### Concerns about our environment

**Calorific value of fuel**

**Solar constant:**

### Behaviour of Gases

**Boyles’ law**

**Charles’ law**

**Gay-Lussac’s Law:**

**Combined form of Boyles’ Law and Charles’ Law**

**Equation of state for an ideal gas:**

**Relationship between temperature in Celsius and absolute scale:**

**Value of pressure in different unit**

### Chemical Calculations

**Law of conservation of mass**

### Thermal Phenomena

**Linear expansion of solid**

**Relation among the coefficients of expansion of solid:**

**Expansion of liquid:**

**Thermal conductivity:**

**Thermal current:**

**Thermal Resistance:**

### Light

**Relation between the radius of curvature (r) and the focal length (f) of a spherical mirror for paraxial rays:**

**Images formed by a concave mirror:**

**Image formed by a convex mirror:**

**Wave theory of light:**

**Principle of reversibility of light:**

**Real and apparent depth**

**Refraction through optical slabs**

**Refraction through prism**

**Image formed by convex lens:**

**Images formed by concave lens:**

**Linear magnification**

### Current Electricity

**Coulomb's law:**

**Electric potential difference**

**Electro Motive Force (EMF)**

**Electric current**

**Ohm's law**

**EMF and internal resistance of a cell**

**Resistance (R) of a conductor having length (l) and area of cross-section (A) is given by**

### Concerns about our environment

**Calorific value of fuel **

Amount of heat energy liberated on burning of a fuel = (mass of fuel) x (calorific value of fuel)

**Solar constant:**

Heat energy produced by incident solar radiation = (solar constant) x (Area) x (time)

where solar constant =1.4 kJ.m2.s-1 = 1.4 k.W.m2 .

### Behaviour of Gases

**Boyles' law **

- For a fixed mass of gas at constant temperature,

P1V1 = P2V2 = K= constant

**Charles' law **

- For a fixed mass of gas at constant pressure,

v_t=v_0left(1+frac t{273}right)` or `frac{V_1}{T_1}=frac{V_2}{T_2}=K(constant)

**Gay-Lussac's Law: **

- For a fixed mass of gas at constant volume

frac{P_1}{T_1}=frac{P_2}{T_2}=K

**Combined form of Boyles' Law and Charles' Law **

- For a fixed mass of gas when P and T vary

frac{P_1V_1}{T_1}=frac{P_2V_2}{T_2}=k(constant)

**Equation of state for an ideal gas: **

For n mole of an ideal gas, PV = nRT

Where P= Pressure of gas

V= Volume of gas

R = Universal gas constant

T = Absolute temperature in kelvin

**Relationship between temperature in Celsius and absolute scale: **

- t^0c=left(273+tright)K=TK

**Value of pressure in different unit **

1 Pascal (Pa) = 1Nm^{-2}

1 atmosphere (atm) = 1.01325 x 105 Pa = 1.01325 bar

1 bar = 105 Pa

1 atmosphere (atm) = 76cm of Hg = 760 mm of Hg = .76 m of Hg

### Chemical Calculations

In this chapter student face most difficulties but we assure you that after following our method you will easily able to solve question of this chapter.

To become the master of this topic click here

**Law of conservation of mass **

- Mass of reactants = Mass of products
- Molecular weight and vapour density:

iii. Molecular weight of gas = 2 x vapour density

- Calculation of no. of moles in different cases:

- Case 1: When no. of particle is given
- No. of moles = (given weight or mass of compound)/(molecular weight of compound)
- Case 2: When volume of gas is given
- Case 3: When no. of particles (no. of molecules / no. of atom/ no. of ions/ no. of proton, electron or neutron is given)

- Case 3: When no. of particles (no. of molecules / no. of atom/ no. of ions/ no. of proton, electron or neutron is given)

No. of moles = (given no.of particle)/(Avogadro's No.)

[Note: Avogadro’s no. N_A=6.022times10^{23} ]

[Note: In this chapter gram molecular weight, gram molar mass represents the same thing]

### Thermal Phenomena

**Linear expansion of solid **

** **

Coefficient of linear expansion

alpha=frac{L_t-L_0}{L_0Delta t}`or`L_t=L_0left(1+alphaDelta tright)

Where Lt = length of the rod at temperature to C

Lo = length of the rod at temperature 0^0c

Δt = change in temperature

**Relation among the coefficients of expansion of solid: **

alpha=fracbeta2=fracgamma3

**Expansion of liquid:**

For a liquid kept in a container

**Thermal conductivity: **

The quantity of heat Q conducted through a solid bar,

Q = frac{KAleft(theta_2-theta_1right)}d

where k is the coefficient of thermal conductivity

**Thermal current: **

** **

H = frac Qt = frac{KAleft(theta_2-theta_1right)}d

**Thermal Resistance:**

** **

R_{th}=frac1Kleft(frac dAright)

