為什麼[A(org)]=n[An(org)]成立 (第三張圖equation 7.9) 感謝

Experiment 7 Experiment 7 The partition of Organic acid between Water and Organic solvent Objectives Understand the partition of a solute between two immiscible solvents. Introduction A chemical analysis that is performed primarily with the aid of volumetric glassware (e.g., pipets, burets, volumetric flasks) is called a volumetric analysis. For a volumetric analysis procedure, a known quantity or a carefully measured amount of one substance reacts with a to-be-determined amount of another substance with the reaction occurring in aqueous solution. The volumes of all solutions are carefully measured with volumetric glassware. The known amount of the substance for an analysis is generally measured and available in two ways: 1. As a primary standard: An accurate mass (and thus, moles) of a solid substance is measured on a balance, dissolved in water, and then reacted with the substance being analyzed. 2. As a standard solution: A measured number of moles of substance is present in a measured volume of solution - a solution of known concentration, generally expressed as the molar concentration (or molarity) of the substance. A measured volume of the standard solution then reacts with the substance being analyzed. The reaction of the known substance with the substance to be analyzed, occurring in aqueous solution, is generally conducted by a titration procedure. The titration procedure required a buret to dispense a liquid, called the titrant, into a flask containing the analyte. A reaction is complete when stoichiometric amounts of the reacting substances are combined. In a titration this is the stoichiometric point. In this experiment the stoichiometric point for the acid-base titration is detected using a phenolphthalein indicator. Phenolphthalein is colorless in an acidic solution but pink in a basic solution. The point in the titration at which the phenolphthalein changes color is called the endpoint of the indicator. Indicators are selected so that the stoichiometric point in the titration coincides (at approximately the same pH) with the endpoint of the indicator.

求解，謝謝🙏（大一物理）

A model rocket is launched straight upward. Its altitude y as a function of time is given by y = bt - ct², where b = 80 m/s, c = 4.9 m/s², t is the time in seconds, and y is in me- ters. (a) Use differentiation to find a general expression for the rock- et's velocity as a function of time. (b) When is the velocity zero?

想請問這題🙏，有點看不懂圖三的公式是從何而來，卡住了

EXAMPLE 21.11 FIELD OF A UNIFORMLY CHARGED DISK A nonconducting disk of radius R has a uniform positive surface charge density o. Find the electric field at a point along the axis of the disk a distance x from its center. Assume that x is positive. SOLUTION IDENTIFY and SET UP: Figure 21.25 shows the situation. We rep- resent the charge distribution as a collection of concentric rings of charge dQ. In Example 21.9 we obtained Eq. (21.8) for the field on the axis of a single uniformly charged ring, so all we need do here is integrate the contributions of our rings. EXECUTE: A typical ring has charge dQ, inner radius r, and outer radius r + dr. Its area is approximately equal to its width dr times its circumference 2πr, or dA = 2πr dr. The charge per unit area is σ = dQ/dA, so the charge of the ring is do = o da = 2πor dr. We use dQ in place of Q in Eq. (21.8), the expression for the field due to a ring that we found in Example 21.9, and replace the ring 21.25 Our sketch for this problem. Idr dQ X P dEx dEx radius a with r. Then the field component dEx at point P due to this ring is 1 2πσrx dr 4π€0 (x² + ²)3/2 SOLUTION Continued

求證明過程~感謝

7. (II) Atwood's machine was an apparatus that allowed a direct verification of Newton's second law. It could also be used to measure g. Two equal blocks of mass M hang on either side of a pulley; see Fig. 5.56. A small square rider of mass m is placed on one block. When the block is released, it accelerates for a distance H till the rider is caught by a a ring that allows the block to pass. From then on the system moves at a constant speed which is measured by timing the fall through a distance D. Show that (2M + m)D 2mH12 where 1 is the time moved at constant speed. m2 M Hotez D M FIGURE 5.56 Problem 7

一直卡住算不出來 求詳解 謝謝🙏

1. A building locates at x=dſ with a height of h as shown in the right figure. A cannon at origin fires a bullet to bomb the roof of the building, please find out: (a) what is the initial velocity and angle should be to complete this mission? (b) how much time will it take to hit the target? (c) how height the bullet can reach? 2. Similar to the problem #1, now there is a mountain with a height of 2h sitting at d/2. The mission is the same, 2h T firing a cannon to high the roof of the building. Please/10 find out: (a) what is the initial velocity and angle should be to complete this mission by flying the bullet over the mountain? (b) how much time will it take to hit the target? (c) how height the bullet can reach?

