FLUIDS & THERMODYNAMICS AP Physics

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 (m 3 )  density units: kg/m 3

Pressure P = F/A  P = pressure (Pa)  F = force (N)  A = area (m 2 ) Units for pressure: Pascals  1 Pa = 1 N/m 2 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/m 3 )  g = 9.81 m/s 2  h = height of liquid column (m)

Absolute Pressure Absolute pressure is obtained by adding the atmospheric pressure to the hydrostatic pressure P atm + ρgh = P abs 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 force Archimedes’ 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 F buoy = ρVg  F buoy : 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: Beakers String Pulleys Weights/Masses Graduated cylinder (NO BALANCES!) 2. Balloon Race: Determine the buoyant force on your balloon with the balloon, masses & a balance Without 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 (m 3 )  A: cross sectional areas at a point in the pipe (m 2 )  v: the speed of fluid flow at a point in the pipe (m/s)  t: time (s) Comparing two points in a pipe: A 1 v 1 = A 2 v 2 A 1, A 2 : cross sectional areas at points 1 and 2 v 1, v 2 : 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 ρv 2 = constant  P = pressure (Pa)  ρ = density of fluid (kg/m 3 )  g = grav. accel. constant (9.81 m/s 2 )  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 + E int  U = potential energy  K = kinetic energy  E int = 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 (m 3 ) n: number of moles R: 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 m 3 at atmospheric pressure and 25°C.

Ideal Gas Equation P: pressure (Pa) V: volume (m 3 ) N: number of molecules k B : Boltzmann’s constant  1.38 x J/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 K ave = 3/2 k B T  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 K ave

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 = E int = 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

First Law of Thermodynamics

More about “U” U is the sum of the kinetic energies of all the molecules in a system (or gas) U = NK ave U = N(3/2 k B T) U = n(3/2 RT)  since k B = R/N A

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

Isothermal Process (Constant Temperature)

Isobaric Process (Constant Pressure)

Isometric Process (Constant Volume)

Adiabatic Process (Insulated)

Work Calculation of work done on a system (or by a system) is an important part of thermodynamic calculations Work depends upon volume change Work also depends upon the pressure at which the volume change occurs

Done BY a gas Done ON a gas Work

14 & Calculate the work done by a gas that expands from m 3 to 0.80 m 3 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?

Work (Isobaric)

Work is Path Dependent

16 & One mole of a gas goes from state A (200 kPa and 0.5 m 3 ) to state B (150 kPa and 1.5 m 3 ). 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 cycle The 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 cycle b. Graphically estimate the work done by the gas in one cycle c. 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 K a. At constant volume b. 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 2 nd 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

Heat Transfer

Heat Engines

Adiabatic vs. Isothermal Expansion

Carnot Cycle

Work and Heat Engines Q H = W + Q C  Q H : 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  Q C : Waste heat that is dumped into the cold reservoir in the environment

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/Q H = (Q H – Q C ) / Q H  W: Work done by the engine on the environment  Q H : Heat absorbed from hot reservoir  Q C : 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?

Carnot Engine Cycle

Efficiency of Carnot Cycle For a Carnot engine, the efficiency can be calculated from the temperatures of the hot and cold reservoirs. Carnot Efficiency = (T H – T C ) / T H  T H : temperature of hot reservoir (K)  T C : temperature of cold reservoir (K)

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.”

Entropy ΔS = Q/T  ΔS: change in entropy (J/K)  Q: heat going into the system (J)  T: temperature (K) If change in entropy is positive, randomness or disorder has increased Spontaneous changes involve an increase in entropy Generally, entropy can go down only when energy is put into the system