Fluid Mechanics with teacher's notes

More documents

Recommendations

Info

$Holt Math Minnesota Test Prep Workbook for Grade 9$

$Math Skills: More Practice$

source, with a balloon placed over the opening of the flask. As the flask sits over the burner, the temperature of the air inside it increases from T 1 to T 2. According to the ideal gas law, when the temperature increases, either the pressure or the volume—or both—must also increase. Thus, the air inside the flask exerts a pressure (P 2) on the balloon that serves to inflate the balloon. Because the flask is not completely closed, the air expands to a larger volume (V 2) to fill the balloon. When the flask is taken off the burner, the pressure, volume, and temperature of the air inside will slowly return to their initial states. Another alternative form of the ideal gas law indicates the law’s dependence on mass density. Assuming each particle in the gas has a mass m, the total mass of the gas is N × m = M. The ideal gas law can then be written as follows: Ideal Gas Law MATERIALS ✔ 1 plastic 1 L bottle ✔ 1 quarter PV = NkBT = ⎯ Mk ⎯ BT m P = ⎯ Mk ⎯ BT = mV ⎯M ⎯ ⎯k BT rk ⎯ = ⎯ BT ⎯ V m m A real gas can often be modeled as an ideal gas An ideal gas is defined as a gas whose behavior is accurately described by the ideal gas law. Although no real gas obeys the ideal gas law exactly for all temperatures and pressures, the ideal gas law holds for a broad range of physical conditions for all gases. The behavior of real gases departs from the behavior of an ideal gas at high pressures or low temperatures, conditions under which the gas nearly liquefies. However, when a real gas has a relatively high temperature and a relatively low pressure, such as at room temperature and atmospheric pressure, its behavior approximates that of an ideal gas. For problems involving the motion of fluids, we have assumed that all gases and liquids are ideal fluids. Recall that an ideal fluid is a liquid or gas that is assumed to be incompressible. This is usually a good assumption because it is difficult to compress a fluid—even a gas—when it is not confined to a container. A fluid will tend to flow under the action of a force, changing its shape while maintaining a constant volume, rather than compress. Copyright © by Holt, Rinehart and Winston. All rights reserved. Make sure the bottle is empty, and remove the cap. Place the bottle in the freezer for at least 10 min. Wet the quarter with water, and place the quarter over the bottle’s opening as you take the bottle out of the freezer. Set the bottle on a nearby tabletop; then observe the bottle and quarter while the air in the bottle warms up. As the air inside the bottle A third way of writing the ideal gas law may be familiar to you from your study of chemistry: PV = nRT In this equation, n is the number of moles of gas (one mole is equal to 6.02 × 10 23 particles). The quantity R is a number called the molar (universal) gas constant and has a value of 8.3 1 J/(mol•K). NSTA TOPIC: Gas laws GO TO: www.scilinks.org sciLINKS CODE: HF2095 begins to return to room temperature, the quarter begins to jiggle around on top of the bottle. What does this movement tell you about the pressure and volume inside the bottle? What causes this increase in pressure and volume? Hypothesize as to why you need to wet the quarter before placing it on top of the bottle. Fluid Mechanics 339 SECTION 9-4 Teaching Tip Point out that the n in PV = nRT and the N in PV = Nk BT are related through Avogadro’s number (the same remark applies to R and k B). Key Models and Analogies Graphs offer a convenient way to represent the relationship between temperature, volume, and pressure for the following special cases of the ideal gas law: P V P Constant T Constant P Constant V TEACHER’S NOTES This activity is meant to demonstrate that pressure increases with temperature when the volume of a gas is constant. Eventually, the pressure becomes great enough to overcome the weight of the quarter, and it jumps up slightly, allowing air to escape. V T T 339
