Li, J. Atomically dispersed manganese catalysts for oxygen reduction in proton-exchange membrane fuel cells. Jin, Z. Atom-by-atom electrodeposition of single isolated cobalt oxide molecules and clusters for studying the oxygen evolution reaction.
Natl Acad. USA , — Martinez, U. Progress in the development of Fe-based PGM-free electrocatalysts for the oxygen reduction reaction. Wan, C. Molecular design of single-atom catalysts for oxygen reduction reaction. Energy Mater. Zhao, L. Cascade anchoring strategy for general mass production of high-loading single-atomic metal-nitrogen catalysts. Wang, J. Fabrication of single-atom catalysts with precise structure and high metal loading. Ji, S. Chemical synthesis of single atomic site catalysts.
Liu, L. Metal catalysts for heterogeneous catalysis: from single atoms to nanoclusters and nanoparticles. Li, H. Synergetic interaction between neighbouring platinum monomers in CO 2 hydrogenation.
Cichocka, M. A porphyrinic zirconium metal—organic framework for oxygen reduction reaction: tailoring the spacing between active-sites through chain-based inorganic building units. Sours, T. Circumventing scaling relations in oxygen electrochemistry using metal—organic frameworks. Guo, Y. Hydrogels and hydrogel-derived materials for energy and water sustainability.
Fang, Z. Gel electrocatalysts: an emerging material platform for electrochemical energy conversion. Zhao, F. Nanostructured functional hydrogels as an emerging platform for advanced energy technologies. Zhang, N. High-purity pyrrole-type FeN 4 sites as a superior oxygen reduction electrocatalyst.
Energy Environ. Li, X. Modulating the local coordination environment of single-atom catalysts for enhanced catalytic performance. Nano Res. Zhang, J. Controlling N-doping type in carbon to boost single-atom site Cu catalyzed transfer hydrogenation of quinoline. Kaiser, S. Uploaded by Yesu Oscco Baca. Document Information click to expand document information Original Title base-datos. Did you find this document useful? Is this content inappropriate? Report this Document.
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Print this page. Dyslexia is a learning difference that primarily affects the processes involved with fluent reading and writing. It is estimated that dyslexia affects approximately 1 in 10 people, with 1 in 25 classed as severely dyslexic. It is what we now recognise as a neurodivergent condition. Neurodivergence recognises that humans are not all the same. This factsheet gives an overview of how people with dyslexia can use technology to make things easier for them.
Much of this help is built into devices or available for free. Contents include 1. What is dyslexia? How can technology help people with dyslexia? Help with reading for people with dyslexia 4. Help with writing for people with dyslexia 5. Help to get more organised 6. How important is training for people with dyslexia? Assuming the vis- cosity to be negligible, find the volume of gas flowing across the 5, Fig. A wide vessel with a small hole in the bottom is filled with water and kerosene.
A wide cylindrical vessel 50 cm in height is filled with water and rests on a table. Assuming the viscosity to be negligible, find at what height from the bottom of the vessel a small hole should be perforated for the water jet com- ing out of it to hit the surface of the table at Fig.
A bent tube is lowered into a water stream as shown in Fig. To what height h will the water jet spurt? The clearance between the cylinder and the bottom of the vessel is very small, the fluid den- sity is p. Find the static pressure of the fluid in the clearance as a function of the distance r from the axis of the orifice and the cylin- der , if the height of the fluid is equal to h.
What work should be done in order to squeeze all water from a horizontally located cylinder Fig. The friction and viscosity are negligibly small.
A cylindrical vessel of height h and base area S is filled with water. Neglecting the viscosity of wa- ter, determine how soon all the water 1.
A horizontally oriented tube h AB of length 1 rotates with a constant II angular velocity co about a stationary vertical axis 00' passing through the end ho A Fig. The tube is filled with an ideal fluid. The end A of the tube is open, the closed end B has a very small orifice. Demonstrate that in the case Fig. On the opposite sides of a wide vertical vessel filled with water two identical holes are opened, each having the cross-sectional Fig. Find the resultant force of reaction of the water flow- ing out of the vessel.
