41 Learning Methods That Benefit a Lifetime

Chapter 16 Understanding Numbers by Contrast
① The square of 13 is 169, and the square of 14 is 196.

②The density of concentrated hydrochloric acid is 1.19g/cm3, the fire alarm number is 119, and Zhang Qian's second mission to the Western Regions was in 119 BC.

③The density of concentrated sulfuric acid is 1.84g/cm3, the zip code inquiry telephone number is 184, and the year of the Yellow Turban Uprising is also 184.

④空气的密度是1.293／L，把最后一位的3略去为1.29，在29前再加个4整好是氧气的密度，即1.429g／L。可见氧气比空气略重。

⑤ The earth's land area is 1.49 million km2, and the distance between the earth and the sun is 1.49 million km.

⑥ The average distance between the sun and the earth is about 1.5 million km, while the earth's surface area is 5.1 million km2, which is equivalent to swapping the places of integers and decimals.

⑦ The average distance between the sun and the earth is 1.5 million km, which is called an astronomical unit, while the distance between the sun and Pluto is 60 billion km, or 40 astronomical units.

⑧The intersection angle of yellow and red is 23.5°, which is equal to the latitude of the Tropic of Cancer, and the angle between the earth axis and the ecliptic plane is 66.5°, which is equal to the latitude of the North and South Arctic Circles.

⑨二分二至四个节气，是反映地球公转过程中季节的昼夜转换点，这四个节气的日期分别为：春分——3月21日前后，夏至——6月22日，秋分——9月23日，冬至——12月22日前后。从春分算起，月份分别为3、6、9、12，均为3的倍数，而日期分别约为21、22、23、22。

Understanding Mathematical Concepts Using Contrast
①Natural numbers and integers.

自然数即正整数（1、2、3、4、5、6、7、8……），其性质是：有最小，无最大，有顺序性，永远可以施行加乘两种运算。

Integers include positive integers, negative integers, and zero, and their properties are: no minimum, no maximum, sequence, and three operations of addition, subtraction, and multiplication can always be performed.

② Rational and irrational numbers.

Rational numbers include integers, fractions, finite and infinitely recurring decimals.

Its properties are: no minimum, no maximum, sequence, density and discontinuity, and four operations of addition, subtraction, multiplication and division can always be performed (the divisor is not zero).

Irrational numbers refer to infinite non-repeating decimals.Rational and irrational numbers are collectively called real numbers.

③The difference between equation, algebraic formula and equation.

An equation contains an equal sign, an algebraic expression does not contain an equal sign, and an equation is an equation that contains unknowns.

④The relationship and difference between straight line, ray and line segment.

Connection: straight line, ray, and line segment are the relationship between the whole and part, and line segment and ray are part of the straight line.They are all composed of countless points. If one point is taken on the line, the line can be divided into two rays; if two points are taken, it can be divided into a line segment and two rays.A straight line can be obtained by extending both ends of the line segment or extending the ray in reverse.

The difference: a straight line has no endpoints and an infinite length, indicating that the letters of the line are disordered; a ray has an endpoint and an infinite length, indicating that the letters of the ray are ordered; a line segment has two endpoints, and the length can be measured, indicating that the letters of the line segment are disordered.

Memorizing Physical Concepts Using Contrast
① The relationship and difference between pitch, loudness and fret.

connect?Pitch, loudness and timbre (also known as timbre) are the three elements of musical tone.

the difference?The pitch is determined by the vibration frequency of the sounding body; the loudness is determined by the amplitude of the sounding body and the distance from the sound source; the timbre is determined by the nature of the sounding body itself.

②Celsius temperature and thermodynamic temperature.

a.Under standard conditions, the temperature of the mixture of ice and water is defined as 0 degrees, and the temperature of boiling water is defined as 100 degrees. The temperature between 0 degrees and 100 degrees is divided into 100 equal parts, and each equal part is 1 degree Celsius.The unit of temperature in Celsius is degrees Celsius and is represented by the symbol ℃.

b.The lower limit of temperature in the universe is about -273°C, which is called absolute zero.The temperature starting from absolute zero is called thermodynamic temperature.The unit of thermodynamic temperature is Kelvin, abbreviated as Kelvin, represented by the symbol K.

c.The relationship between thermodynamic temperature T and Celsius temperature t is: T=t+273K.

