Name: ________________________ Class: ___________________ Date: __________
ID: A
S15--HPhys Q5 States of Matter PRACTICE Multiple Choice Identify th...
S15--HPhys Q5 States of Matter PRACTICE Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Where is the pressure greater, one meter beneath the surface of Lake Michigan or one meter beneath the surface of a swimming pond? a. In the pond b. In Lake Michigan c. The pressure is approximately the same in both places 2. Which state of matter is associated with the very highest of temperatures? a. liquid b. plasma c. gas d. solid e. both choices B and C are valid. 3. In a large tank of liquid, the hydrostatic pressure at a given depth is a function of: a. depth. b. surface area. c. liquid density. d. Choices a and c are both valid. e. Choices a and b are both valid. 4. A 15 000-N car on a hydraulic lift rests on a cylinder with a piston of radius 0.20 m. If a connecting cylinder with a piston of 0.040-m radius is driven by compressed air, what force must be applied to this smaller piston in order to lift the car? a. 17 000 N b. 15 000 N c. 1 500 N d. 3 000 N e. 600 N 5. A large stone is resting on the bottom of the swimming pool. The normal force of the bottom of the pool on the stone is equal to the: a. weight of the water in the swimming pool. b. weight of the stone. c. difference between the weight of the stone and the weight of the displaced water. d. weight of the water displaced. e. sum of the weight of the stone and the weight of the displaced water. Problem 6. A gas cylinder of volume 0.150 m3 is connected to another cylinder of volume 0.260 m3 by a narrow tube of negligible volume. The system contains air at 32.0°C and 109 kPa. The smaller cylinder is now heated to 82.0°C, but the larger cylinder is maintained at 32.0°C. Calculate the final pressure in the system. 7. A jeweler has made a crown of an alloy of gold and copper. The crown weighs 0.358 N when measured in air and 0.338 N when submerged completely in water. The density of water is 1.00 × 103 kg/m3, the density of copper is 8.92 × 10 3 kg/m3, and the density of gold is 1.93 × 10 4 kg/m3 . Calculate the weight of the gold in the crown. 8. A solid cubical block with a side of 11.0 cm floats in mercury so that 5.48 cm of the side of the block is submerged in the mercury. Water is then poured on the system until the block floats completely submerged. Calculate the height of the water column that was added. The density of water is 1.00 × 103 kg/m3 and the density of mercury is 13,590 kg/m3. 9. A scale is used to record the height of mercury in a barometer. The scale was calibrated at 14.6°C. The barometer records the height of mercury as 768 mm on a day when the room temperature is 34.4°C. Calculate the correct atmospheric pressure as height of mercury column at 0.0°C. The coefficients of linear expansion of the material of the scale is 2.60 × 10 −5 (°C)–1 and of mercury is 6.00 × 10 −5 (°C)–1. 10. Divisions are marked correctly on a measuring scale at a temperature of 11.1°C. What will be the percentage error if the scale is used on a day when the temperature is 32.2°C? The coefficient of linear expansion of the material of the scale is 1.60 × 10 −5 (°C)–1.
