fluid flows, mass is conserved
Provided there are no inlets or outlets in a stream of flowing fluid, the same mass per unit time must flow everywhere in the stream
The volume per unit time of a liquid flowing in a pipe is constant throughout the pipe
We can say this because liquids are generally not compressible, so mass conservation is also volume conservation for a liquid
Fluid Flow Continuity
V = Avt V: volume of fluid (m3) A: cross sectional areas
at a point in the pipe (m2)
v: the speed of fluid flow at a point in the pipe (m/s)
t: time (s)
Comparing two points in a pipe:
A1v1 = A2v2
A1, A2: cross sectional areas at points 1 and 2
v1, v2: speeds of fluid flow at points 1 and 2
Practice 4 & 5
4. 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 in which the diameter is 3.0 cm? How much water per second flows through the pipe?
5. 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 is reduced to 6.5 m at an area where the canal narrows to 5.0 m, how fast will the water be moving through the narrower region?
Bernoulli’s Theorem
The sum of the pressure, the potential energy per unit volume, and kinetic energy per unit volume at any one location in the fluid is equal to the sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any other location in the fluid for a non-viscous incompressible fluid in streamline flow
All other considerations being equal, when fluid moves faster, pressure drops
Bernoulli’s Theorem
P + ρgh + ½ ρv2 = constant P = pressure (Pa) ρ = density of fluid
(kg/m3) g = grav. accel. constant
(9.81 m/s2) h = height above lowest
point v = speed of fluid flow at
a point in the pipe (m/s)
6. Knowing what you know about Bernoulli’s principle, design an airplane wing that you think will keep an airplane aloft. Draw a cross section of the wing.
Thermodynamics
Thermodynamics is the study of heat and thermal energy
Thermal properties (heat & temperature) are based on the motion of individual molecules, so thermodynamics overlaps with chemistry
Total Energy:E = U + K + Eint
U = potential energy
K = kinetic energy Eint= internal or
thermal energy
Total Energy
Potential and kinetic energies are specifically for “big” objects, and represent mechanical energy
Thermal energy is related to the kinetic energy of the molecules of a substance
Temperature & Heat
Temperature is a measure of the average kinetic energy of the molecules of a substance. (like how fast the molecules are moving) The unit is °C or K. Temperature is NOT heat!
Heat is the internal energy that is transferred between bodies in contact. The unit is Joules (J) or sometimes calories (cal)
A difference in temperature will cause heat energy to be exchanged between bodies in contact. When two bodies are the same temp, they are in thermal equilibrium and no heat is transferred.
Ideal Gas Law
P: initial & final pressure (any unit)V: initial & final volume (any unit)T: initial & final temperature (K)
T in Kelvins = T in °C + 273
#7
7. Suppose an ideal gas occupies 4.0 L at 23°C and 2.3 atm. What will be the volume of the gas if the temperature is lowered to 0°C and the pressure is increased to 3.1 atm?
Ideal Gas Equation
If you don’t remember this from chem, you shouldn’t have passed!
P: pressure (Pa)V: volume (m3)n: number of molesR: gas law constant 8.31 J/(mol K)T: temp (K)
8
8. Determine the number of moles of an ideal gas that occupy 10.0 m3 at atmospheric pressure and 25°C.
Ideal Gas Equation
P: pressure (Pa)V: volume (m3)N: number of
moleculeskB: Boltzmann’s
constant 1.38 x 10-23J/K
T: temperature (K)
9. Suppose a near vacuum contains 25,000 molecules of helium in one cubic meter at 0°C. What is the pressure?
Kinetic Theory of Gases
1. Gases consist of a large number of molecules that make elastic collisions with each other and the walls of their container
2. Molecules are separated, on average, by large distances and exert no forces on each other except when they collide
3. There is no preferred position for a molecule in the container, and no preferred direction for the velocity
Average Kinetic Energy of a Gas
Kave = 3/2 kBT Kave = average kinetic energy (J) kB = Boltzmann’s constant (1.38 x 10-
23J/K) T = Temperature (K)
The molecules have a range of kinetic energies, so we take the Kave
10 & 11
10. What is the average kinetic energy and average speed of oxygen molecules in a gas sample at 0C°?
11. Suppose nitrogen and oxygen are in a sample of gas at 100°C:a) What is the ratio of the average kinetic energies for the two molecules?b) What is the ratio of their average speeds?
Thermodynamics
The system boundary controls how the environment affects the system (for our purposes, the system will almost always be an ideal gas)
If the boundary is “closed to mass,” that means mass can’t get in or out
If the boundary is “closed to energy,” that means energy can’t get in or out
What type of boundary does the earth have?
First Law of Thermodynamics
The work done on a system + the heat transferred to the system = the change in internal energy of the system.
