Showing posts with label Class 11 phys. Show all posts
Showing posts with label Class 11 phys. Show all posts

CLASS 11 Kinetic Theory of Gases Notes

  April 06, 2023    

 Kinetic Theory of Gases


# Assumption of Ideal Gas

1) Volume of gas is same as that of vessel.

2) A gas consist of large number of identical, tiny and elastic particles called molecules.

3) In a gas molecules are moving in all possible direction with all possible speed randomly.

4) Size of molecules << average separation.

5) Molecules exert no force on each other.

6) Molecules obeys newton's law of motion.

7) Collision between is perfectly elastic.

8) Time of collision is negligible.


NOTE: SINCE THERE IS NO INTERACTION BETWEEEN MOLECULES, NO POTENTIAL ENERGY OF SYSTEM EXIST.


# Behaviour of Real Gas

1) Size of molecules is not negligible.

2) Volume of gas < Container Volume.

3) Due to some interaction between molecules pressure is always reduced.

4) As some interaction exist, hence potential energy exists. 

5) Collision between molecules are not perfectly elastic, hence some energy is loss.


NOTE: AT VERY HIGH TEMPRATURE AND LOW PRESSURE A REAL GAS BEHAVES LIKE AN IDEAL GAS.


# Boyle's Law

T = Constant 

PV = nRT

Hence, PV = Constant


# Charles's Law

P = Constant

PV = nRT

Hence, V∝ T


# Gay-Lussac Law

V = Constant

PV = nRT

Hence, P ∝ T


# Avagardo's Law

At same temperature and pressure, equal volume of all gases contains equal number of molecules.

N = nNA


# Dalton's Partial Pressure Mixture Law

The pressure exerted by mixture of non-reactive gases is equal to the sum of partial pressure of each component of gases present in mixture.

P = P1 + P2 + P3 + ..........


# Ideal Gas Law

1) Molar Form

PV = nRT 

Hence, PV = NRT/NA

2) Molecular Form

PV = NKT                        K = Boltzmann Constant = 1.38 * 10^-23

3) Density Form

P = ρRT/M


# Degree of Freedom

Number of ways of a system can be have energy is defined as degree of freedom.

→ It is of three type:- Translational, Rotational and Vibrational.


Degree of freedom               Monoatomic           Linear Molecules          Non-Linear Molecules

Translational                                  3                                   3                                      3 

Rotational                                       0                                   2                                      3 

Vibrational                                      0                                3N-5                                 3N-6

Total                                                3                                  3N                                    3N


# Root Mean Square Speed

1) Molar Form

Vrms = √ (3RT/M)

2) Molecular Form

Vrms = √ (3KT/M)

3) Density Form

Vrms = √ (3P/ρ)


# Average Velocity

1) Molar Form

Vavg =  √ (8RT/πM)

2) Molecular Form

Vavg = √ (8KT/πm)

3) Density Form

Vavg = √ (8P/πρ)


# Most Probable Speed

Speed which is common in maximum number of molecules of a gas is defined as most probable speed.

1) Molar Form

Vmp = √ (2RT/M)

2) Molecular Form

Vmp = √ (2KT/m)

3) Density Form

Vmp = √ (2P/ρ)


# Pressure Exerted by Gas


P = M(Vrms)^2/3V


# Law of Equipartition of Energy

According to law of equipartition of energy the average energy associated with per-degree of freedom per molecule is KT/2.

Avg. Energy/degree of freedom per molecule = KT/2

1) Molecular Form

Avg. Energy = ⨏NKT/2

2) Molar Form

Avg. Energy = ⨏nRT

# Important Formulas

1) Cp = (1+ ⨏/2)R
2) Cv =  ⨏R/2
3) Y = Cp/Cv








  

Class 11 Units and Measurement Note

  March 27, 2023    

 UNITS AND MEASUREMENTS 


# Physical Quantities

The quantity which can be measured by an instrument and which describes the laws of physical world.

= numerical value* unit(a comparison)


# Types of Physical Quantities

a) Fundamental Quantities: which do not depend upon any other quantities.

  • Length (metre)
  • Mass (kilogram)
  • Time (second)
  • Electric current (ampere)
  • Thermodynamic temperature (kelvin)
  • Amount of substance (mole)
  • Luminous intensity (candela)

b) Derived Quantities: which are made up of fundamental quantities.

Example: Area = L*L = m^2


# Dimension

Dimensions are the powers to which fundamental units are raised in order to express the derived unit of a quantity.

  • Length (metre)                                                                  = [L]
  • Mass (kilogram)                                                                = [M]
  • Time (second)                                                                   = [T]
  • Electric current (ampere)                                                  = [A]
  • Thermodynamic temperature (kelvin)                              = [K]
  • Amount of substance (mole)                                            = [mol]
  • Luminous intensity (candela)                                           = [cd]


# Principle of Homogeneity 

The dimensions of an equation must be same.


# Application of Dimension Analysis 

1) Checking the correctness of an equation: For a correct equation dimensions of each term of                                                                                       L.H.S  = dimensions of terms of R.H.S.

    Example: F = ma

                    [MLT-2] = [M][LT-2] 

                    Hence Proved


2) Conversion of unit: n1u1 = n2u2

     Example: Convert 1N to Dyne

                     the dimensional formula of Force F=[M1L1T−2]

                        So a = 1, b = 1, c = −2

                         Now because Newton is in m.k.s system, we have

                        M1​=1kg                                  M2​=1g

                        L1​=1m                                     L2​=1cm

                        T1​=1s                                        T2​=1s

                        n1​=1Newton                    n2​=?                       

