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Physics 8: Fluids Name __________________________ A. Static Fluids (10-1 to 10-7) 1. states of matter a. solid 1. shape and size unchanged by pressure 2. useful properties are mass and force b. fluid 1. flows under pressure 2. two phases a. liquid—incompressible b. gas—compressible 3. useful properties are density and pressure a. density, = m/V (kg/m 3 ) b. pressure, P = F/A (Pa—Pascal) c. plasma—ionized atoms at high temperature 2. Pascal's principle a. pressure applied to a confined fluid is equal to the pressure throughout the fluid b. P in = P out F in /A in = F out /A out c. W in = W out F in d in = F out d out 3. pressure in a liquid, P = gh Steps Algebra start with substitute mg for F g substitute V for m substitute Ah for V simplify P = F g /A P = mg/A P = Vg/A P = Ahg/A P = gh a. equal in all directions and to object surface b. not used with gases because density isn't constant c. absolute pressure 1. absolute = fluid pressure + air pressure 2. P = gh + P o (P o 1 x 10 5 Pa = 100 kPa) 4. Archimedes' principle, F b = f V o g a. the buoyant force (weight loss when an object is submerged) = weight of displaced fluid (m f = f V o ) 1. f = fluid density 2. V o = object's submerged volume Steps Algebra start with substitute gh for P regroup substitute h for h 2 h 1 substitute V for hA F b = F 2 – F 1 = (P 2 P 1 )A F b = (gh 2 gh 1 )A F b = g(h 2 h 1 )A F b = ghA F b = f V o g b. partially submerged: F g = F b m o g = f V sub g o V o = f V sub 1. fraction submerged: V sub /V o = o / f 2. F submerge = F b F g = f V o g o V o g = ( f o )V o g c. partially supported: F support = F g – F b = ( o f )V o g F b = F g – F support = (m in air – m in fluid )g d. specific gravity s.g. = object / fluid = m air /(m air m fluid ) oject = (s.g.) fluid ( H2O = 1 g/cm 3 = 1000 kg/m 3 )
Transcript
Page 1: Physics - Oak Park Independent · Web viewfrom one body to another (we will limit our discussion to heat transfer from a high temperature body to a low temperature body)

Physics 8: Fluids Name __________________________A. Static Fluids (10-1 to 10-7)

1. states of mattera. solid

1. shape and size unchanged by pressure2. useful properties are mass and force

b. fluid1. flows under pressure2. two phases

a. liquid—incompressibleb. gas—compressible

3. useful properties are density and pressure a. density, = m/V (kg/m3) b. pressure, P = F/A (Pa—Pascal)

c. plasma—ionized atoms at high temperature 2. Pascal's principle

a. pressure applied to a confined fluid is equal to the pressure throughout the fluid

b. Pin = Pout Fin/Ain = Fout/Aout

c. Win = Wout Findin = Foutdout

3. pressure in a liquid, P = ghSteps Algebra

start withsubstitute mg for Fg

substitute V for msubstitute Ah for Vsimplify

P = Fg/AP = mg/AP = Vg/AP = Ahg/AP = gh

a. equal in all directions and to object surfaceb. not used with gases because density isn't constant c. absolute pressure

1. absolute = fluid pressure + air pressure2. P = gh + Po (Po 1 x 105 Pa = 100 kPa)

4. Archimedes' principle, Fb = fVoga. the buoyant force (weight loss when an object is

submerged) = weight of displaced fluid (mf = fVo)1. f = fluid density2. Vo = object's submerged volume

Steps Algebrastart withsubstitute gh for Pregroupsubstitute h for h2 – h1

substitute V for hA

Fb = F2 – F1 = (P2 – P1)AFb = (gh2 – gh1)AFb = g(h2 – h1)AFb = ghAFb = fVog

b. partially submerged: Fg = Fb

mog = fVsubg oVo = fVsub

1. fraction submerged: Vsub/Vo = o/f

2. Fsubmerge = Fb

– Fg = fVog – oVog = (f – o)Vog

c. partially supported: Fsupport = Fg – Fb = (o – f)VogFb = Fg – Fsupport = (min air – min fluid)g

d. specific gravity s.g. = object/fluid = mair/(mair

– mfluid)oject = (s.g.)fluid (H2O = 1 g/cm3 = 1000 kg/m3)

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B. Fluid flow (10-8 to 10-10)1. streamline—fluid layers slide by each other2. turbulent—eddy currents (increase viscosity)3. volume flow rate

a. V/t = Al/t = Av (m3/s)b. assume constant volume when water moves

through closed system, then V/t = A1v1 = A2v2

4. Bernoulli's equation, P + gh + ½v2 = Ca. based on conservation of energy

Steps Algebrastart withsubstitute PA for Fp

l for dsubstitute V for Al

WP = FPdWp = PAdWp = PAlWp = PV

start withsubstitute V for m

Ug = mghUg = Vgh

start withsubstitute V for m

K = ½mv2

K = ½Vv2

total energy is constantdivide both sides by V

PV + Vgh + ½Vv2 = constantP + gh + ½v2 = C

b. three types of problems1. plumbing system:

P1 + gy1 + ½v12 = P2 + gy2 + ½v2

2

2. leaking tank (P1 = P2, y2 = 0 and v1 = 0):gy1 = ½v2

2 v22 = 2gy1

(same for an object that falls y1 meters!)3. lift caused by moving air (y1 = y2):

P1 – P2 = ½v22 - ½v2

2 (F1 – F2)/A = ½(v2

2 – v12)

Flift = ½(vtop2 – vbottom

2)AC. Kinetic theory—Gases (13-2, 13-6 to 13-10)