With the slit closed, the vessel is filled with water. Find the resultant force of reaction of the water flowing out of the vessel immediately after the slit is opened.
Find the moment of reaction forces of flowing water, acting on the tube's walls, relative to the point 0. A side wall of a wide open tank is provided with a narrow- ing tube Fig.
Neglecting the viscosity of the water, find the horizontal component of the force tending to pull the tube out of the tank. C Z Fig. A cylindrical vessel with water is rotated about its ver- tical axis with a constant angular velocity co. Find: a the shape of the free surface of the water; b the water pressure distribution over the bottom of the vessel along its radius provided the pressure at the central point is equal to Po.
The clearance between the disc and the horizontal planes Fig. The end effects are to be neglected. A long cylinder of radius R1 is displaced along its axis with a constant velocity vo inside a stationary co-axial cylinder of radius R2. The space between the cylinders is filled with viscous liq- uid.
Find the velocity of the liquid as a function of the distance r from the axis of the cylinders. The flow is laminar. The inner cyl- inder is stationary while the outer one is rotated with a constant angular velocity co 2. The fluid flow is laminar. Find: a the volume of the fluid flowing across the section of the tube per unit time; b the kinetic energy of the fluid within the tube's volume; c the friction force exerted on the tube by the fluid; d the pressure difference at the ends of the tube.
All the distances 1 are equal. What is the maximum diameter of the sphere at which the flow around that sphere still remains laminar? Here the characteristic length is taken to be the sphere diameter. A rod moves lengthwise with a constant velocity v relative to the inertial reference frame K.
In a triangle the proper length of each side equals a. Find the perimeter of this triangle in the reference frame moving relative to it with a constant velocity V along one of its a bisectors; b sides. A rod flies with constant velocity past a mark which is stationary in the reference frame K. In the frame K it takes At 20 ns for the rod to fly past the mark. Find the prop- er length of the rod. Find: a the proper lifetime of this muon; b the distance travelled by the muon in the frame K "from the muon's standpoint".
A rod moves along a ruler with a constant velocity. Find the proper length of the rod and its velocity relative to the ruler. In the reference frame fixed to one of the rods the time interval between the moments, when the right and left ends of the rods coincide, is equal to At.
What is the velocity of one rod relative to the other? At a certain moment both particles decay simultaneously in the reference frame fixed to them. What time interval between the moments of decay of the two particles will be observed in the frame K?
Which particle decays later in the frame K? A rod AB oriented along the x axis of the reference frame K moves in the positive direction of the x axis with a constant velocity v. The point A is the forward end of the rod, and the point B its rear end.
Find: a the proper length of the rod, if at the moment tothe coordi- nate of the point A is equal to xA, and at the moment t8the coordi- nate of the point B is equal to x8; b what time interval should separate the markings of coordinates of the rod's ends in the frame K for the difference of coordinates to become equal to the proper length of the rod.
Suppose the moment when the clock B' gets opposite the clock A is taken for the beginning of the time count in the reference frames fixed to each of the rods. There are two groups of mutually synchronized clocks K and K' moving relative to each other with a velocity v as shown in Fig. The moment when the clock A' gets opposite the clock A A' Fig. Draw the approximate position of hands of all the clocks at this moment "in terms of the K clocks"; "in terms of the K' clocks". The reference frame K' moves in the positive direction of the x axis of the frame K with a relative velocity V.
Suppose that at the moment when the origins of coordinates 0 and 0' coincide, the clock readings at these points are equal to zero in both frames. Find the displacement velocity x of the point in the frame K at which the readings of the clocks of both reference frames will be permanent- ly identical. At two points of the reference frame K two events occurred separated by a time interval At. Demonstrate that if these events obey the cause-and-effect relationship in the frame K e.
