Specific heat of gases

We have already known about the specific heat of gases at constant pressure and constant volume.
When the gas is heated at constant pressure, there is increase in its internal energy, temperature and the volume of the gas, on other hand, when the gas is heated at constant volume, then there is increase in the internal energy and the temperature.
The difference between these two processes is, at constant pressure, there is increase in volume in addition because of work is done by the gas to get expansion.
The amount of heat supplied to the gas at constant volume dQ=CvdT
The amount of heat supplied to the gas at constant pressure dQ'=CpdT
dQ'=CvdT+dW, in this equation,
we can understand that only dW term is presented in addition to CvdT.
So, we can write CpdT=CvdT+dW
Generally, under some constant pressure, suppose the gas is moved a distance 'dx'

Principle of method of mixtures

When we touch with very heat water, we can't bear more than one minute in touch with the heat water, within few seconds we keep us away from the heat water, but when we touch with some heated water, then after sometime we feel its temperature is same but little over our body temperature. Why it happens? think...
I will tell you, when two bodies at different temperatures touch with each other, then after some time, they get intermediate temperature between the temperatures of two bodies because there is flow of heat from hot body to cold body, we can say it in another manner, i.e., the heat loss by hot body is equal to cold body. We called it as principle of mixtures.
Using this principle, we can find out specific heat experimentally. The important point to remember in this principle is it is applicable only when there is no external loss or gain to the system of cold and hot bodies.

molar specific heat

'mole' is the term is used for the gas components but not for liquids and solids. In case of gases we used to find out molar specific heat instead of specific heat. Because it is difficult to find out the mass of a gas comparing with find out moles of gas

Heat capacity and specific heat

Before discussing about this topic, we need to know the difference between temperature and heat.
Heat is energy form, on other hand temperature is telling about the thermal equilbrium of a body when it touch with another body.
But there is relation between heat and temperature, i.e., represented by thermal capacity.
In order to raise the temperature of the body, it is needed to supply the amount heat to the body.
thermal capacity is defined as the amount of heat supplied to the body to raise the temperature of the body through unity i.e., 1degree centigrade.
If small modification is done in above definition, then we can obtain the definition of the specific heat. So, specific heat is defined as the amount of heat supplied to the unit mass of the body to raise its temperature through unity
In notations, thermal capacity and specific heat is as follows

The first law of thermodynamics

The first law of thermodynamics states that the amount of heat supplied to the system is equal to the algebraic sum of the change in internal energy of the system and external work done by system.
Depending on the signs of changes in Q and W, we can draw some important point in this topic.

Introduction of first law of thermodynamics

Before, going through the concept of first law of thermodynamics, we have a short glance on Joule's law because it is the first step for the first law of thermodynamics.
When certain amount of work is done, then equivalent quantity of heat is produced, conversely we can say that in order to do some mechanical work certain amount of heat is needed.
Suppose we take a electric heater, in order to heat the water i.e., work, equivalence of heat is needed. Again, that is supplied as current to the heater, that current is produced due to some mechanical work at turbines of water electricity equipment at dams, i.e., it is cycling process or cumulative process of producing heat and mechanical work and their equivalence, that can be identified as proportionality constant 'J'. Whatever, Joule explained same one is extended by the first law of thermodynamics.
In order to understand the first law of thermodynamics, we take the example of boiling of the water in vessel on a stove. When the heat is supplied to the vessel containing the water, first of all,
molecules of water get accelerated or moved, i.e., internal energy increases and then the boiled water produces water vapour which causes the closed plate of vessel to fall down, i.e., there is some external work is done on the plate.
From this example, we conclude that whatever heat is supplied to the system,one part is used to increase internal energy, the remaining part is used to do external work.
Another example, we take a bike, when petrol is poured in the tank of the bike and started, the engine produces heat in which one part causes the molecules of the petrol to be moved, i.e.,
internal energy and then another part is used to move the bike, i.e., the external work

Internal energy

Internal energy is more in gases than liquids and solids. For example, when the rice is boiling in a vessel which has closed with a plate, then the plate moves, finally it falls down from the vessel to the ground because the internal energy of gases causes it falls down.
Internal energy has ingrediants of potential energy and kinetic energy.
Potential energy arises due to interaction of atoms in the molecules and also one atom with another atom
Kinetic energy arises due to translatory,rotational and vibrational motion molecules. Mainly, translatory motion of molecules occurs due to thermal energy applied on the system. So, different molecules of gas gets different energies, so that there is random motion of molecules. For that, according to classical mechanics, we can get only average translatory kinetic energy of gas molecules which is given by

At absolute temperature T=0K, the translational kinetic energy becomes zero, so that the internal energy is only due to the vibrational and rotational kinetic energies of gases. This energy is called zero point energy.
There is no change in the internal energy due to exchange of temperature with the system, but to there is change in the internal energy due to exchange of heat, because when heat is the energy quantity.
One of the important point to remember is that when external energy is applied on the system, the internal energy increases due to translational kinetic energy of molecules of the gas.

Joule's law in thermodynamics

When two palms are rubbed with the fastest manner, then suddenly heat is generated, so we can't continue this process further because we can't bare it.
we have done some work i.e., rubbing the two palms, so that works turns into heat. From this example, we conclude the equivalence of mechanical work to heat. That relation is formulated by Joule. He says that the mechanical work is done on the system then proportional heat is produced from the system.
Therefore, the mechanical work W on the system is proportional to the heat produced Q from the system, i.e.,
In order to produce unit quantity of heat, mechanical work done is W=product of (J,1) where Q=1calory
then Joule's constant J=4.18joule/calory, since 1joule=4.18calory, from this we have derived the value of Joule's constant.