1
Name: ________________________
ID: A
11. A certain bicycle tire should be inflated to 250 kPa before it is used. If the tire is at 230 kPa when the air in the tire is at 25°C, what temperature does the air in the tire have to reach for the proper pressure in the tire to be attained? Assume that expansion of the tire itself is negligible. 12. A 3.22×10–5-m3 glass tube filled with xenon is pressurized to 6.00 atm. The temperature of the gas is 22.0°C. a. How many moles of gas are in the tube? b. What is the mass of the gas in the tube? (Xenon has a molar mass of 131.29 g/mol.) 13. Two pistons are connected to a fluid-filled reservoir. The first piston has an area of 3.002 cm2, and the second has an area of 315 cm2. a. If the first cylinder is pressed inward with a force of 50.0 N, what is the force that the fluid in the reservoir exerts on the second cylinder? b. A third cylinder is connected to the reservoir. When the second cylinder is pressed inward with a force of 50.0 N, the fluid in the reservoir exerts a force of 135 N on the third cylinder. What is the area of the third cylinder? 14. A wooden raft that measures 1.20 m × 0.85 m × 0.10 m has a mass of 9.77 kg. of the raft is to stay afloat in fresh water, what is the maximum amount of additional mass that can be added to the raft? 15. Free diving is a sport in which the contestants attempt to reach the greatest depth possible underwater without using supplemental oxygen. The world record for free diving is 85 m. What is the pressure of water at this depth? 16. Atmospheric pressure at sea level is measured as 101,325 Pa. What is the weight of the column of air above a 1-cm2 patch of ground? 17. A 100.0-L chamber contains an ideal gas at a temperature of 20.0°C and a pressure of 15 atm. One wall of the chamber moves as a piston and reduces the volume of the chamber to 75 L while raising the temperature to 27.0°C. What is the new pressure under these conditions? 18. An ideal gas is trapped in a cylinder 1.0 m long and with a diameter of 12.5 cm. The pressure inside is measured as 3.0×105 Pa with a temperature of 29°C. How many gas molecules are contained within this cylinder? 19. What is the volume of 1 mol of an ideal gas under standard temperature and pressure of 1.013×105 Pa and 0°C? 20. A car with a mass of 1.0×103 kg rests on a hydraulic lift that is 2.0 m wide and 10.0 m long. The lift is connected to a second cylindrical piston with only a 14.0-cm diameter and a hand pump. What force is necessary to lift the car off the ground using only the hand pump? 21. A piston contains 0.102 m3 of gas at an initial pressure of 217 kPa and an initial temperature of 23.0°C. Use these as the starting conditions for the following questions. a. What is the new pressure of the gas when the volume of the cylinder is reduced to 0.074 m3 while the temperature remains constant? b. If the volume remains constant at 0.102 m3, what will be the pressure of the gas at 81°C? c. What is the new pressure of the gas when the temperature is reduced to 11°C and the volume of the cylinder is increased to 0.256 m3? 22. A cube of stainless steel, 0.30 m on each side, is completely submerged in water. a. What is the buoyant force on the cube? b. What is the apparent weight of the cube? (The density of stainless steel is 8.0×103 kg/m3.) c. What volume of steel would have to be removed from the center of the cube in order for the cube to float?
2
ID: A
S15--HPhys Q5 States of Matter PRACTICE Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 DIF: 2 2. ANS: B PTS: 1 DIF: 1 TOP: 9.1 States of Matter | 9.2 The Deformation of Solids 3. ANS: D PTS: 1 DIF: 1 TOP: 9.4 Variation of Pressure with Depth | 9.5 Pressure Measurements 4. ANS: E PTS: 1 DIF: 2 TOP: 9.4 Variation of Pressure with Depth | 9.5 Pressure Measurements 5. ANS: C PTS: 1 DIF: 2 TOP: 9.6 Buoyant Forces and Archimedes's Principle PROBLEM 6. ANS: 115 kPa PTS: 1 7. ANS: 0.334 N
DIF:
3
TOP: Calculate the pressure, volume, and number of moles in a gas.;
PTS: 1 8. ANS: 5.04 cm
DIF:
3
TOP: Apply Archimedes' principle to buoyancy.
PTS: 1 DIF: 9. ANS: 767 mm of mercury
3
TOP: Apply Archimedes' principle to buoyancy.
DIF:
3
TOP: Calculate the expansion of solids.
DIF:
3
TOP: Calculate the expansion of solids.