1. temperature scales a. 2 relative scales: oF, oCb. 1 absolute scale: K = oC + 273 (use Kelvin

temperature for all calculations except T)2. molecular kinetic energy

a. per mole: K = 3/2RT = ½Mv2

R = 8.31 J/mol•KM = mass per mole in kg

b. per molecule: K = 3/2kBT = ½v2

kB = R/6.02 x1023 = 1.38 x 10-23 J/K = M/6.02 x 1023

3. ideal gasa. no cohesive force or appreciable volumeb. PV = nRT = NkBT

P = pressure in Pa (1 x 105 Pa = 1 atm)V = volume in m3 (1 m3 = 1000 L)n = moles of moleculesN = number of molecules (N = n x 6.02 x 1023)T = temperature in K

c. sample of gas: P1V1/T1 = P2V2/T2

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D. Heat (13-3 to 13-4, 14-1 to 14-8)1. heat, internal energy and temperature

a. internal energy (U) is the sum of bond energy, energy of position and kinetic energy.

b. temperature (T) is related to the kinetic energy per mole of molecules (K = 3/2RT)

c. heat (Q) is the transfer of internal energy (U) from one body to another (we will limit our discussion to heat transfer from a high temperature body to a low temperature body)

2. laws governing heat transfer (thermodynamics)a. If bodies are at the same temperature, there is no

heat transfer between them b. heat naturally flows from hotter to cooler body until

two bodies reach the same temperature 1. internal energy—U: –Uhot + Ucold = 02. entropy—S = Q/T: -Q/Thot + Q/Tcold > 0

c. heat flow, Qin = U + Wout 1. U: change in internal energy2. Wout: work done as body expands (gases)3. conservation of energy principle4. rate of heat flow: H = Qin/t = kA(TH – TL)/L

a. k: thermal conductivityb. A: exposed surface areac. TH – TL: outside/inside temperaturesd. L is thickness

5. 2 modes of heat transfera. conduction: heat transfer through elastic

collisions from hot atoms to cool atomsb. radiation: hot molecules emit photons

E = hf (human body glows infrared)6. convection: fluids move between hot and cold

locations because of pressure/density differences (convection currents)

3. thermal expansion of solids: L = LoT4. measuring heat flow

a. liquids and solids (Wout 0)1. Q = U = mcT

a. specific heat, c, is property of material (water = 4180 J/kg•K)

b. T can be in oC or K2, hot object added to cool fluid: |Qhot| = |Qcold|

mhotchot(Thot – Tfinal) = mcoldccold(Tfinal – Tcold)3. rate of heat transfer: power, P = Q/t

b. monatomic gas1. constant volume (Wout = 0): Qin = U = 3/2nRT2. constant pressure (Wout 0)

a. Wout = PV = nRT (only when P = 0)b. Q = Uin + Wout

Q = 3/2nRT + 2/2nRT = 5/2nRTE. Heat Engines (15-1 to 15-2, 15-4 to 15-6)

1. PV diagram (monatomic gas)a. heating a gas changes pressure and/or volumeb. work is done when volume changesc. useful formulas:

1. PV = nRT T = PV/nR)2. U = 3/2nRT = 3/2PV or 3/2PV3. Win = –PV4. U = Qin + Win

d. idealized processes on PV diagram for a gas P adiabatic (Q = 0)

isometric (V = 0)

Po isobaric (P = 0)

isothermal (T = 0)

Vo V

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e. interpretation of graphs 1. move away from origin +T and +U2. move toward y-axis (compression) +Win 3. area under the curve = -Win

f. Summary calculations for each process

Process T (T2 – T1)U = Qin + Win

Isometric(V = 0) PV/nR

3/2PV3/2nRT = U 0

Isobaric(P = 0) PV/nR

3/2PV3/2nRT U – Win –PV

Isothermal(T = 0) 0 0 = -Win = -Qin

Adiabatic(Q = 0) = Win 0 = U

2. heat cycle a. ideal (Carnot) system takes a body of gas through

a complete cycle where U = 0

b. solving heat cycle problems determine T at each state determine Qin, Win and U for each process

o isometric, Isobaric, use above formulaso Isothermal, adiabatic, use given valuesomissing values, use:

for any step: U = Qin + Win

for cycle: T = U = 0, Qin – Qout = Wout – Win

c. ideal (Carnot) efficiency: ec = (THigh – TLow)/THigh d. first law efficiency: e = |Wout – Win|/Qin

Waste = Qin(1 – e)e. heat engine vs. heat pump

1. heat engine takes in heat to perform work P – Area Win = QL – QH

Vheat engine expands at TH, contracts at TL

Win < 0 (work is done by the engine)2. heat pump uses work to remove heat

P + Area Win = QH – QL

Vheat pump expands at TL, contracts at TH Win > 0 (work is done to the refrigerator)

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Experiments1. Specific Gravity Lab

a. Mass a weight in air and submerged in water.mair (g) mH2O (g)

b. Calculate the following from the data.Formula Calculation

s.g. s.g. = mair/(mair – mH2O)

= s.g.(H2O)

2. Bernoulli Laba. Measure the following distances from the hole in the

plastic bottle. Distance from the hole to

the table top (dy)Distance from hole to the

water surface (y1)

b. Calculate where the water that drains from the hole in the plastic bottle will land.

Formula Calculation

t dy = ½gt2

vx gy1 = ½vx2

dx dx = vxt

c. Place the 50-mL beaker at the predicted distance dx from the hole in the plastic bottle so that the water will land in the beaker. Adjust the position if necessary. Measure the adjusted distance dx’.

dx dx’ % Difference

3. Gas Law Constant Lab a. Mass 0.20 g of Magnesium. Measure the temperature,

pressure and volume of the gas generated when the magnesium reacts with HCl.

mMg

(g)V (mL) T

(oC)P (Pa)

Vo Vf Plab PH2O

b. Calculate the following from the data.Formula Calculation

n n = mMg/24.3

Vm3 Vm3 = (Vo – Vf)10-6

TK TK = ToC + 273

PPa PPa = Plab – PH2O

R R = PPaVm3/nTK

% 100(8.31 – R)/8.31

4. Calorimetry lab a. Mass the iron washers and holder and place in boiling

water for 5 minutes. Add 100 mL of water to a Styrofoam cup and measure its temperature. Add the boiling hot steel to the Styrofoam cup of water, measure the highest temperature,