③ melting and solidification.

a.The change of matter from solid to liquid is called melting; from liquid to solid is called solidification.

b.Solids absorb heat when they melt, and liquids release heat when they solidify.

④ melting point and freezing point.

a.The melting temperature of the crystal is called the melting point, and the freezing temperature of the crystal is called the freezing point.

b.For the same substance, the freezing point is the same as the melting point.

⑤ crystal and amorphous.A solid with a fixed melting point is a crystal, and a solid without a fixed melting point is an amorphous. The difference between the two is whether there is a definite melting point.

⑥ vaporization and liquefaction.

a.The change of matter from liquid to gas is called vaporization, and the change from gas to liquid is called liquefaction.

b.Heat is absorbed when a liquid vaporizes, and heat is released when a gas is liquefied.

c.There are two methods of liquefaction, one is to lower the temperature, and the other is to pressurize.

⑦ Evaporation and boiling.

a.Evaporation and boiling are two forms of vaporization.

b.The vaporization phenomenon that occurs on the surface of a liquid at any temperature is called evaporation, and the violent vaporization phenomenon that occurs simultaneously in the interior and surface of a liquid at a certain temperature is called boiling.

c.The temperature at which a liquid boils is called the boiling point.

⑧ sublimation and sublimation.

a.Sublimation occurs when a substance changes directly from a solid state to a gaseous state, and when a substance changes directly from a gaseous state to a solid state, it is called desublimation.

b.Substances absorb heat during sublimation and release heat during desublimation.

⑨Mass and gravity.

a.Mass refers to the amount of matter contained in an object, and gravity refers to the gravitational force of the earth on an object;

b.Mass has only magnitude and no direction, and is a scalar quantity, while gravity is a vector with both magnitude and direction;

c.Where the mass is constant, the gravity changes with the position;
d.The mass is measured by a balance, and the gravity is measured by a spring;

e.The unit of mass is generally expressed in kilograms, and the unit of gravity is generally expressed in Newtons.

⑩Pressure and pressure.

Pressure is the force that presses perpendicularly on the surface of an object.

Pressure is the pressure per unit area of ​​an object.

Memorizing Chemical Concepts Using Contrast
① Molecules and atoms.

a.Molecules are the smallest particles that maintain the chemical properties of substances, and atoms are the smallest particles that undergo chemical changes.

b.Some substances are composed of molecules, such as water and oxygen; others are directly composed of atoms, such as mercury.

② atoms and elements.An element is a general term for a class of atoms with the same nuclear charge.

③ mixture and pure substance.

A mixture is a mixture of two or more substances that do not react chemically with each other, and each substance in the mixture maintains its original properties, such as air.

A pure substance is made up of one substance, such as oxygen.

④Physical changes and chemical changes.

The change in which other substances are not produced when a substance changes is called a physical change; the change in which other substances are produced during a change is called a chemical change, also called a chemical reaction.For example: Diffusion, crystallization, etc. are physical changes, while combustion, weathering, etc. are chemical changes.

When a chemical change occurs, it must be accompanied by a physical change, and when a physical change occurs, a chemical change does not necessarily occur.

When substances change, two kinds of changes often occur at the same time. At this time, it depends on which one is the main one. The key difference lies in whether new substances are formed or not.

⑤Physical and chemical properties.

The properties that a substance exhibits without chemical changes, such as color, state, smell, melting point, hardness, density, etc., are called physical properties.

The properties that a substance exhibits during chemical changes, such as flammability, stability, acidity, alkalinity, etc., are called chemical properties.

⑥Element and compound.

A pure substance composed of the same element is called an element.

Pure substances composed of different elements are called compounds.

⑦Atomic weight and formula weight.

Use 12/1 of the atomic mass of 12C as a "weight" to weigh other atomic masses, and the number of "weights" needed is the atomic weight of the atom being weighed.

The sum of the atomic weights of the atoms in a chemical formula is the formula weight.

⑧Standard status and usual status.

The standard condition is 1 standard atmosphere, 0°C.

The normal condition is 1 standard atmospheric pressure, 20°C.

⑨Ionic compounds and covalent compounds:

Compounds formed by the interaction of anions and cations are ionic compounds, such as NaCl, NaOH, ZnSO4, etc.