求解法 謝謝 （普通物理）

1. Consider a particle moving with the acceleration vs. time graph as in Fig. 1. a, and to are constants with unit in m/s2 and s. Assume the particle is at rest and at origin (L) at t = 0. (a) Find the velocity v(t) for each interval (i.e. 0<t< to, to <t< 2to, 2t, <t (b) Find the displacement x(t) of the particle for each interval. (c) What are the velocity and displacement of the particle at t = 3t0? Fig. 1 an 2ao w ao to to 8:03 来搜寻 co 33°C D

求解答案是否正確

Multiple-choice questions: (70 points) write the letter of statement that is not true: 1. A.B.U The Drude Model: (a) It is a classical approach using concepts from the kinetic theory of gases. (b) A relaxation-time approximation is used where the probability of collision is l/t. (c) No forces act on the electrons in between collisions. (d) It predicts accurately the electronic heat capacity of metals. 2. The Sommerfeld Model: (a) The crystal potential is replaced by an average Coulomb potential. (b) The separation of states is so close that a continuum model can be applied. (c) The electrons are highly localized due to a strong crystal potential. (Q) The energy of the highest occupied state at 0 K is the Fermi energy. 3. Density of states in k-space, N(k): (a) N(k) is determined by the boundary value conditions. (b) For lattices in any dimensions, N(k) is constant in k-space. (C) N(k) depends on the direction and magnitude of k. (d) It is directly proportional to the volume of the crystal. E影響, c 4. The Fermi surface of a metal: (a) is responsible for many of the transport properties of the metal, (b) depends on the nature of the chemical bonds, (c) is always a sphere, (d) can involve mixing of electron orbitals. ✓ 5. The conductivity of a material () increases with the mobility of its carriers, (b) increases with the density of carriers, (C) it is inversely proportional to the energy gap. cogu changes with temperature. 6. BID Plasmons: (a) They are an important characteristic of the Sommerfeld electron gas model. (b) Plasmons occur spontaneously in metals. (c) They are related to charge density oscillations. (d) The Plasmon energy is typically of the order of 10 eV. The Fermi energy Ef in intrinsic semiconductors 8) is usually close to y E, at OK (b) it ACiD. can increase or decrease with temperature depending on the ratio of hole and electron effective masses, (c) it represents the point at which the probability of occupation is 12, even though there may not been any states with that energy, (d) its value relative to the electronic bands must remain unaffected in the presence of defects or interfaces.

e.f.g這三題不知道要如何解釋，請各位大神幫忙解題謝謝

1-8. Consider two inertial reference frames. When an observer in each frame measures the following quantities, which measurements made by the two observers must yield the same re- sults? Explain your reason for each answer. (a) The distance between two events (6) The value of the mass of a proton (c) The speed of light (d) The time interval between two events (e) Newton's first law (f) The order of the elements in the periodic table (g) The value of the electron charge

請問第七題怎麼解

60 s, turn 90 20 km/h for 2.0 min, turn 90° to the point, (a) how far are you from your starting point, and what direction relative to your initial direction of travel are you? V During volcanic eruptions, chunks of solid rock can be blasted out of the volcano; these projectiles are called volcanic bombs. Figure 4-22 shows a cross section of Mt. Fuji, in Japan. (a) At what initial speed would a bomb have to be ejected, at angle 0o = 60.0° to the horizontal, from the vent at A in order to fall at the foot of the volcano at B, at vertical distance h = 2.60 km and horizontal distance d = 9.40 km? Ignore, for the moment, the effects of air on the bomb's travel. (b) What would be the time of flight? (c) Would the effect of the air increase or decrease your answer in (a)?onatlar slow orl w moito Movisio Olovo vibolov te tootsodio dos olvistatani se moltotib nur no vodo as vd botu 29 vd baidot otsi Nomstl moll bottom 12 A plane flies 5 then 1100 km sout) trip, what are the displacement, the velocity, and (e) is 13 An astronau of 4.5 m. (a) Wha eration has a ma minute are requ period of the m 14 A basebal mum height al after reaching that is 86.0 m (a) What may ball? (b) How the ball strike blitt 00 Troede Vibolov sister sam 12 d B 15 The ran also on the place to plac broad jump (where g= by how mu instead in 1 Figure 4-22 Problem 7. 8 Oasis A is 90 km due west of oasis B. A desert camel leaves A and takes 55 h to walk 75 km at 37° north of due east. Next it takes 45 h to walk 65 km due south. Then it rests for 5.0 h. What are the (G) magnitu Cia

力學 救救我 謝謝！（第三題不用）

1. Considerathin rod ofuniform linear mass density pL with mass 4/ and length /, find the gravitational potential。dp/有)。at a perpendicular distance Afrom the center ofthe rod. You may find the integral in (E.6) in Appendix E useful 2. A spherical planet of radius 人> consists ofacore of radius 有/ with uniform density pi. and a thick outer cloud of dust with umiform density p: Find the force (magnitude and direction) onamass箇inside the dust cloud ata position ARp from the planetcenter( 吃<訪<記), 3. Use Fermat's principle by applying calculus of variation to minimize the time oflight passing from medium ofrefractive index jg, to another medium ofrefractive index >, derive the Snells law ofrefraction: js光 名2s 銷 4. Consider the Atwood machine oftwo masses connected by amassless string oflength 7overapulley ofradius gas shown, (a) Write down the total kinetic energy and potential energy in terms of the coordinatex Hence obtain the Lagrangian ofthe system. (b) Derive the Lagrange's equation of motion and hence find the acceleration ofthe masses. x 和二 工