PTS: 1 10. ANS: –0.0338% PTS: 1
1
ID: A 11. ANS: P1 V1 P2 V2 = T1 T2
T2 = =
P 2 T1 P1
(250 kPa) (273K + 0K) 230 kPa
= 297 K =24° C PTS: 1 12. ANS: a. PV = nRT
n=
PV RT
Ê ˆÊ ˆ (6.00atm) ÁÁ 1.01325 × 105 Pa/atm ˜˜ ÁÁ 3.22 × 10 −5 m3 ˜˜ Ë ¯Ë ¯ = ÊÁ ˆ˜ 3 Á 8.31 Pa ⋅ m / mol ⋅ K ˜ (273 K+22K) Ë ¯ = 7.99 × 10 −3 mol b. m = nM = (7.99×10–3 mol)(131.29 g/mol) = 1.05 g PTS: 1
2
ID: A 13. ANS:
a.F 2 =
F1 A2 A1
Ê ˆ (50.0 N) ÁÁ 315 cm2 ˜˜ Ë ¯ = ÊÁ 2ˆ Á 3.002 Cm ˜˜ Ë ¯ = 5.25 × 10 3 N b. =
F2 F3 = A2 A3
A3 =
F3 A2 F2
Ê ˆ (135 N) ÁÁ 315 cm2 ˜˜ Ë ¯ = (50.0 N) = 8.50 × 10 2 cm2 PTS: 1 14. ANS: Fg = Fbuoyant, so Fg = ρfluidVg mg = ρfluidVg m = ρfluidV m = mexisting + madded mexisting + madded = rfluidV madded = ρfluidV – mexisting = (1.00×103 kg/m3)(1.2 m)(0.85 m)(0.10 m) – (9.77 kg) = 92 kg PTS: 1 15. ANS: P = ρhg = (1.00×103 kg/m3)(85 m)(9.80 m/s2) = 8.3×105 Pa PTS: 1
3
ID: A 16. ANS: F P= A
ÊÁ ˆ˜ ÁÁ ˜˜ 1 m2 Á ˜˜ F = PA = (101,325Pa)(1.0cm ) ÁÁ Á 1 × 10 4 cm2 ˜˜ Ë ¯ 2
ÁÊÁ 3.0 × 10 5 Pa ˜ˆ˜ (π ) (0.0625 m) 2 (1.0 m) Ë ¯ = ÁÊÁ 8.31 Pa ⋅ m3 / mol ⋅ K ˜ˆ˜ (302 K) Ë ¯ = 1.467mol ÊÁ ˆ Á 6.022 × 10 23 molecules ˜˜˜ ˜˜ = 8.8 × 10 23 molecules 1.467 molÁÁÁÁ ˜˜ 1 mol Á Ë ¯ PTS: 1
4
ID: A 19. ANS: PV = nRT
V=
nRT P
Ê ˆ (1.0 mol) ÁÁ 8.31 Pa ⋅ m3 / mol ⋅ K ˜˜ (273 K) Ë ¯ = 5 1.013 × 10 Pa = 0.022m3 PTS: 1 20. ANS: F1 A2 F2 = A1
ÊÁ ˆÊ ˆ 2 Á 1.0 × 10 3 kg ˜˜ ÁÁ 9.80 m/s 2 ˜˜ (π ) (0.070 m) Ë ¯Ë ¯ = (2.0 m) (10.0 m) = 7.5N PTS: 1
5
ID: A 21. ANS: a.P 1 V 1 = P 2 V 2
P2 =
P1 V1 V2
ÊÁ ˆÊ ˆ Á 2.17 × 10 5 Pa ˜˜ ÁÁ 0.102m3 ˜˜ Ë ¯Ë ¯ = ÊÁ 3ˆ ˜ Á 0.074 m ˜ Ë ¯ = 3.0 × 10 5 Pa = 3.0 × 10 2 kPa P1 V1 P2 V2 b. = = T1 T2 P2 =
P 1 V 1 T2 T1 V2
and V 1 = V 2 , so P 2 =
P1 T2 T1
ÊÁ ˆ Á 2.17 × 10 5 Pa ˜˜ (273K +81 K) Ë ¯ = (273K +23 K) = 2.60 × 10 5 Pa = 2.60 × 10 2 kPa c.
P1 V1 P2 V2 = T1 T2
P2 =
P 1 V 1 T2 T1 V2
ÁÊÁ 2.17 × 10 5 Pa ˜ˆ˜ ÁÊÁ 0.102 m3 ˜ˆ˜ (273K +11° K) Ë ¯Ë ¯ = Ê ˆ Á (273K +23 K) Á 0.256 m3 ˜˜ Ë ¯ = 8.30 × 10 4 Pa = 83.0 kPa PTS: 1
6
ID: A 22. ANS: a. Fbuoyant = ρfluidVg = (1.00×103 kg/m3)(0.027 m3)(9.80 m/s2) = 260 N b. Fapparent = Fg – Fbuoyant Fg = ρsteelVg Fapparent = ρsteelVg – Fbuoyant = (8.0×103 kg/m3)(0.027 m3)(9.80 m/s2) – (260 N) = 1.9×103 N c.F buoyant = F g-floating
F g-floating = F g − F removed F g-floating = g(m1 − m removed ) F g-floating = ρ steel g(V 1 − V removed ) F buoyant = ρ steel g(V 1 − V removed ) V removed =