### Light

**Relation between the radius of curvature (r) and the focal length (f) of a spherical mirror for paraxial rays:**

r=2for,f=frac r2

**Images formed by a concave mirror: **

**Image formed by a convex mirror:**

** **

Snell's law

When a light ray enters into the second medium from the first medium, then refractive

index (R.I) of the second medium with respect to the first medium is given by

1mu_2=frac{sinleft(iright)}{sinleft(rright)}

**Wave theory of light: **

Absolute R.I of a medium, mu=frac(Velocity of light in air or vacuum)(velocity of light in medium)

**Principle of reversibility of light:**

When a ray after refraction, retraces its path, then

^amu_b=frac1{bmu_a}

(where a is the rarer and b is the denser medium)

**Real and apparent depth**

When an object is situated in an optically denser medium 2, then when viewed normally from the rarer medium 1,

1mu_2=frac{Real depth}{Apperent depth}

**Refraction through optical slabs **

- Incident ray is parallel to emergent ray
- Angle of incidence (i) is equal to angle of emergence (e)

**Refraction through prism **

Angle of deviation (δ) = Angle of incidence Angle of (i1) +Angle of emergence (i2) - Angle of prism (A).

Angle of refraction at the first face (r1) + Angle of incidence at the second face (r2) = angle of prism (A).

**Image formed by convex lens:**

**Images formed by concave lens:**

**Linear magnification **

- Linear magnification (m) = (Linear size of the image )/(Linear size of the object ) = (distance of the image from lens )/(distance of the object from lens)

ii Power of lens = frac1f (m)=frac{100}f(cm)

iii. Relation among speed (c), wavelength (λ) and frequency (ν)of light wave: c=νλ

### Current Electricity

**Coulomb's law: **

If two-point charges q1 and q2 are separated by a distance r in a medium, then the force of attraction or repulsion F between them is given by

F=frac1{4piin_0}frac{q_1q_2}{r^2}

**Electric potential difference**

** **

- If W work is done to bring Q coulomb of positive charge from infinity to a particular point in an electric field, then potential at that point

V=frac WQ or W=V.Q

- If W joule of work is done to move a coulomb of charge from a point A to another point B, then potential difference between A and B

V_A-V_B=frac WQ

**Electro Motive Force (EMF)**

If W work is done to move Q charge around a complete circuit, then EMF of the cell

E=frac WQ

**Electric current**

If a charge Q flows through a cross-section of a conductor in t seconds, then magnitude of current

I=frac Qt

**Ohm's law **

If the current flowing through the conductor is I when the potential difference across it's two ends is V, then according to Ohm's law, V = I.R where R is the resistance of the conductor.

**EMF and internal resistance of a cell**

When I current is flowing through a closed circuit driven by a cell having emf E and internal resistance r, then terminal potential difference across the cell is given by,

V = E - I.r,

where I.r is known as lost volt or potential drop across r.

**Resistance (R) of a conductor having length (l) and area of cross-section (A) is given by**

R=rhofrac lA

where ρ is known as resistivity or specific resistance of the material of the conductor.

**Conductivity **

Reciprocal of resistivity is known as conductivity. It is represented by

sigma=frac1rho=frac l{RA}

**Resistances connected in series**

When resistances R1, R2, R3, R4 etc. are joined in series, the equivalent resistance

R = R1+ R2+ R3+R4+……….

[ In this diagram, V1, V2, V3, are potential across R1, R2, R3 and their values are V1=I x R1; V2=I x R2 V3=I x R3 and V = V1 + V2 + V3]

[ Note: In Series combination current through each resistance remain same but there is voltage or potential drop across each resistance and its value is equal to IR, where I = Total current flowing through wire R = Resistance though which current is flowing.]

