Internal Energy

Internal Energy

Introduction : The total energy of the system is given by sum of its kinetic and potential energy, which exist due to motion and shape of the body. There exist an energy which is due to random motion of atoms and molecules of the system called as internal energy of the system. We are going to discuss this internal energy in details.

Internal energy of a system is defined as energy due to random and disordered motion of the molecules.

Internal energy of the system can be considered as the sum of kinetic energy, potential energy and vibrational energy of the molecules or atoms.

For eg: Let us consider a cup of tea which is placed on the table. Here you can see that cup is stationary which tells that kinetic energy of the body is zero, and as it is not displaced potential energy can be considered zero. On the other hand the molecule of the tea is in random motion due to some energy, this energy is called as internal energy of the body.

Internal energy of the body is mathematically calculated based on degree of freedom of the atom/ molecule. Let us understand degree of freedom., i

Mathematically , internal energy is expresses by 'U'.

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Degree of Freedom : It is defined as total numbers of coordinates  or independent quantities required to describe the position and configuration of a system completely.

For monoatomic gases,

Let us consider Helium (He).It can move in three direction in a space i.e  in x , y, z direction. 

Thus it has only 3 degree of freedom.

Energy associated with each degree of freedom is 1/2KT

Total energy for monoatomic molecule will be 3/2KT

For diatomic gases,

Let us consider a diatomic molecule like Oxygen O₂  or Nitrogen N₂ ,

It is free to move in 3 translation direction i.e in x , y, z direction. In additional it is free to perform rotational motion around Y and Z direction, if molecule is situated on X axis. As it is situated on X axis it cannot rotate around X axis in the sense there will be no change in position of molecule while rotating on X axis.

Translation degree of freedom: 3

Rotational degree of freedom :2

Degree of freedom : 5

Energy associated with each degree of freedom is 1/2KT

Total energy for diatomic molecule will be 5/2KT

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_{│<<<Thermal Equilibrium}││ _Heat>>>│ 

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Thermal Equilibrium

Thermal Equilibrium

Introduction: We have seen that if some cube of ice is kept at room temperature, the heat get transfers from surrounding into the ice cube. The temperature of the ice increases and at certain instant of time the temperature becomes equal to room temperature and the exchange of heat stops. Thus the body attain equilibrium. We are going to learn in detail about thermal equilibrium.

Thermal equilibrium is studied at macroscopic level. (Pressure, Volume, Temperature ,Mass, etc ) are the macroscopic parameter which is of interest in determining thermal equilibrium of the state.

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Case I: Consider a body having adiabatic wall, then there will be no transfer of heat as well as matter from system to surrounding hence there will be no change in temperature and state of the system. △q = 0.

If there is no change in state and property of the system, the system is said to be in thermal equilibrium.

The system in above diagram is in thermal equilibrium as there is no exchange of heat due to adiabatic wall.

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Case II : Consider two system A and B having adiabatic wall with surrounding and diathermic wall  with each other, then there will be no transfer of heat as well as matter from system to surrounding but there will be transfer of heat from system A to system B as  T_A >  T_B at t= 0 sec, hence there will be exchange of heat from system A to system B and thus change in temperature and state of the system. 

At t= T sec , T_A =  T_B hence there will be no exchange of heat from system A to system B and thus system A and system B will be in thermal equilibrium with each other.

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Zeroth Law of Thermodynamics : If system A is in thermal equilibrium with system B (T_A =  T_B) and system B is in thermal equilibrium with system C (T_B =  T_C) , then system A is in thermal equilibrium with system C (T_A =  T_C).

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Thermodynamics

Thermodynamics

Introduction : In our daily life we have seen that after rubbing our hands, heat is developed in the hand which signifies that work has been converted into heat energy. Thus thermodynamics deals with work and heat. on the other hand the steam locomotive engine uses heat energy to do work. Thus, heat and work are analogous to each other which is related to thermodynamics. In this chapter we are going to study about thermodynamics in details.

Photo by Paul Macallan on Unsplash

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Thermodynamics: Thermodynamics is a branch of study which deals with the study of conversion of heat into different form of energy.

The Thermodynamical model involve  three important thing viz:

Thermodynamic Model

a) System: A  system is a part(quantity of matter )whose properties is to be studied.

b) Wall: A wall is an enclosed boundary which distinguish the system from the surrounding and allows the matter and heat to transfer.

Wall can be classified into two types:

1) Adiabatic wall : The wall that do not allow transfer of heat from system to surrounding as well as surrounding to system is called as adiabatic wall.

2) Diathermic wall : The wall that allow transfer of heat from system to surrounding as well as surrounding to system is called as adiabatic wall.

c) Surrounding: Everything external of the system is known as surrounding or the environment in which the system is placed.

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Thermodynamics System

There are different types of system on the basis of possible transfer of mass and matter with the surrounding    

1) Open System : The system which allow the exchange of heat and matter with the environment is called as open system. Eg( Boiling milk, water ,tea)

2) Closed system : The system that allow only exchange of  heat but does not allow transfer of matter is called as Closed system Eg( Hot cup of tea covered with lid.