                         Using the formula

                         n2​=n1​​[M1/M2]a[L1/L2]b[T1/T2]c

                         n2​=1[1kg/1g]1[1m/1cm]1[1s/1s]−2

                         n2​=1[1000g/1g]1[100cm/1cm]1×1

                        n2​=1000×100=100000=105 dynes

                     

3) Deriving relation between physical quantities:

    Example: Force on a particle depend upon mass of the particle and acceleration of the particle. Find                         the equation for F.

                     F ∝ mx, F ∝ ay

                        F = k mx ay

                        [MLT-2] = [M]x[LT-2] y

                        [MLT-2] = [MxLyT-2y]

                        Therefore x = 1, y = 1

                         F = [MLT-2] = km1a1


# Limitations of Dimension Analysis

1) Can't find value of constant.

2) Can't apply in expression having trignometric, exponential, logarithmic functions.

3) Can't apply in equation having more than one term.


# Rules of Significant digits

Significant figures tells us that the number of digits in a measured value, we are confident of.

1) All non-zero digits are significant.

2) Zero between two non-zero and significant digits are significant.

3) Initial zero's are never significant.

4) Trailing zero's are significant if they appear after decimal.

5) Order of magnitude is never significant.

6) Pure number or constant have infinite significant figures.

NOTE: While changing units number of significant digits remain same.


# Calculation of significant figures

1) Addition and Subtraction: The result of this function is rounded off to the same number of decimal places as present in the value with least decimal places.

2) Multiplication and Division: The result is rounded off to same number of significant figures as present in the value with least significant figures.


# Error Analysis

Difference between the measured value and the actual value is error.

1) Absolute error: The magnitude of difference between the true value and the measured value of the quantity.

ΔX= X-X1


2) Mean absolute error: 

△Xmean  = |△X1| + |△X2|+ ……. |△Xn|/n


3) Relative/Fractional error: 

= △X/X


4) Percentage error:

=  △X/X*100


# Propagation of error

1) Addition and Subtraction: Error are always added and subtracted in addition and subtraction.

 △x =  △a ±  △b


2) Multiplication and Division: 

 △x/x =  △a/a +  △b/b


# Quantities raised to some power

x = apbq/cr

△x/x = p(△a/a) + q(△b/b) + r(△c/c)












  

Class 11 Mechanical Properties Of Solids

  March 23, 2023    

Mechanical Properties of Solids

 

# Elasticity

Property of body by virtue of which, it tends to regain its original size and shape, when applied force is removed is known as Elasticity.

# Plasticity

Object have no tendency to regain their shape and got their permanent shape, such substance is called "plastic" and property is called Plasticity.

# Stress

Restoring force per unit area set up inside the body is called stress and is measured by the magnitude of force acting on unit area of the body in equilibrium.

 

Stress = Restoring Force / Area 

 

                                                                                          Unit= N/m2, pa (Pascal), Kg m-1 sec-2

 

NOTE: Pressure is always normal to area but on other side stress can be Normal, Longitudinal and Tangential. Also, Pressure is always compressive in nature and on other side stress may be compressive or tensile in nature.

# Type of stress

1)    1) Longitudinal/ Normal Stress

a)      a)Tensile Stress                                                                         

              Tensile Stress = F⊥/A                                                            

 

b)     b) Compressive Stress

               Compressive Stress = F⊥/A

 

2)   2) Shear/ Tangential stress

 

        Shear/Tangential Stress = FTang/A

 

 3) Volumetric/ Bulk/ Hydraulic Stress

             Bulk Stress= F⊥/A= △P

# Strain

Strain is defined as change in configuration divided by original configuration.

=Change in configuration/Original configuration

àIt is dimensionless or unit less.

# Type of strain

1)   1) Longitudinal strain

             =△L/L

2)   2) Shear strain

             =△x/L

3)   3) Volumetric/ Bulk/ Hydraulic strain

             =△V/V

 

# Hooke’s law

It States that, with in elastic limit, the stress developed in a body is proportional to strain produced in body due to stress.

Stress ∝ Strain

Stress= (Modulus of elasticity) (Strain)

àModulus of elasticity is a constant depends upon type of object or material.

# Type of Modulus of Elasticity

1)     1) Young’s Modulus (Y)

 


Y=Longitudinal stress/Longitudinal strain=F⊥L/A△L

Unit= Nm-2/Pa

 

NOTE: Y is independent of size, shape, only depends upon nature and material.

NOTE: Generally, as temperature increases, Y decrease.

2)    2)  Modulus of rigidity (ɳ)

 


                                     ɳ=Shearing stress/Shearing strain= (FTang)( ϕ)/A          [tanϕ=ϕ=△x/L]

àOnly define for solids, for liquid and gas it is zero.

3)    3)  Bulk modulus (K)/(β)

 


                                                              K=  -dP/dV*(V)                [  à Slope of P-V Graph]

 

# Compressibility (c)

C=1/Bulk Modulus[K]

 

# Poisson’s ratio (σ)



σ=Lateral strain/longitudinal strain= - △D(L)/△L(D)

àIt is dimensionless.

 

# Stress-Strain Curve




 Elastic Limit: It is the maximum stress on which removal, the bodies regain their original dimension.

2)     Yield Limit: At this point wire begins to flow like viscous fluid.

3)     Ultimate/Breaking Point: At this point wire is about to break or get broken. The stress at this point is called breaking/tensile strength of that wire.

NOTE: Length of graph decides the nature of object, whether it is ductile or brittle, if plastic range is relatively high it is ductile otherwise brittle.

 

# Elastic Potential Energy

 

△U=  Stress* Strain* Volume/2

 

# Depression at the Middle of Beam


                  = WL3/4Ybd3








  

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