SECTION 9-4 Classroom Practice The following may be used as teamwork exercises or for demonstration at the chalkboard or on an overhead projector. PROBLEM The ideal gas law A sealed tank with a volume of 0.10 m 3 contains air at 27°C under pressure 1.8 × 10 4 Pa. The valve can withstand pressures up to 5.0 × 10 4 Pa. Will the valve hold if the air inside the tank is heated to 227°C? Answer Yes, the pressure will go up only to 3.0 × 10 4 Pa. The volume of a weather balloon is 8.0 m 3 at 3.0 × 10 2 K under atmospheric pressure. The balloon rises to an altitude where the temperature is 2.0 × 10 2 K and the pressure is ⎯ 1 2 ⎯ of atmospheric pressure. What is its new volume? Answer 11 m 3 340 340 SAMPLE PROBLEM 9E PROBLEM SOLUTION 1. DEFINE 2. PLAN 3. CALCULATE 4. EVALUATE Chapter 9 The ideal gas law Given: V 1 = 15 L P 1 = 2.0 atm T 1 = 310 K V 2 = 12 L P 2 = 3.5 atm Unknown: T 2 = ? This section, however, considers confined gases whose pressure, volume, and temperature may change. For example, when a force is applied to a piston, the gas inside the cylinder below the piston is compressed. Even though an ideal gas behaves like an ideal fluid in many situations, it cannot be treated as incompressible when confined to a container. Pure helium gas is contained in a leakproof cylinder containing a movable piston, as shown in Figure 9-17. The initial volume, pressure, and temperature of the gas are 15 L, 2.0 atm, and 310 K, respectively. If the gas is rapidly compressed to 12 L and the pressure increases to 3.5 atm, find the final temperature of the gas. Choose an equation(s) or situation: Because the gas undergoes a change and no gas particles are lost, the form of the ideal gas law relating the initial and final states should be used. P ⎯ 1V1 ⎯ = ⎯ T1 P2V2 ⎯ T2 Rearrange the equation(s) to isolate the unknown(s): T2P1V1 = T1P2V2 T2 = T1⎯P 2V2 ⎯ P1V1 Substitute the values into the equation(s) and solve: ⎯ T2 = (310 K)⎯( 3. 5 atm) ( 12 L) ( 2. 0 atm) ( 15 L) T 2 = 4.3 × 10 2 K Because the gas was compressed and the pressure increased, the gas temperature should have increased. 430 K > 310 K Gas Figure 9-17 CALCULATOR SOLUTION Your calculator should give the answer as 434. However, because the values in the problem are known to only two significant figures, the answer should be rounded to 430 and expressed in scientific notation. Copyright © by Holt, Rinehart and Winston. All rights reserved.
Page 1 and 2: Chapter 9 Overview Section 9-1 defi
Page 3 and 4: Section 9-1 Demonstration 1 Volume
Page 5 and 6: SECTION 9-1 The Language of Physics
Page 7 and 8: SECTION 9-1 Demonstration 4 Lifting
Page 9 and 10: SECTION 9-1 PRACTICE GUIDE 9A Solvi
Page 11 and 12: SECTION 9-2 STOP 326 Misconception
Page 13 and 14: SECTION 9-2 Visual Strategy Figure
Page 15 and 16: SECTION 9-2 Classroom Practice The
Page 17 and 18: Section 9-3 Demonstration 7 Fluid f
Page 19 and 20: SECTION 9-3 Misconception STOP Aler
Page 21 and 22: SECTION 9-3 Classroom Practice The
Page 23: Section 9-4 Demonstration 10 Temper
Page 27 and 28: Chapter 9 Summary Teaching Tip Ask
Page 29 and 30: 9 REVIEW & ASSESS 12. because the p
Page 31 and 32: 9 REVIEW & ASSESS 42. 7.1 m 43. 17
Page 33 and 34: 9 REVIEW & ASSESS 63. 60.9 m/s 2 64
Page 35 and 36: Chapter 9 Laboratory Exercise NOTE
Page 37 and 38: CHAPTER 9 LAB Boyle’s Law Apparat

Fluid Mechanics with teacher's notes

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?