Iron Washers Waterm (kg) To Tf m (kg) To Tf

100o C 0.100 kg

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b. Calculate the following from the data.Formula Calculation

TFe T = To – Tf

TH2O T = Tf – To

QFe QFe = QH2O = mcT

cFe QFe = mcT

% 100(450 – cFe)/450

Practice ProblemsA. Static Fluid

1. If one material has a higher density than another, does this mean that the molecules of the first material must be more massive than those of the second?(A) yes (B) no

2. Consider what happens when you push both a pin and a blunt end of a pen against your skin with the same force. What will determine whether your skin will be punctured?(A) the pressure on your skin(B) the net applied force on your skin

3. You are walking out on a frozen lake and you begin to hear the ice cracking beneath you. What is your best strategy for getting off the ice safely? (A) stand absolutely still and don't move a muscle(B) slide your feet (with lifting them) to move towards shore(C) lie down flat on the ice and crawl toward shore

4. While swimming near the bottom of a swimming pool, you let out a small bubble of air. As the bubble rises toward the surface, what happens to its diameter?(A) decreases (B) same (C) increases

5. Three containers are filled with water to the same height and have the same surface area at the base, but the total weight of water is different for each. Which container has the greatest total force acting on the base?

(A) (B) (C) (D) tie6. When a hole is made in the side of a water bottle, water

flows out and follows a parabolic trajectory. If the container is dropped in free fall, the water flow will(A) diminish (B) stop(C) go in a straight line (D) curve upward

7. When you drink liquid through a straw, which below is primarily responsible for this to work?(A) water pressure (B) gravity(C) inertia (D) atmospheric pressure

8. You put a straw into a glass of water, place your finger over the top so no air can get in or out, and then lift the straw from the liquid. You find that the straw retains some liquid. How does the air pressure P inside the straw compare to atmospheric pressure PA?(A) P > PA (B) P = PA (C) P < PA

9. In a mercury barometer at room pressure, the height of the mercury column in a glass tube is 760 mm. If another mercury barometer is used that has a larger diameter tube, how high will the column of mercury be in this case?(A) greater (B) same (C) less

10. Thermometers often use mercury or alcohol in a thin glass tube, but barometers never use alcohol. Why?(A) mercury is less flammable(B) mercury's color is easier to see(C) mercury is less toxic than alcohol(D) mercury is more dense than alcohol

11. Imagine holding two identical bricks in place under water. Brick A is just beneath the surface of the water, while brick B is held about two feet down. The force needed to hold brick B in place is (A) greater (B) same (C) less

Questions 12-13 A beaker filled completely with water is placed on a scale and weighs 29 N. A block is carefully placed in the beaker at the same time water overflows out of the beaker.

12. The block is made of wood and floats in the water. When placed on the scale the beaker and floating block will weigh (A) < 29 N (B) = 29 N (C) > 29 N

13. The block is made of aluminum and sinks. When placed on the scale the beaker and sunk block will weigh (A) < 29 N (B) = 29 N (C) > 29 N

14. A raft carrying a large tank is floating in a pool. The tank is then thrown overboard and sinks. What happens to the water level in the pool with respect to the pool side?(A) rise (B) same (C) drop

Questions 15-19 Object A floats in pail of water with ¾ of its volume submerged.

15. What is the ratio of the density of object A to that of water?(A) ¼ (B) ¾ (C) 4/3 (D) 4

16. Object A is now placed in oil with a density half that of water. What fraction of object A is above the fluid line?(A) 0 (B) ¼ (C) ½ (D) ¾

17. Water is added to the empty pail to a level above the top of object A, the object will(A) move up slightly (B) stay at the same place(C) move down slightly (D) float to the top

18. Oil is added to the pail with water from question 17 to a level above the top of object A, the object will(A) move up slightly (B) stay at the same place(C) move down slightly (D) float to the top

19. Object A, in a pail of water, is observed on the moon. What fraction of its volume is submerged?(A) < ¾ (B) = ¾ (C) > ¾

Questions 20-21 A helium balloon is placed in an inverted air-filled jar, which rests on a table. The balloon floats to the top of the jar.

20. If the air is replaced with helium, where will the balloon be? (A) at the top (B) in the middle (C) at the bottom

21. If the jar if lifted off the table, but the helium remains in the jar, where will the balloon end up?(A) top (B) middle (C) bottom (D) ground

22. A rubber balloon is filled with water and just enough trapped air so that it floats. The balloon is placed in a glass cylinder also filled with water and is sealed with a flexible cap. When you push down on the flexible cap, the balloon(A) sinks down (B) stays put (C) rises up

23. How does a liquid differ from a solid or gas?

24. What is the mass of a piece of gold ( = 1.93 x 104 kg/m3) that has a volume of 22 cm3?

25. Why is the formula P = gh useful for liquids but not gases?

26. At what depth in water is the added pressure equal to 1 atm (1.0 x 105 Pa)?

27. What is the absolute air pressure, in Pa, in a tire that has a gauge pressure reading of 30 lbs/in2? (1 atm = 14.7 lbs/in2)

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28. a. 1,000 N of force is used to raise a 10,000 N car. What is the ratio of the cross-sectional area of the lift piston to the force piston (A2/A1)?

b. How far does the force piston move to lift the car 2 m?

29. How much mass (M) must be added to a diver (85-kg, 0.090-m3) to allow him to float under water?

30. What percentage of the volume of a floating iceberg is above sea water? (ice = 920 kg/m3, sea water = 1030 kg/m3)

31. What volume of helium is needed to lift a load of 800 kg? (air = 1.29 kg/m3, He = 0.18 kg/m3)

32. What is the specific gravity of a piece of metal that has a mass of 125 g in air and 78.7 g in water?

33. A crown's "weight" in air is 14.7 kg. What is its "weight" under water if it is made of

gold (s.g. = 19.3)

lead (s.g. = 11.3)

34. The weight of a 300 N piston compresses gas in a tank.a. What is the pressure on the gas generated by the

piston, which has a radius of 0.050 m?

b. What is the total pressure in the tank if the atmospheric pressure is 1 x 105 Pa?