**Resistances connected in parallel**

** **

For a number of resistances like R1, R2, R3 etc. connected parallelly, the equivalent resistance

frac1R=frac1{R_1}+frac1{R_2}+frac1{R_3}[katex]</p> <p style="user-select: auto;"> <p style="user-select: auto;"> <p style="user-select: auto;"> <p style="user-select: auto;">In this diagram I1, I2, I3 are current through resistor R1, R2, R3 where the value of</p> <p style="user-select: auto;"> <p style="user-select: auto;">[katex]I_1=left(frac{frac1{R_1}}{frac1{R_1}+frac1{R_2}+frac1{R_3}}right)I; I_2=left(frac{frac1{R_2}}{frac1{R_1}+frac1{R_2}+frac1{R_3}}right)I; I_3=left(frac{frac1{R_3}}{frac1{R_1}+frac1{R_2}+frac1{R_3}}right)I

where I = total current in the circuit its value is I = I1 +I2+I3

[ Note: In Parallel combination Voltage or potential through each resistance remain same but there is potential drop across each resistance and its value is equal to IR, where I = Total current flowing through wire R = Resistance though which current is flowing.]

**Cells in series **

When n number of cells each of emf E and internal resistance r are connected in series, then current I is given by

left(i=frac E{R+frac nR}right)

where R is the external resistance.

**Cells in parallel **

When n cells each of emf E and internal resistance r are connected in parallel to an external resistance R, then current I is given by

I=frac E{R+frac rn}=frac{nE}{nR+r}`

**Joule's law of heating: **

If H amount of heat is produced in a conductor of resistance R, when a steady current is passed through it for time t, then H=I^2RTjoule or

where J = Joule’s equivalent = 4.2 J/cal.

**Electrical energy: **

The energy W supplied by a cell or battery in providing current I ampere for t second through a resistor R under a potential difference of V volt is given by,

W=V.I.t=frac{V^2}Rt=I^2Rt

**Electrical Power: **

Electrical power is the electrical work done per unit time.

P=frac Wt=V.I=frac{V^2}R=I^2R

### Atomic Nucleus:

**Trick to remember 20 elements of periodic table: **

**Trick to remember atomic weight:**

** **

Elements having even atomic no., Atomic weight = 2 x Atomic No.

Elements having odd atomic no., Atomic Weight = 2 x Atomic No.+1

[ Note: This rule is not valid for the element having following atomic No.]

Atomic Number Atomic weight

1 1

4 9

7 14

17 35.5

18 40

**Radioactive transformations:**

There are three types of radioactive transformations

**α decay:**

_{Z}X^{A }= _{Z-2}Y^{A-4}+ _{2}He^{4} (α -particle)

**β decay:**

_{Z}X^{A }= _{Z+1}Y^{A}+ _{-1}β^{ o} (β-particle)

**iii. γ decay: **

Formation of radio isotope:

**Mass defect **

For a nuclide _{Z}X^{A }the mass defect,

**Binding energy: **

According to mass energy equivalence,

Binding energy

1 MeV = 1.6 x 10^{-13} J

For 1 amu mass defect, binding energy E = 931 MeV.

**Binding energy per nucleon: **

B/A=Total binding energy/number of nucleon=frac{Delta mc^2}A

### Physical and chemical properties of Matter:

**Periodic Table & Periodicity of Properties of the elements: **

** **

- according to the modern periodic law, the properties of the elements are a periodic function of their atomic numbers.

- Variation of different properties of elements across a period and down a group:

Ionic and covalent bonding:

**Octet rule**

Atoms of various elements (except H, Li and Be) combine either by transfer of valence electron(s) from one atom to another (gain or loss) so that they have eight electrons (an octet) in their outermost valence shell.

**Duplet rule: **

The elements close to Helium (Li, H, Be) in the periodic table attain the stable electronic configuration of He (K = 2) by gaining or losing of electrons in their outermost valence shell.

### Organic Chemistry:

**Word root according to no. of carbon present:**

**Method to convert one form to another:**

**Classification of isomerism**

R=rhofrac lA`

**Conductivity**

**Resistances connected in series**

**Resistances connected in parallel**

**Cells in series**

**Cells in parallel**

**Joule's law of heating:**

**Electrical energy:**

**Electrical Power:**

### Atomic Nucleus:

**Trick to remember 20 elements of periodic table:**

**Trick to remember atomic weight:**

**Radioactive transformations:**

**i. α decay:**

_{Z}X

^{A }=

_{Z-2}Y

^{A-4}+

_{2}He

^{4}(α -particle)

**ii. β decay:**

_{Z}X

^{A }=

_{Z+1}Y

^{A}+

_{-1}β

^{ o}(β-particle)

**iii. γ decay:**

**Mass defect**

_{Z}X

^{A }the mass defect,

**Binding energy:**

^{-13}J

**Binding energy per nucleon:**

### Physical and chemical properties of Matter:

**Periodic Table & Periodicity of Properties of the elements:**

**Octet rule**

**Duplet rule:**

### Organic Chemistry:

**Word root according to no. of carbon present:**

**Method to convert one form to another:**

**Classification of isomerism**

Good