The space-time diagram of Fig. Find: a the time interval between the events A and B in the reference frame where the two events occurred at the same point; b the distance between the points at which the events A and C occurred in the reference frame where these two events are simulta- neous. The velocity components of a particle moving in the xy plane of the reference frame K are equal to vx and vi,. Find the veloc- ity v' of this particle in the frame K' which moves with the velocity V relative to the frame K in the positive direction of its x axis.
What is the length of each rod in the reference frame fixed to the other rod? Two relativistic particles move at right angles to each other in a laboratory frame of reference, one 'with the velocity v1and the other with the velocity v2.
Find their relative velocity. An unstable particle moves in the reference frame K' along its y' axis with a velocity v'. In its turn, the frame K' moves relative to the frame K in the positive direction of its x axis with a velocity V.
The x' and x axes of the two reference frames coincide, the y' and y axes are parallel. Find the distance which the particle tra- verses in the frame K, if its proper lifetime is equal to At0. A particle moves in the frame K with a velocity v at an angle 0 to the x axis. Find the corresponding angle in the frame K' moving with a velocity V relative to the frame K in the positive di- rection of its x axis, if the x and x' axes of the two frames coincide.
The rod AB oriented parallel to the x' axis of the reference frame K' moves in this frame with a velocity v' along its y' axis. In its turn, the frame K' moves with a velocity V relative to the frame K as shown in Fig. Find the angle 0 between the rod and the x axis in the frame K.
The frame K' moves with a constant velocity V relative to the frame K. The boost stage lasted y. Find how much in per cent does the rocket velocity differ from the velocity of light at the end of the boost stage. What distance does the rocket cover by that moment? From the conditions of the foregoing problem determine the boost time Toin the reference frame fixed to the rocket. How many times does the relativistic mass of a particle whose velocity differs from the velocity of light by 0.
The density of a stationary body is equal to po. How much in per cent does the proton velocity differ from the velocity of light? What work has to be performed in order to increase the velocity of a particle of rest mass mo from 0.
Compare the result obtained with the value calculated from the classical for- mula. Find the velocity at which the kinetic energy of a particle equals its rest energy. Find how the momentum of a particle of rest mass m 0 de- pends on its kinetic energy.
Calculate the momentum of a proton whose kinetic energy equals 5C0 MeV. A beam of relativistic particles with kinetic energy T strikes against an absorbing target.
The beam current equals I, the charge and rest mass of each particle are equal to e and mo respectively. Find the pressure developed by the beam on the target surface, and the power liberated there. A sphere moves with a relativistic velocity v through a gas whose unit volume contains n slowly moving particles, each of mass m.
Find the pressure p exerted by the gas on a spherical surface ele- ment perpendicular to the velocity of the sphere, provided that the particles scatter elastically. Show that the pressure is the same both in the reference frame fixed to the sphere and in the reference frame fixed to the gas. Find the time dependence of the particle's velocity and of the distance covered. Find the force acting on the particle in this reference frame. Proceeding from the fundamental equation of relativistic dynamics, find: a under what circumstances the acceleration of a particle coin- cides in direction with the force F acting on it; b the proportionality factors relating the force F and the accele- ration w in the cases when F.
A relativistic particle with momentum p and total energy E moves along the x axis of the frame K. The photon energy in the frame K is equal to a. Making use of the transformation formulas cited in the foregoing problem, find the energy a' of this photon in the frame K' moving with a velocity V relative to the frame K in the photon's motion direction.
Demonstrate that the quantity E2 — p2c2for a particle is an invariant, i. What is the magnitude of this invariant? Make use of the invariant E2— p2c2remaining con- stant on transition from one inertial reference frame to another E is the total energy of the system, p is its composite momentum. A particle of rest mass mo with kinetic energy T strikes a stationary particle of the same rest mass. Find the rest mass and the velocity of the compound particle formed as a result of the collision.
A stationary particle of rest mass mo disintegrates into three particles with rest masses m1, m2, and m3. Find the maximum total energy that, for example, the particle m1may possess.
A relativistic rocket emits a gas jet with non-relativistic velocity u constant relative to the rocket. Find how the velocity v of the rocket depends on its rest mass m if the initial rest mass of the rocket equals mo. Find the mass of the released gas.