35. What is the water pressure in a pipe that is 45 m below the water level in the city's water storage tank?

36. In a hydraulic system, cylinder A with a 100 cm2 cross section is connected by fluid to cylinder B with a 10 cm2 cross section. 2000 N of force push on the cylinder A's piston. Determinea. the force generated on cylinder B's piston?

b. the distance piston B moves if piston A moves 5 cm.

37. What is the density of a log when 65% of the volume is submerged in water ( = 1000 kg/m3)?

38. An aluminum ( = 2700 kg/m3) object has a mass of 27 kg. The object is attached to a string and immersed in a tank of water. Determinea. the volume of the object.

b. the tension in the string.

39. What volume of helium will support a load of 1000 kg? (air = 1.29 kg/m3, He = 0.18 kg/m3)

B. Fluid Flow40. Water flows through a 1-cm diameter pipe connected to a

½-cm diameter pipe. Compared to the speed of the water in the 1-cm pipe, the speed in the ½-cm pipe is(A) ¼ (B) ½ (C) 2 (D) 4

41. A blood platelet drifts along with the flow of blood through an artery that is partially blocked. As the platelet moves from the wide region into the narrow region, the blood pressure(A) increases (B) same (C) decreases

42. A person's blood pressure is generally measured on the arm, at approximately the same level as the heart. How would the results differ if the measurement were made on the person's leg instead?(A) higher (B) same (C) lower

43. Smoke is drawn up a chimney on a windy day. The draw on a windy day compared to a calm day is(A) faster (B) same (C) slower

44. Consider the diagram in your notes (B3). a. How many times bigger is A1 compared to A2 if the

diameter, d1, is two times the diameter, d2?

b. How many times faster is v2 compared to v1?

45. Consider the water pipe in your notes (B4). What is P2 when P1 = 3 x 105 Pa, v1 = 2 m/s, v2 = 5 m/s, y1 = 0 m, y2 = 4 m?

46. A water leaks out of a hole 5 m below the surface in a tank. a. What is the velocity of water that leaks out of the tank?

b. What is the radius of the hole in the water tank if the volume rate flow out of the leak is 3 x 10-3 m3/s?

47. a. Air flows past the upper surface of an airplane wing at 250 m/s and past the lower surface of the wing at 200 m/s. The density of air is 1.0 kg/m3 and the area of the wing is 20 m2. What is the net lift on the wing?

b. Racing cars have a rear spoiler, which is able to keep the car from lifting up at high speeds. Describe the design of the spoiler.

48. When a truck passes you on the left, your car initially is pushed right then pulled left. Why?

49. Water flows at a rate of 0.5 m/s through a 4-cm diameter pipe on the first floor of a house. a. What is the cross-sectional area of the pipe?

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b. What is the volume flow rate in the 4-cm pipe?

c. What is the velocity of the water in a 2.6-cm diameter pipe on the second floor of the house.

d, The pressure in the 4-cm pipe is 3 atm. What is the pressure in the 2.6 cm section that is elevated 3 m?

50. Air ( = 1 kg/m3) passes over a roof at 60 m/s. Determinea. the pressure difference between the attic air and the

air passing over the roof.

b. the upward force exerted on the roof (area = 300 m2).

C. Kinetic Theory—Gases51. Which is the largest unit, 1o C, 1 K or 1o F?

(A) 1oC (B) 1 K (C) 1oF (D) 1oC and 1 K52. It turns out -40o C is the same temperature as -40o F. Is

there a temperature where the Kelvin and Celsius scales agree?(A) yes 0oC (B) yes, -273oC(C) yes, 0 K (D) no

53. Which has more molecules, one mole of N2 or one mole of O2?(A) N2 (B) O2 (C) tie

54. Which weighs more, one mole of N2 or one mole of O2?(A) N2 (B) O2 (C) tie

55. Two identical cylinders at the same temperature contain the same gas. If A contains three times as much gas as B, which cylinder has the higher pressure?(A) A (B) B (C) tie

56. Two identical cylinders at the same pressure contain the same gas. If A contains three times as much gas as B, which cylinder has the higher temperature?(A) A (B) B (C) tie

57. Two cylinders at the same temperature contain the same gas. If A has twice the volume and half the number of moles as B, how does the pressure of A compare with the pressure of B?(A) PA = ¼PB (B) PA = ½PB (C) PA = 2PB

58. A partially filled, sealed plastic water bottle sits out in the sun, heating the air inside. What happens to the bottle?(A) it expands (B) nothing (C) it shrinks

59. What happens to the volume of a balloon if you put it in the refrigerator?(A) it expands (B) nothing (C) it shrinks

60. In the formulas K = 3/2RT and PV = nRTa. The value of R is (_________).b. Why must you use the Kelvin temperature scale for

these calculations?

c. What is the Kelvin temperature for 25oC?

61. Consider oxygen gas (O2) at 22oC.a. What is the temperature in Kelvin?

b. What is the mass of one mole in kg?

c. What is the mass of one molecule in kg?

d. What is the average kinetic energy of a molecule?

e. What is the kinetic energy of a mole?

f. What is the average speed?

62. Consider one mole of helium gas at room temperature (22oC) and pressure (1.0 x 105 Pa).a. What is the volume (in m3)?

b. What is the volume (in m3) of one helium atom with an atomic radius is 5 x 10-11 m?

c. What is the volume (in m3) of one mole of helium atoms?

d. What percentage of the total volume (part a) is taken up by the helium atoms (part c)?

e. What is the volume when the pressure is increased to 2.0 x 105 Pa and the temperature is raised to 44oC?

63. A 0.01 m3 vessel contains 0.02 kg of an ideal gas at 50oC and a pressure of 3 x 105 Pa. Determine thea. kinetic energy per molecule

b. moles of gas are in the vessel (R = 8.31).

c. molar mass of the gas.