Compounds that form molecules by sharing electron pairs are covalent compounds, such as H2O, CO2, HCl, etc.

⑩ suspension, emulsion, solution.

A mixture of small solid particles suspended in a liquid is called a suspension, such as muddy water.A mixture of small droplets dispersed in a liquid is called an emulsion, such as milk.

Molecules of one or several substances are dispersed into another substance to form a uniform and stable mixture called a solution, such as liquor.Uniformity, stability, transparency and other properties are the characteristics of solutions that are different from suspensions and emulsions.Solutions can be classified into liquid, gaseous, and solid states, and usually refer to the liquid state.

Different {1} saturated solution and unsaturated solution.

A solution in which a certain solute cannot be dissolved in a certain amount of solvent at a certain temperature is called a saturated solution of this solute.

A solution that can continue to dissolve a certain solute in a certain amount of solvent at a certain temperature is called an unsaturated solution of this solute.

The key difference is the ability to continue to dissolve.

Qu {1} acid, alkali, salt.

A compound in which all cations generated during ionization are hydrogen ions is called an acid. HCl, HNO3, H2SO4 are all acids.

A compound whose anions are all hydroxide ions during ionization is called a base. NaOH, KOH, and Ca(OH)2 are all alkalis.

Compounds that form metal ions and acid ions upon ionization are called salts. Na2CO3, NaCl, MgSO4 are all salts.

紞{1} acidic oxides and basic oxides.

Oxides that can react with bases to form salt and water are called acidic oxides, and most non-metallic oxides are acidic oxides.

Oxides that can react with acids to form salt and water are called basic oxides, and most metal oxides are basic oxides.

Oxidation and reduction of {1}.

The process of atoms or ions losing electrons is called oxidation; the process of atoms or ions gaining electrons is called reduction.

The chemical reaction in which electrons are gained or lost or shifted is an oxidation-reduction reaction.

In the same oxidation-reduction reaction, the total number of electrons gained and lost by the oxidizing agent and reducing agent is equal.

In the oxidation-reduction reaction, the substance that gains electrons is the oxidant, and the oxidant itself decreases in valence during the reaction and is reduced; in the oxidation-reduction reaction, the substance that loses electrons is the reducing agent, and the valence of the reducing agent itself increases during the reaction. High, oxidized.

Spinning {1} weathering and deliquescence.

Weathering is a phenomenon in which crystalline hydrates naturally lose part or all of their crystalline water at room temperature, causing the crystals to deform and be destroyed.Weathering is a chemical change process.For example: Na2CO3·10H2O and Na2SO4·H2O can lose water and become white powder.Deliquescence is a phenomenon in which a substance absorbs water and dissolves itself in humid air to form a saturated solution.Deliquescence is mostly a physical change process, and some are chemical change processes.For example: CaCl2 can deliquescence into a solution, so CaCl2 is a commonly used desiccant.

Dan{1} combustion, slow oxidation and spontaneous combustion.

Combustion, slow oxidation, and spontaneous combustion are all chemical reactions.From the point of view of the reaction conditions, all substances that can be oxidized are in contact with oxygen (or other substances); the difference is the degree of reaction.

Combustion can only occur when the temperature reaches the ignition point of combustibles; slow oxidation can be carried out at normal temperature; spontaneous combustion is a slow oxidation reaction at normal temperature, and the heat generated by the slow oxidation reaction is not easy to dissipate under certain circumstances for substances with lower ignition points , so that the heat accumulates, the temperature rises, and it reaches the ignition point and spontaneously burns.

From the perspective of phenomenon, combustion is a violent reaction of luminescence and heat generation; slow oxidation generates heat, but it is not easy to detect the change of temperature rise; spontaneous combustion is similar to slow oxidation before reaching the ignition point, and it is the same phenomenon as combustion after reaching the ignition point.

紤{1} mole and the amount of substance.

The mole is the unit of the amount of matter, and the amount of matter refers to the physical quantity of the number of specified particles (molecules, atoms, ions, electrons, protons, neutrons) contained in the matter.

The unit of the amount of matter is the mole. Without the unit of mole, the amount of matter loses its specific meaning.

(End of this chapter)