3) Isolated system : The system that do not allow exchange of heat as well as matter with the environment is called as Isolated system.

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Magnetization and Magnetic Field

Magnetization and Magnetic Field

Introduction :In previous topic we have studied about orbital magnetic dipole moment  and the net magnetic dipole moment leads to magnetic property in a substances. Let us focus on new term magnetization which is related to magnetic property of a substance.

Magnetization(Mz) is defined as net magnetic dipole moment per unit volume.

Magnetization is a vector quantity  and it's SI unit A/m.

Dimension :[ L^-1 M⁰ T⁰ I¹] 

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Let us study magnetization of a ferromagnetic material like Iron. Let us consider a solenoid having n turns per unit length and carries a current I. 

thus the magnetic field inside the solenoid is given by

B₀ = μ₀nI 

B₀ = μ₀H -----(A) (nI = H)

However, if any conductor is placed inside the solenoid , the magnetic field inside is larger than B₀ and it is written as,

B = B₀  + B_M -----(B)

From theory it is found that B_M is directly proportional to Magnetization M_z 

B_M ∝ M_z

B_M = μ₀ M_z -----(C)

Putting (A) and (C) in (B) we get,

B = μ₀H + μ₀ M_z 

B = μ₀(H + M_z) ----(D)

Equation (D) gives total Magnetic field or Magnetic Intensity 

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 Mathematically, magnetization and magnetic Intensity is related as 

M_z ∝ H

M_z= χ H ----(E)

where χ  is called a magnetic Susceptibility.

From (D) and (E)

B = μ₀(H + χ H) 

B = μ₀(1 + χ )H

B = μ₀μ_rH    

  ---(μ_r =1 + χ ) is a dimensionless quantity called as relative magnetic permeability.

B = μH   -----(μ = μ₀μ_r)

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_{│<<<Magnetic Dipole Moment  of an electron>│} 

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Magnetic Dipole moment of a revolving Electron

Introduction : We have already studied that the revolving electron in a nucleus is similar to current flowing through a circular loop. This revolution of electron leads to orbital magnetic moment and thus gives rise to magnetic property in any substance. Let us derive some equation for Magnetic Dipole moment of a revolving Electron.

Multiplying Equation C by me, we get

  _{│<<<Origin of Magnetism>│ │Magnetization>>>│} 

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Magnetic materials

Magnetic materials

Introduction : The word magnet, was first used for iron ore magnetite ( Fe₃O₄) which was found in magnesia. The natural magnet which is found in nature is called as Loadstone. It has two important properties viz. directive and attractive property. If a magnet is suspended freely using a string , it comes to rest in north south direction which describe the descriptive property . If the loadstone is dipped in iron fillings, they get attracted to the loadstone which tells us about attractive property. We will discuss more about it in details.

Origin of magnetism

Origin of magnetism

We have already studied that, flowing charges in  a conductor  produces magnetic field. Thus magnetism is cause of moving charges. In case of an atom, negatively charged (Electron)  revolve around the nucleus which is similar to current flowing in a circular loop called as "current loop". This circular loop of the electron constitutes orbital magnetic moment . While revolving in a circular orbit electron spins about it's own axis, constituting spin magnetic moment. Thus the total magnetic moment (M) of any atom is vector sum of orbital magnetic moment and spin magnetic moment.

Generally in  any substance, atomic magnetic moment are in random direction  such that net magnetic moment is zero. thus such substance do not show magnetic property.

If any substance has it's atomic magnetic moment in a specific direction, then the magnetic moment is not zero, thus such substance shows magnetic properties and are called as magnetic material.

 _{│Magnetic Dipole moment of an electron>>>│} 

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Logical Question

Q1) The position of a particle in a rectangular coordinate system is (3,2,5). What will the position vector be?

1. 3i^+2j^+5k^
2. 3i^−2j^−5k^
3. 5i^+2j^+3k^
4. 2i^+5j^+3k^

 Q2)  What is the displacement vector of the particle that moves from point P (2,3,5) to point Q (3,4,5)?

1. i^+j^+5k^
2. 2i^+4j^+6k^
3. i^+j^
4. i^+j^  +10k^

Q3)  What is the vertical component of the force 5 N acting on a particle along a direction making an angle of 600 with vertical ?

1. 3 N
2. 2.5 N
3. 10 N
4. 4 N

Q4) Which of the following is a scalar quantity?

1. Acceleration
2. Electric Field
3. Work
4. Displacement

Q5) How many numbers of base SI units are there?

       a. 5

       b. 10

       c .7

       d .9

Q6) What is the dimensional formula of torque and energy

      a. [ML-3T-2] and [MLT-2]

      b.  [ML2T-2] and [MLT-2]

      c.  [ML2T-2] and [ML2T-2]

      d.  [MLT2] and [ML2T2]

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