D. Heat64. Two objects are made of the same material, but have

different masses and temperatures. If the objects are brought into thermal contact, which one will have the greatest change in temperature?(A) the one with the higher initial temperature(B) the one with the lower initial temperature(C) the one with the greater mass(D) the one with smaller mass

65. Two different objects receive the same amount of heat. Which of the following choices is NOT a reason why the objects may have different changes in temperature?(A) they have different initial temperature(B) they have different mass(C) they have different specific heat

66. Two equal-mass liquids, initially at the same temperature, are heated for the same time over the same stove. You measure the temperatures and find that one liquid has a higher temperature than the other. Which liquid has a higher specific heat?(A) cooler one (B) hotter one (C) tie

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67. The specific heat of concrete is greater than that of soil. A baseball field and the surrounding parking lot are warmed up during a sunny day. Which would you expect to cool off faster in the evening when the sun goes down?(A) field (B) lot (C) tie

68. Water has a higher specific heat than sand. Therefore, on the beach at night, breezes would blow(A) from ocean to beach (B) from beach to ocean

69. 1 kg of water at 100oC is poured into a bucket that contains 4 kg of water at 0oC. Find the equilibrium temperature.(A) 10oC (B) 20oC (C) 50oC (D) 80oC

70. A 1-kg block of silver (c = 234 J/kg•K) is heated to 100oC, then dunked in a tub of 1 kg of water (c = 4186 J/kg•K) at 0oC. What is the final equilibrium temperature?(A) < 50oC (B) 50oC (C) > 50oC

71. Given your experience of what feels cooler when you walk on it, which surface has the higher thermal conductivity?(A) rug (B) tile

72. Two drinking glasses are stuck, one inside the other. How would you get them unstuck?(A) run hot water over them both(B) run hot water over the inner glass(C) run hot water over the outer glass

73. What happens to a hole in a sheet of metal that is heated?(A) expand (B) contract

74. Write the words that are defined below.

is the total energy of a body

measures the "warmth" of an object

is transferred between two bodies at different temperatures

75. Fill in the missing word about heat transfer.When two objects are the same temperature __ heat is transferredWhen heat is transferred to a system, it either increases the systems __ or the system performs __When two objects are at different temperatures, heat naturally flows from the __object to the __ object.

76. Write the form of heat flow described below.Energy transfer through collisionsPhotons are emitted from hot objectsHot fluid moves to cooler location

77. What factors affect the rate that heat is conducted through a piece of glass?

78. Write the form of heat transfer that is reduced by the following home construction elements.

Double-paned windowsOverhangs along the south sideWeather striping around windows and doors

79. A 20-cm long bimetal strip of brass ( = 19 x 10-6 oC-1) and aluminum ( = 26 x 10-6 oC-1) is heated from 22oC to 150oC. How much longer is the aluminum side?

80. Why is the formula, Q = mcT, used for solids and liquids, but not gases?

81. How much heat is needed to raise the temperature of 100 g of lead (c = 130 J/kg•K) from 20oC to 25oC?

82. 120 g of an alloy is heated to 200oC then placed in 500 g of 25oC water (c = 4200 J/kg•K) contained in a 200 g aluminum cup (c = 900 J/Kg•K). The final temperature is 31.5oC. What is the specific heat of the alloy?

83. How much time will it take to raise the temperature of 500 mL of water from 22oC to 100oC using a 750 W heater?

84. What is the diameter of a hole cut in steel ( = 12 x 10-6 oC-1) when it is heated to 600oC if it is 0.1000 m at 20oC?

85. How much heat is needed to raise the temperature of a 2-kg aluminum (c = 900 J/kg•K) vat filled with 20 kg of alcohol (c = 2400 J/kg•K) from 10oC to 75oC?

86. What is the final temperature when 150 cm3 of 75oC water (c = 4200 J/kg•K) is added to a 50-g Al (c = 900 J/kg•K) cup at 25oC?

E. Heat Engines87. What is the change in internal energy of a system if 2000 J

of heat is added to the system and the system does 1000 J of work to the system?

88. How much heat is added to one mole of helium for each of the following?a. Isometric change from 200 K to 400 K.

b. Isobaric change from 200 K to 400 K.

c. Isothermic change that does 1000 J of work to the gas.

d. Adiabatic change that does 1000 J of work to the gas.

89. The temperature of 0.0010 m3 of He ( = 0.179 kg/m3) is increased from 250 K to 750 K at constant volume.a. How many moles of helium are heated?

b. How much heat is required?

c. How much power is needed to heat the helium in 1 s?

90. Which process (isobaric, isothermic, or adiabatic) would use the least amount of work to compress a gas? Explain.

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91. The initial conditions for 1 mole of monatomic gas are 0.10 m3 and 1.0 x 105 Pa.a. What is the temperature of the gas?

b. The gas pressure is doubled isometrically.(1) What is the new temperature?

(2) How much work is done to the gas, Win?

(3) How much heat did the gas absorb?

(4) What is the change in internal energy, U?

c. The gas is returned to its initial condition and then its volume is doubled isobarically.(1) What is the new temperature?

(2) How much work is done to the gas, Win?

(3) How much heat did the gas absorb?

(4) What is the change in internal energy, U?

d. The gas is returned to its initial condition and then 1.0 x 104 J of heat is added to the gas isothermically. (1) What is the new temperature?

(2) How much work is done to the gas, Win?

(3) What is the change in internal energy, U?

e. The gas is returned to its initial condition and then the 1.0 x 104 J of work is done to the gas adiabatically. (1) How much heat did the gas release?

(2) What is the change in internal energy, U?

f. Graph each change described in parts b-e below.

2 Po

Po

Vo 2 Vo

g. Complete the chart for the processes b-e by indicating whether the value is +, – or 0 (unchanged)

Process U Qin Win

isometric (b)isobaric (c)isothermic (d)adiabatic (e)

92. Answer the questions for the Isothermal-adiabatic cycle in your notes (2a). a. Starting from point a, indicate in the diagram whether

the change +, –, or 0 (unchanged).Process T U = Qin + Win

1. Isothermal expansion2. Adiabatic expansion3. Isothermal

compression4. Adiabatic compression

Changeb. Check the appropriate step.

1 2 3 4generate power for the heat engineheat gained to the systemheat lost by the systemc. What does the region enclosed by the cycle represent?