Two identical vessels are connected by a tube with a valve letting the gas pass from one vessel into the other if the pressure differ- ence Op 1. Up to what value will the pressure in the first vessel which had vacuum initially increase? The mass of the mixture is equal to m 5. Find the ratio of the mass of hydrogen to that of helium in the given mixture. Find the density of this mixture, assuming the gases to be ideal. A vertical cylinder closed from both ends is equipped with an easily moving piston dividing the volume into two parts, each con- taining one mole of air.
A vessel of volume V is evacuated by means of a piston air pump. One piston stroke captures the volume AV. How many strokes are needed to reduce the pressure in the vessel times? The process is assumed to be isothermal, and the gas ideal. Find the pressure of air in a vessel being evacuated as a func- tion of evacuation time t. The vessel volume is V, the initial pressure is Po.
The process is assumed to be isothermal, and the evacuation rate equal to C and independent of pressure. The evacuation rate is the gas volume being evacuated per unit time, with that volume being measured under the gas pressure attained by that moment. A smooth vertical tube having two different sections is open from both ends and equipped with two pistons of different areas Fig.
Each piston slides within a respective tube section. One mole of ideal gas is enclosed between the pistons tied with a non-stretchable thread. By how many kelvins must the gas between the pistons Fig. Draw the approximate p vs V plot of this process. A tall cylindrical vessel with gaseous nitrogen is located in a uniform gravitational field in which the free-fall acceleration is equal to g.
Find the corresponding temperature gradient. Let us assume that air is under standard conditions close to the Earth's surface. Presuming that the temperature and the molar mass of air are independent of height, find the air pressure at the height 5. An ideal gas of molar mass M is contained in a tall vertical cylindrical vessel whose base area is S and height h. The temperature of the gas is T, its pressure on the bottom base is Po. Assuming the temperature and the free-fall acceleration g to be independent of the height, find the mass of gas in the vessel.
An ideal gas of molar mass M is contained in a very tall vertical cylindrical vessel in the uniform gravitational field in which the free-fall acceleration equals g. Assuming the gas temperature to be the same and equal to T, find the height at which the centre of gravity of the gas is located. A horizontal cylinder closed from one end is rotated with a constant angular velocity 0 about a vertical axis passing through the open end of the cylinder.
The outside air pressure is equal to Po, the temperature to T, and the molar mass of air to M. Find the air pressure as a function of the distance r from the rotation axis. The molar mass is assumed to be independent of r. Carry out the calculations both for an ideal and for a Van der Waals gas. Find the Van der Waals parameters for this gas. Find the isothermal compressibility x of a Van der Waals gas as a function of volume V at temperature T. Making use of the result obtained in the foregoing problem, find at what temperature the isothermal compressibility x of a Van der Waals gas is greater than that of an ideal gas.
Examine the case when the molar volume is much greater than the parameter b. Demonstrate that the interval energy U of the air in a room is independent of temperature provided the outside pressure p is constant.
Find the gas temperature increment resulting from the sudden stoppage of the vessel. Two thermally insulated vessels 1 and 2 are filled with air and connected by a short tube equipped with a valve. The volumes of the vessels, the pressures and temperatures of air in them are known V1, pi, T1and V 2, p2, 7'2.
Find the air temperature and pressure established after the opening of the valve. Find how much the internal energy of the gas will change and what amount of heat will be lost by the gas. Then, as a result of the isobaric process, the gas expanded till its temperature got back to the initial value. Find the total amount of heat absorbed by the gas in this process. The gases are assumed to be ideal. Find the specific heat capacities cv and cpfor a gaseous mix- ture consisting of 7.
One mole of a certain ideal gas is contained under a weight- less piston of a vertical cylinder at a temperature T. The space over the piston opens into the atmosphere.
What work has to be performed in order to increase isothermally the gas volume under the piston it times by slowly raising the piston?