ΔU = W + Q ΔU = Eint = thermal energy (NOT potential energy
– how stupid is that?) W = work done on the system (related to change
in volume) Q = heat added to the system (J) – driven by
temperature difference – Q flows from hot to cold
More about “U”
U is the sum of the kinetic energies of all the molecules in a system (or gas)
U = NKave
U = N(3/2 kBT)U = n(3/2 RT)
since kB = R/NA
12 & 13
12. A system absorbs 200 J of heat energy from the environment and does 100 J of work on the environment. What is its change in internal energy?
13. How much work does the environment do on a system if its internal energy changes from 40,000 J to 45,000 J without the addition of heat?
Gas Process
The thermodynamic state of a gas is defined by pressure, volume, and temperature.
A “gas process” describes how gas gets from one state to another state
Processes depend on the behavior of the boundary and the environment more than they depend on the behavior of the gas
Work
Calculation of work done on a system (or by a system) is an important part of thermodynamic calculations
Work depends upon volume changeWork also depends upon the pressure at
which the volume change occurs
14 & 15
14. Calculate the work done by a gas that expands from 0.020 m3 to 0.80 m3 at constant atmospheric pressure.
How much work is done by the environment when the gas expands this much?
15. What is the change in volume of a cylinder operating at atmospheric pressure if its thermal energy decreases by 230 J when 120 J of heat are removed from it?
16 & 17
16. One mole of a gas goes from state A (200 kPa and 0.5 m3) to state B (150 kPa and 1.5 m3). What is the change in temperature of the gas during this process?
17. One mole of a gas goes from state A (200 kPa and 0.5 m3) to state B (150 kPa and 1.5 m3).
a. Draw this process assuming the smoothest possible transition (straight line)
b.Estimate the work done by the gas
c. Estimate the work done by the environment
Work Done by a Cycle
When a gas undergoes a complete cycle, it starts and ends in the same state. the gas is identical before and after the cycle, so there is no identifiable change in the gas.
ΔU = 0 for a complete cycleThe environment, however, has been changed
Work Done By Cycle
Work done by the gas is equal to the area circumscribed by the cycle
Work done by the gas is positive for clockwise cycles, and negative for counterclockwise cycles. Work done by the environment is opposite that of the gas
18
Consider the cycle ABCDA, where State A: 200 kPa, 1.0 m3 State B: 200 kPa, 1.5 m3 State C: 100 kPa, 1.5 m3 State D: 100 kPa, 1.0 m3
a.Sketch the cycleb.Graphically estimate the work done by the
gas in one cyclec.Estimate the work done by the environment in
one cycle
19
Calculate the heat necessary to change the temperature of one mole of an ideal gas from 600 K to 500 Ka. At constant volumeb. At constant pressure (assume 1 atm)
Second Law of Thermodynamics
No process is possible whose sole result is the complete conversion of heat from a hot reservoir into mechanical work (Kelvin-Planck statement)
No process is possible whose sole result is the transfer of heat from a cooler to a hotter body (Clausius statement)
Basically, heat can’t be completely converted into useful energy
Heat Engines
Heat engines can convert heat into useful work
According to the 2nd Law of Thermodynamics, Heat engines always produce some waste heat
Efficiency can be used to tell how much heat is needed to produce a given amount of work
Work and Heat Engines
QH = W + QC
QH: Heat that is put into the system and comes from the hot reservoir in the environment
W: Work that is done by the system on the environment
QC: Waste heat that is dumped into the cold reservoir in the environment
20
20. A piston absorbs 3600 J of heat and dumps 1500 J of heat during a complete cycle. How much work does it do during the cycle?
Efficiency of Heat Engine
In general, efficiency is related to what fraction of the energy put into a system is converted to useful work
In the case of a heat engine, the energy that is put in is the heat that flows into the system from the hot reservoir
Only some of the heat that flows in is converted to work. The rest is waste heat that is dumped into the cold reservoir
Efficiency of Heat Engine
Efficiency = W/QH = (QH – QC) / QH
W: Work done by the engine on the environment QH: Heat absorbed from hot reservoir
QC: Waste heat dumped into cold reservoir
Efficiency is often given as percent efficiency
YOUR TASK: find the efficiency of your hair dryer
21
A coal-fired stream plant is operating with 33% thermodynamic efficiency. If this is a 120 MW plant, at what rate is heat energy used?
Efficiency of Carnot Cycle
For a Carnot engine, the efficiency can be calculated from the temperatures of the hot and cold reservoirs.
Carnot Efficiency = (TH – TC) / TH
TH: temperature of hot reservoir (K)
TC: temperature of cold reservoir (K)
22 & 23
22. Calculate the Carnot efficiency of a heat engine operating between the temperature of 60 and 1500°C.
23. For #22, how much work is produced when 15 kJ of waste heat is generated?
Entropy
Entropy is disorder, or randomness
The entropy of the universe is increasing. Ultimately, this will lead to what is affectionately known as “Heat Death of the Universe.”