93. One mole of gas is initially at point A (100 kPa, 0.01 m3). The gas is heated at constant volume until it reaches point B (200 kPa), and then expands at constant pressure to point C (0.02 m3). Heat is removed at constant volume to point D (100 kPa), then contracts at constant pressure to point A.a. label points A, B, C and D. P (kPa)

200

100

0.01 0.02 V (m3)b. What are the temperatures at each point?

A

B

C

D

c. Complete the chart by calculating each value.Step U = Qin + Win

A B

B C

C D

D A

Change

d. Why must the change in Qin + Win = 0?

e. Calculate the area inside the box diagram?

f. Determine the first law efficiency?

g. Determine the Carnot efficiency?

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94. An ideal gas undergoes a cyclic process as shown on the graph of pressure P versus volume V.

Indicate in the chart whether the change is positive (+), negative (–), unchanged (0), or can't tell (?).

Process T U = Qin + Win

A BB CC DD EE A

Change95. A power plant generates 120 MW (1.2 x 108 J/s) of

electricity at 40% efficiency. Determinea. The electric energy generated in 1 hour.

b. The energy supplied to the power plant in 1 hour.(Hint: electric output = work)

c. Heat discarded by the power plant.

d. The change in temperature of 1 x 108 kg of water (c = 4200 J/kg•K) that absorb all the discarded heat in 1 hr.

96. What is U for an isothermic process?

97. How is work represented on a PV diagram?

98. Which process would require the most work to double the volume of a gas, isothermic, adiabatic or isobaric?

99. How much work is done on 0.30 moles of gas during an adiabatic expansion that drops the temperature from 1150 K to 400 K?

100.One mole of an ideal gas, initially at 273 K, is heated at a constant pressure of 2 x 105 Pa until the volume doubles. Determine the a. initial volume of the gas (R = 8.31 J/mol•K).

b. work done to the gas during the expansion.

c. change in internal energy of the gas.

d. Heat added to the gas.

101.One mole of gas initially at point A (50 kPa, 0.01 m3), increases pressure isometrically to point B (100 kPa), then expands isothermically to point C (0.02 m3), and finally is compressed isobarically to point A. The work done by the gas during one cycle is 200 J.a. Sketch the heat cycle.

P (kPa)

100

50

0.01 0.02 V (m3)b. What are the temperatures at each point?

A

B

C

c. Complete the chart.

Step U = Qin + Win

A B

B C

C A

Changed. In which step is work done to the gas?

e. What is the total heat added to the gas?

f. How much heat is exhausted during one cycle?

g. Determine the first law efficiency?

h. Determine the Carnot efficiency?

102.An ideal gas undergoes a cyclic process as shown on the graph of pressure P versus volume V.

Indicate in the chart whether the change is positive (+), negative (–), unchanged (0), or can't tell (?).Process T U = Qin + Win

X YY ZZ X

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Change103.A engine operates at an input temperature of 1000 K while

producing 1000 J of useful work per hour. The engine has a Carnot efficiency of 30 % and a first law efficiency of 20 %.Determine the a. input heat used each hour.

b. exhaust heat produced each hour.

c. exhaust temperature.

Practice Multiple ChoiceBriefly explain why the answer is correct in the space provided.Questions 1-2 The spring scale reads 0.45 kg when

the rock is suspended in air and 0.36 kg when the rock is fully submerged in water.

1. The buoyant force that the fluid exerts on the object is(A) 1.3 N (B) 0.9 N(C) 0.75 N (D) 0.33 N

2. The density (in kg/m3) of the rock is (A) 200 (B) 800 (C) 1,250 (D) 5,000

3. An object weighs 15,000 N. When it is submerged in a liquid that has a density of 1500 kg/m3, its apparent weight is 7500 N. What is the density (in kg/m3) of the object?(A) 1,500 (B) 2,000 (C) 3,000 (D) 6,000

4. Two dams are alike in every respect (i.e. height, width and thickness of dam) except the length of the lake behind the dam. The first lake extends 1 km away from its dam; the second 5 km. The force exerted on the first dam is: (A) equal to the force on the second dam (B) greater than the force on the second dam (C) less than the force on the second dam

5. Each beaker is filled to the same depth with the same liquid and the area of the flat bottom is the same for each.

Which ranks the beakers from greatest to least force exerted by the liquid on the flat bottom? (A) I > III > II > IV (B) I > IV > III > II(C) II > III > IV > I (D) force on each is the same

6. What is the force exerted by a wind, which generates a pressure difference of 3 x 104 Pa, on the 3 m by 20 m side of a house trailer? (A) 0.5 N (B) 500 N (C) 1800 N (D) 1.8 x 106 N

7. What is the absolute pressure (in Pa) 3 m down in a swimming pool, when atmospheric pressure is 1 x 105 Pa?(A) 3 x 104 (B) 7 x 104 (C) 1.1 x 105 (D) 1.3 x 105

8. A rock is thrown into a swimming pool that is at a uniform temperature. While the rock sinks, the buoyant force (A) is zero (B) increases (C) decreases (D) is constant

Questions 9-11 Two pistons are connected in a hydraulic lift. The diameter of the large piston is ten times that of the small.

9. How many times larger is the cross-sectional area of the larger piston compared to the smaller?(A) 10 (B) 20 (C) 50 (D) 100

10. A 500-N force is applied to the smaller piston. What load can be lifted by the larger piston? (A) 5,000 N (B) 50,000 N (C) 500,000 N (D) 5,000,000 N

11. If the load is lifted 2 m, how far is the smaller piston moved?(A) 0.2 m (B) 2 m (C) 20 m (D) 200 m

Questions 12-13 A 1500-kg stone of volume 0.5 m3 is lowered to the bottom of a lake on the end of a rope.