The friction of the piston against the cylinder walls is negligibly small. A piston can freely move inside a horizontal cylinder closed from both ends. Initially, the piston separates the inside space of the cylinder into two equal parts each of volume Vo, in which an ideal gas is contained under the same pressure Poand at the same tem- perature. What work has to be performed in order to increase isother- mally the volume of one part of gas i1times compared to that of the other by slowly moving the piston?
Draw the approximate plots of isochoric, isobaric, isother- mal, and adiabatic processes for the case of an ideal gas, using the following variables: a p, T; b V, T. Find: a the gas temperature after the compression; b the work that has been performed on the gas. In both cases the initial state of the gas was the same. Find the ratio of the respective works expended in each compression.
A heat-conducting piston can freely move inside a closed thermally insulated cylinder with an ideal gas. In equilibrium the piston divides the cylinder into two equal parts, the gas temperature being equal to To. The piston is slowly displaced. Find the gas tem- perature as a function of the ratio of the volumes of the greater and smaller sections. The adiabatic exponent of the gas is equal to y. Find the rate v with which helium flows out of a thermally insulated vessel into vacuum through a small hole.
The flow rate of the gas inside the vessel is assumed to be negligible under these con- ditions. Find the amount of heat obtained by the gas in this process if the gas temperature increased by AT. At what values of the polytropic constant n will the heat capacity of the gas be negative? Find the molar heat capacity of argon in this process, assuming the gas to be ideal. Find: a the amount of heat obtained by the gas; b the work performed by the gas.
The initial vol- ume of the gas is equal to V0. As a result of expansion the volume in- creases itimes. Find: a the increment of the internal energy of the gas; b the work performed by the gas; c the molar heat capacity of the gas in the process. An ideal gas whose adiabatic exponent equals y is expanded so that the amount of heat transferred to the gas is equal to the de- crease of its internal energy.
Find: a the molar heat capacity of the gas in this process; b the equation of the process in the variables T, V; c the work performed by one mole of the gas when its volume increases 11 times if the initial temperature of the gas is To. Find: a the work performed by the gas if its temperature gets an in- crement AT; b the molar heat capacity of the gas in this process; at what value of a will the heat capacity be negative?
Find: a the work performed by the gas and the amount of heat to be transferred to this gas to increase its internal energy by AU; b the molar heat capacity of the gas in this process.
An ideal gas has a molar heat capacity Cv at constant volume. Find: a heat capacity of the gas as a function of its volume; b the internal energy increment of the gas, the work performed by it, and the amount of heat transferred to the gas, if its volume increased from V1 to V2. Find: a heat capacity of the gas as a function of its volume; b the amount of heat transferred to the gas, if its volume in- creased from V1 to V 2.
An ideal gas has an adiabatic exponent y. Find: a the work performed by one mole of the gas during its heating from the temperature To to the temperature n times higher; b the equation of the process in the variables p, V. Find the work performed by one mole of a Van der Waals gas during its isothermal expansion from the volume V1 to V2 at a temperature T. The gas is assumed to be a Van der Waals gas.
For a Van der Waals gas find: a the equation of the adiabatic curve in the variables T, V; b the difference of the molar heat capacities CI, — Cvas a func- tion of T and V. Two thermally insulated vessels are interconnected by a tube equipped with a valve. The valve having been opened, the gas adiabatic- ally expanded. Assuming the gas to obey the Van der Waals equation, find its temperature change accompanying the expansion. Assuming that the gas exhausted is nitrogen, find the number of its molecules per 1 cm3and the mean distance between them at this pressure.
A vessel of volume V. Find the concentration of helium atoms in the given mixture. Find the pressure exerted by the beam on the wall assuming the mo- lecules to scatter in accordance with the perfectly elastic collision law. Determine the ratio of the sonic velocity v in a gas to the root mean square velocity of molecules of this gas, if the molecules are a monatomic; b rigid diatomic.
A gas consisting of N-atomic molecules has the temperature T at which all degrees of freedom translational, rotational, and vi- brational are excited.
