Degree of freedom & first law thermodynamic

Degree of freedom

These are the total number of independent coordinate a body can have 
                                                 Or 
Total number of method of exchanging energy

For monoatomic gases

Size of particle is very-2 small ,so it does not have ratational 
Kenetic energy.

It has only 3-direction  x,y,z
Through which it can exchange energy

For diatomic gas 

It has 3-translational and 2-rotational  through which it can exchange energy

For triangular gas


It can 3-translational and 3-rotational method through which it can exchange energy

Now we will discucuss
.....................

Law of  equipartition of energy

It means energy distribution in all direction will same 
(in x , y , z direction energy will be same)

For monoatomic gases 
    In x-direction energy = kt/2
     In y-direction energy = kt/2
     In z-direction energy = kt/2
So here we can write total energy = kt/2+kt/2+kt/2
                                                              =3kt/2

Note-
Energy of rotation is equal to energy of transnational motion        

Now we will talk about the first law of thermodynamic 

Ques rises what is first law thermodynamic

first law of thermodynamics states that the increase in internal energy is equal to the total heat added and work done by the surroundings.

it can be well understood by observing below

Now 
thermodynamical  system- It is system that can Represent in term of Thermodynamical co-ordinate

There are three thermodynamical constant 
 Pressure
Volume
Temp

Pressure can be measure by putting are applying pressure  at equilibrium
             i.e   applied pressure =  internal Pressure

Conservation of linear momentum

Conservation of linear momentum

According to principle of conservation of linear momentum in case of perfectly elastic collision both the linear momentum and kenetic energy of system conserved

imp---

if mass of balls are same than after the  collision it exchanges the velocity

Now let us suppose that the ball is moving toward a wall

P(initial)= (m*v)*i  ,  (i denote the motion in only x direction)

P(final)=  -(m*v)*i ,

So change in momentum of ball

=p(f) – p(i)   ,

=(-2mv)*i

Now let suppose there are ‘n’  no of molecules in the container having possible velocity

V1=(Vx1)i +(Vy1)j +(Vz1)k

V2=(Vx2)i +(Vy2)j +(Vz2)k

.

.

.

.

Vn=(Vxn)i +(Vyn)j +(Vzn)k

Pressure on the wall due to x-component of velocity

For ball

 change in momentum of ball

=p(f) – p(i)   ,

=(-2mv)*i

For wall

change in momentum of ball

=p(f) – p(i)   ,

=(2mv)*i

 2l/v sec = time taken in 1 collision

I sec =v/2l collision

F= p*frequency

=2mv*v/2l

=mV2/l

F(x)= mv2/l(x1) + mv2/l(x2) + mv2/l(x3)…………..mv2/l(xn)

As

Pressure =force/area

=and area=L*L

Pressure in x direction= mV2/L +mv2/L + mv2/L+……………mv2/L

                                             1        +      2     +        3  +…………….     N

 Same as pressure in Y direction

= mV2/L +mv2/L + mv2/L+……………mv2/L

      1        +      2     +        3  +…………….     N

And  Z-direction

= mV2/L +mv2/L + mv2/L+……………mv2/L

       1        +      2     +        3  +…………….     N

Now according to pascal law the pressure on any surface of container is always  same means by all component

So

Px = Py = Pz = P

Adding all the pressure

P + P +P =m(V2 + V2 + V2………..             V2)/L3

     

                       1       2   3                               n

3P = m(V2 + V2 + V2………..             V2)/L3

               1       2       3                           n

P= m(V2 + V2 + V2………..             V2)/3*L3

            1       2       3     .............  n

L3=V(volume of container)

P = = m(V2 + V2 + V2………..             V2)/3*V

               1       2       3                           n

This is nothing but maxwell’s theory of kenetic gases

Assumption with kenetic theory of gases

Assumption with kenetic theory of gases

1-The molecule of gas moves all direction with all possible velocity during motion,the molecules colloid with one another but the collision do not effect the molecular density of gases

2-The motion of molecules is random

(the center of mass f gas remain at rest)

3-Between two collisiona molecules move in straight line with uniform velocity this is because no force act on the particle b/w the collision.The distance covered by molecules is  called mean free path

4-The diamension of the molecules may be neglected as compared to the dimension of free path.

5-No approciable force of attraction or repulsion by molecule on in another accept during collision

6-Collision between  melecules and with the wall of the container or perfectlly elastic and the time of impact is of neglagible duration

(elastic collision means no change of linear momentum and kenetic energy )

Nelastic collision means no change of momentum but energy change

7-Molecules obey newtons law of motion

Type of frame Or Reference

There are two type of frame

~Inertial  frame of reference

~Non inertial frame of reference

Inertial  frame or reference

Frame said to be inertial when it obey Newton’s law  of inertia(newton”s first  law)

Defination –

The frame relative to which a body not acted by any external force remain unaccelerated ,are inertial frames

Non-inertial frame

Frame that does not obey  the the Newton’s law.

Defination-

A frame of reference is said to be non- inertial frame when a body not acted upon any external

Forces,is accelerated

How to considered Frame of Reference

Frame of reference

Definition

Any system relative (with respect to ) to which the motion or rest of an body can be described 
simply called frame of reference

ex-
let suppose a boy and his father  travelling in car boy thrown a ball upward in vertical direction
his father observe that ball moves vertically upward ( because both father and son are in same frame of reference i.e in car)
 now lets suppose his uncle is standing on the ground (at rest)
if he observe the ball ,a parabolic path of motion of same ball ( now there are two frame one is in motion other is at rest)
this is because ball as observed from a ground seems to have a horizontal component of velocity and this will be equal to the velocity of car.
vertical component of velocity equal to the velocity of the ball..
 so here we can see that same event is described in different ways by different observer.
so the motion is relative .

vertical motion -when view by his father in the car 

parabolic -when observe by his uncle  

PREFACE

Friends this is blog about the physics for all student ,
The motive of our blog is to provide clear and logical concept & principle of every topic of physics in a simple way.
In spite of my best effort, it may  be possible some error may be crept in.
I shell acknowledge with gratitude if any error is brought in my choice.

Suggestion from professors and student for improvement of this always welcome


Purushottam gupta
New Delhi