12. What buoyant force acts on the stone?(A) 5 N (B) 50 N (C) 500 N (D) 5,000 N

13. What is the tension when the stone is submerged?(A) 3,500 N (B) 5,000 N(C) 10,000 N (D) 15,000 N

14. Water is flowing through a pipe with a cross-sectional area of 30 cm2 at a velocity of 4 m/s. What is the velocity of the water in a section of the pipe where the cross-sectional area is 50 cm2? (A) 1.2 m/s (B) 3.6 m/s (C) 2.4 m/s (D) 4.8 m/s

15. Water is pumped into one end of a long pipe at a rate of 50 liters per minute. The water is emerges from the other end of the pipe at a rate of 20 liters per minute. The reason for this decrease in volume flow rate is (A) the water is being pumped uphill (B) the pipe diameter is not the same at the two ends(C) there is friction in the pipe(D) there is a leak in the pipe

16. An ideal gas confined in a box initially has pressure P. If the absolute temperature of the gas is doubled and the volume of the box is quadrupled, the pressure is(A) ⅛ P (B) ¼ P (C) ½ P (D) P

17. A pitched baseball, which rotates counterclockwise about a vertical axis as seen from above, will curve: (A) to the pitcher's right (B) to the pitcher's left(C) upward (D) downward

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18. The absolute temperature of a sample of monatomic ideal gas is doubled at constant volume. What effect, if any, does this have on the pressure and density of the sample of gas?

Pressure Density (A) Remains the same Remains the same(B) Remains the same Doubles (C) Doubles Remains the same(D) Doubles Is 4 times greater

Questions 19-20 An ideal gas molecule at absolute temperature, T, has kinetic energy, K, and velocity, v.

19. What is the kinetic energy at 4T?(A) ¼K (B) ½K (C) 2K (D) 4K

20. What is the velocity at 4T?(A) ¼v (B) ½v (C) 2v (D) 4v

21. If wind blows at 30 m/s over your house, the net force on the roof (area = 400 m2) is (A) 100,000 N (B) 150,000 N(C) 180,000 N (D) 200,000 N

22. Water flows out of a hole at 4 m/s. What is the height of the water above the hole inside the bucket?(A) 0.8 m (B) 1.25 m (C) 2.5 m (D) 1.5 m

23. The area of an airplane wing is 100 m2. What is the lift force on the wing when the speed of air below and above the wing 200 m/s and 250 m/s respectively?(A) 2,500 N (B) 11,250 N (C) 4.2 x l05 N (D) 1.125 x l06 N

24. At best, a person can reduce the pressure in the lungs about 1 x 104 Pa below atmospheric pressure. How high can a person suck water up a straw? (A) 0.1 m (B) 0.3 m (C) 1.0 m (D) 3.0 m

25. If a crown of density 14,000 kg/m3 weights 140 N in air, the force needed to support it when submerged in water is:(A) 100 N (B) 130 N (C) 140 N (D) 150 N

26. A rowboat has a volume of 1.5 m3 and a mass of 40 kg. How many 70-kg people can the boat support?(A) 15 (B) 19 (C) 20 (D) 21

27. An object floats in water and displaces 150 cm3 of water. The same object floats in oil, displacing 375 cm3 of that oil. The density (in kg/m3) of the oil is: (A) 1,500 (B) 1,100 (C) 600 (D) 400

28. Water is flowing through a horizontal pipe with a constriction. At one end of the pipe we have A1 = 10 cm2, v1 = 4 m/s, and P1 = 500 kPa. In the constriction of the pipe we have A2 = 2 cm2. The pressure (in kPa) in the constriction is: (A) 120 (B) 308 (C) 480 (D) 690

29. A T-shaped tube with a constriction is inserted in a vessel containing a liquid.

What happens if air is blown through the tube from the left? (A) The liquid level in the tube rises up into the tube. (B) The liquid level in the tube falls below the level of the

surrounding liquid. (C) The liquid level in the tube remains where it is. (D) The air bubbles out at the bottom of the tube.

30. A sample of an ideal gas is in a tank of constant volume. The sample absorbs heat energy so that its temperature changes from 300 K to 600 K. If v1 is the average speed of the gas molecules before the absorption of heat and v2 is their average speed after the absorption of heat, what is the ratio v2/v1? (A) ½ (B) 1 (C) √2 (D) 2

31. A square steel plate with 1.00 m long sides has a hole in its center 0.100 m in diameter. If the plate is heated until its sides become 1.01 m long, the diameter of the hole will be (A) 0.090 m (B) 0.099 m (C) 0.100 m (D) 0.101 m

32. Which of the following statements is NOT a correct assumption of the classical model of an ideal gas? (A) The molecules are in random motion. (B) The volume of the molecules is negligible compared

with the volume occupied by the gas. (C) The molecules obey Newton's laws of motion. (D) The collisions between molecules are inelastic.

33. If the gas in a container absorbs 275 J of heat, has 125 J of work done on it, and then does 50 J of work, what is the increase in the internal energy of the gas? (A) 100 J (B) 200 J (C) 350 J (D) 400 J

34. The temperatures on each side of a window with area A and thickness d are T2 and T1, respectively. Increasing which of the following would decrease the rate that heat is conducted through the glass? (A) T2 – T1 only (B) d only (C) A only (D) A and T2 – T1

Questions 35-36 A 1.5-kg piece of metal (c = 200 J/kg•K) and initial temperature of 100oC is dropped into an insulated jar that contains 3.0-kg of liquid (c = 1,000 J/kg•K) and initial temperature of 0oC. The piece of metal is removed after 5 s, at which time its temperature is 20oC.

35. The temperature of the liquid after the metal is removed is (A) 0oC (B) 4oC (C) 8oC (D) 10oC

36. The average rate at which heat is transferred while the piece of metal is in the liquid is (A) 4,000 J/s (B) 4,800 J/s(C) 6,000 J/s (D) 9,600 J/s

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Questions 37-38 An ideal gas initially at temperature To, pressure Po, and volume Vo is compressed to one-half its initial volume. The process may be adiabatic (process 1), isothermal (process 2), or isobaric (process 3).