Find the mean energy of molecules in such a gas. What fraction of this energy corresponds to that of transla- tional motion? Suppose a gas is heated up to a temperature at which all degrees of freedom translational, rotational, and vibrational of its molecules are excited.
Find the molar heat capacity of such a gas in the isochoric process, as well as the adiabatic exponent y, if the g as consists of a diatomic; b linear N-atomic; c network N-atomic molecules. An ideal gas consisting of N-atomic molecules is expanded isobarically. Assuming that all degrees of freedom translational, rotational, and vibrational of the molecules are excited, find what fraction of heat transferred to the gas in this process is spent to perform the work of expansion.
How high is this fraction in the case of a monatomic gas? Find the adiabatic exponent y for a mixture consisting of v1moles of a monatomic gas and v2 moles of gas of rigid diatomic molecules. How much in per cent and in what way will the gas pressure change on a sudden stoppage of the vessel? A gas consisting of rigid diatomic molecules is expanded adiabatically. A gas consisting of rigid diatomic molecules was initially under standard conditions.
Find the mean kinetic energy of a rotating molecule in the final state. How will the rate of collisions of rigid diatomic molecules against the vessel's wall change, if the gas is expanded adiabatically rl times?
How many times will the rate of collisions of molecules against a vessel's wall be reduced as a result of this pro- cess? A gas consisting of rigid diatomic molecules was expanded in a polytropic process so that the rate of collisions of the molecules against the vessel's wall did not change. Find the molar heat capacity of the gas in this process. The temperature of a hydrogen and helium mixture is T K.
At what value of the molecular velocity v will the Maxwell distribution function F v yield the same magnitude for both gases? At what temperature of a gas will the number of molecules, whose velocities fall within the given interval from v to v dv, be the greatest? The mass of each molecule is equal to m. The mass of each molecule is m, and the temperature is T. Using the Maxwell distribution function, calculate the mean velocity projection vx and the mean value of the modulus of this projection I vx I if the mass of each molecule is equal to m and the gas temperature is T.
From the Maxwell distribution function find vi , the mean value of the squared vx projection of the molecular velocity in a gas at a temperature T. Making use of the Maxwell distribution function, calculate the number v of gas molecules reaching a unit area of a wall per unit time, if the concentration of molecules is equal to n, the temperature to T, and the mass of each molecule is m. Using the Maxwell distribution function, determine the pressure exerted by gas on a wall, if the gas temperature is T and the concentration of molecules is n.
Compare the value obtained with the reciprocal of the mean velocity. A gas consists of molecules of mass m and is at a temperature T. Making use of the Maxwell velocity distribution function, find the corresponding distribution of the molecules over the kinetic energies c. Determine the most probable value of the kinetic energy cp.
Does ep correspond to the most probable velocity? Find the most probable values of a the velocity of the molecules in the beam; compare the result obtained with the most probable velocity of the molecules in the vessel; b the kinetic energy of the molecules in the beam.
An ideal gas consisting of molecules of mass m with concen- tration n has a temperature T. Using the Maxwell distribution func- tion, find the number of molecules reaching a unit area of a wall at the angles between 0 and 0 dO to its normal per unit time. From the conditions of the foregoing problem find the num- ber of molecules reaching a unit area of a wall with the velocities in the interval from v to v dv per unit time.
Find Avogadro's number from these data. Assuming the temperature T and the free-fall acceleration g to be independent of the height, find the height at which the concentrations of these kinds of molecules are equal. A very tall vertical cylinder contains carbon dioxide at a certain temperature T. Assuming the gravitational field to be uni- form, find how the gas pressure on the bottom of the vessel will change when the gas temperature increases times.
A very tall vertical cylinder contains a gas at a tempera- ture 7'. Assuming the gravitational field to be uniform, find the mean value of the potential energy of the gas molecules. Does this value depend on whether the gas consists of one kind of molecules or of several kinds? Find the mass of a mole of colloid particles if during their centrifuging with an angular velocity co about a vertical axis the con- centration of the particles at the distance r2 from the rotation axis is 11 times greater than that at the distance r1 in the same horizontal plane.
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