37. Which process does the most mechanical work on the gas?(A) 1 (B) 2 (C) 3 (D) all the same

38. Which process results in the highest temperature? (A) 1 (B) 2 (C) 3 (D) all the same

39. Which is always a characteristic of an adiabatic process? (A) The temperature does not change (T = 0). (B) The pressure does not change (P = 0). (C) The internal energy does not change (U = 0). (D) No heat flows into or out of the system (Q = 0).

40. An engine absorbs 100 J of heat and exhausts 60 J. What is the efficiency of the engine? (A) 40 % (B) 60 % (C) 67 % (D) 150 %

41. The maximum efficiency of a heat engine that operates between temperatures of 1500 K in the firing chamber and 600 K in the exhaust chamber is most nearly (A) 33 % (B) 40 % (C) 60 % (D) 67 %

42. Three identical samples of an ideal gas are taken from initial state I to final state F along the paths IAF, IF, and IBF.

Which must be true? (A) The work done by the gas is the same for all paths. (B) The heat absorbed by the gas is the same for all paths. (C) The change in internal energy is the same for all paths. (D) The expansion along path IF is isothermic.

43. A block (c = 100 J/kg•K) falls 100 m. If half of the potential energy lost by the fallen block is converted to internal energy, the temperature change of the block is most nearly (A) 1 K (B) 5 K (C) 10 K (D) 25 K

Questions 44-45 A thermodynamic system is taken from an initial state X along the path XYZX.

44. Which is negative for the process XY? (A) Qin (B) Win (C) U (D) Qin and U

45. For which is U negative? (A) XY (B) YZ (C) ZX (D) XYZX

Questions 46-47 An ideal gas undergoes the process below.

46. During which process is no work done on or by the gas? (A) AB (B) BC (C) CD (D) DE

47. At which point is the gas at its highest temperature? (A) A (B) B (C) C (D) D

Questions 48-50 A cylinder with a movable piston contains 0.1 mole of a monatomic ideal gas. The gas, initially at state a, can be taken through either of two cycles, abca or abcda. The following information is known about this system.

(1) For path c a: Qin = 685 J(2) For path c a: Win = -120 J(3) For path a b: U = -450 J(4) For path b c: Win = 75 J

Use the following options. (A) 565 J (B) 805 J (C) 450 J (D) 150 J

48. What is U for the path c a?

49. How much heat is removed for the path a b?

50. How much work is done in the process c d a?

Practice Free Response1. A 0.6-kg object at 100oC is dropped into a 0.1-kg container

(c = 840 J/kg•K) that holds 0.2 kg of water (c = 4190 J/kg•K) at 20oC. The system reaches an equilibrium temperature of 50oC. Determinea. the heat gained by the water.

b. the heat gained by the glass container.

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c. the heat lost by the metallic object.

d. the specific heat of the metallic object.

2. A large rectangular raft ( = 650 kg/m3) is floating on a lake. The surface area of the top of the raft is 8.2 m2 and its volume is 1.80 m3. The density of water is 1000 kg/m3.

A = 8.2 m2

h water line

a. Calculate the height h of the portion of the raft that is above the surrounding water.

b. Calculate the maximum number of 75-kg people that can be on the raft without the top of the raft sinking.

3. Three objects of identical mass attached to strings are suspended in a large tank of liquid, as shown.

a. Must all three strings have the same tension?

The tension in the string supporting A (V = 1.0 x 10-5 m3 and = 1300 kg/m3) is 0.0098 N.b. Calculate the buoyant force on object A.

c. Calculate the density of the liquid.

d. Some of the liquid is now drained until only half of A is submerged. Would the tension increase, decrease, or remain the same? Justify your answer.

4. A 0.025 m3 vessel contains 1 mole of argon gas (M = 0.040 kg/mol) at 400 K. Determine a. the pressure.

The gas is heated at constant pressure to a volume of 0.055 m3. Determine b. the work (Win) done during the expansion.

c. the change in internal energy of the gas.

d the heat added to the gas.

e. the final temperature of the gas.

5. The large container is filled with water ( = 1000 kg/m3). A small hole of area 2.5 x 10-6 m2 is opened in the side of the container a distance h below the water surface, which allows a stream of water to flow through the hole and into a beaker. At the same time, water is also added to the container so that h remains constant. The amount of water collected in the beaker in 2.0 minutes is 7.2 x 10-4 m3.

a. Calculate the volume rate of flow of water from the hole in m3/s.

b. Calculate the speed of the water as it exits from the hole.

c. Calculate the height h of water needed above the hole to cause the speed you determined in part (b).

d. Calculate the distance d from the small hole to the table top, which would produce a value of x = 0.50 m.

e. Suppose that there is now less water in the container so that the height h is reduced to h/2. Where will the water hit the tabletop?

6. The cylinder contains 2.2 kg of water vapor initially at a volume of 2.0 m3 and an absolute pressure of 3.0 x 105 Pa. This state is represented by point A in the PV diagram. a. Calculate the temperature of the water vapor at point A.

The absolute pressure of the water vapor is increased at constant volume to 4.0 x 105 Pa at point B, and then the volume of the water vapor is increased at constant pressure to 2.5 m3 at point C, as shown in the PV diagram.

b. Calculate the temperature of the water vapor at point C.

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c. Does the internal energy of the water vapor for the process A B C increase, decrease, or remain the same? Justify your answer.

d. Calculate the work done on the water vapor for the process A B C.

7. A 0.03 mol sample of helium is taken through the cycle shown in the diagram.

a. Determine the(1) temperature at point C.

(2) the volume at point C, VC.

b. Complete the chart.U Qin Win

A B

B C

C A

Overall

8. A 0.20 m diameter cylinder fitted with a frictionless piston, initially fixed in place. The cylinder contains 2.0 moles of nitrogen gas at an absolute pressure of 4.0 x 105 Pa.a. Calculate the force that the nitrogen gas exerts on the

piston.

b. Calculate the volume of the gas if the temperature of the gas is 300 K.

c. In a certain process, the piston is allowed to move, and the gas expands at constant pressure and pushes the piston out 0.15 m. Calculate how much work is done by the gas.

d. Is heat energy transferred to or from the gas in the process in part (c)? Justify your answer.


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