Thermal equilbrium

In winter, due to coolness, our body rises its temperature mean while in summer, due to hotness,
our body lows its temperature, whatever may be, our body is main tool to maintain thermal equilbrium in order to protect itself.
Here we discuss about the term 'temperature', in order to understand this term we have to know about zeroth law of thermodynamics.
Suppose if two bodies are in thermal equilbrium, then it is difficult to measure the heatness of the bodies, so that we have to take another body to keep in contact with that bodies in order to measure its heatness. Like that, the term we used to measure is temperature i.e., it is that inner property of heat of a body when a body is in contact with another body to take it to thermal equilbrium.
Clearly, we say that 'temperature' characterises the thermal equilbrium of the system of bodies, i.e., temperature is a property which denotes when the system is equilbrium or not.
For example, when we measure the temperature of a person who has suffered from fever, we keep the thermometer in his mouth, whenever mercury in thermometer is thermally equilbrium with the heatness of the body, thermometer indicates some reading which tells thermal equity value i.e., the temperature of the body of the person.
"When two bodies A and B are individually thermal equilbrium with another body C, then automatically bodies A and B are become thermally equilbrium with each other."
This is called zeroth law of thermodynamics.

Introduction to thermodynamics

Dynamics denotes only the matter about the mechanical work which is done by some force externally.
Thermodynamics denotes the inter-relation between the heat and the mechanical work. This subject has different parameters to identify characterstics of the matter when it undergoes some heat.
In case of dynamics we studied the parameters such as force, inertia, momentum, work and energy, meanwhile in case of thermodynamics we studied internal state of a system with the help of the variables such as pressure, volume, temperature, entropy and internal energy.
Like three Newton's laws of motion in dynamics, we have also three laws of thermodynamics in thermodynamics.
we have different characterstics such as conduction, convection and radiation of heat and also black body characterstics. These properties will be discussed in further articles.

conservative and non-conservative forces

conserve means what work is done it is not shown externally, it means suppose an object projects upwards with some velocity, in its path its kinetic energy changes, but whenever it reaches to the ground it kinetic energy is same as when it projects.
Therefore the applied force here is conservative.
we take an ideal spring, it is exerted by some force, then with same force again it gets stretched to get original shape. Here the force is elastic force.
Here the important point to remember is that the work done by the conservative force depends only upon the points on which the force applied but not on the path followed by the force.
In case non-conservative force, the work done by the force depends upon the points of locations of the force and also path followed by the force.
For example, the frictional force and electromagnetic induction are the examples of non-conservative forces. Once, frictional force applies on the object, then it can't be regained, i.e., that force is dissipated, only through applied force on the object.
Here one important point is to remember is that work-energy theorem is applicable for conservative force only but not for non-conservative forces because the path followed by the non-conservative forces, kinetic energy of the object varied periodically up and down, so it is difficult to find out the change in kinetic energy.

Work-energy theorem

If a body moves to further, there must be change in its kinetic energy, how it happens? only when an external force is applied on the system of body. (or)When work is done by the unbalanced or resultant force on the body is equal to change in its kinetic energy.
But this theorem is applicable only when constant force is applied on the body. Therefore, there must be no change or no variation in the force, this is remember
We know the Newton's second law, that F=ma
The work done by the force W=F.S=ma.s
Here v and u are the final and initial velocities of the body when resultant or unbalanced force applied on the body. Do you have doubt? why constant force causes to change the velocity of the body? Here one important point to remember is that when constant force applied continuously, then the body overcomes the frictional force and viscous force gradually, that causes resultant force to accelerate the body, so that the body gets the velocity v.

The energy possessed by the bullet when strike with wooden plank

Suppose a marble is hit on a wooden plank, a bullet is hit the wooden plank. Can you imagine what happened as difference between these?, of course, you think that bullet has more energy than marble, so it makes a hole in the wooden plank, but the marble can't
Let a bullet of mass m moving with velocity v strike the wooden plank and penetrate through a distance x before coming to rest.
initial velocity of the bullet(u)=V
final velocity of the bullet(v)=0
After penetration, the distance travelled by the bullet in to the wooden plank (s)=x
then according to kinematic equation v^2-u^2=2as
therefore

Concept of energy

In physiological meaning, energy is the effect, but in case of physics it is the cause because physics treats the total energy in the universe is always constant, it can't be destroyed and created, but it can be transformed from one form to another form without any loss or dissipation.
So, in dynamics we mainly deals with the mechanical energy which is in the form of potential energy and kinetic energy.
Potential energy is the energy possessed by virtue of its state or position.
For example, water on hill top and stretched string have potential energy. A certain mass m is kept at the height h, then the potential energy possessed by the mass is P.E.=mgh
In a stretched spring, the stored potential energy P.E.=(1/2)Kx^2
Kinetic energy is the energy possessed by virtue of the body moving with some velocity
Suppose a car of mass m is moving with velocity v, then the kinetic energy of the car K.E.=(1/2)mv^2

Concept of power

If you put a competition between two persons to eat certain food with in very little time, then the person who eats the total food completely before another person with in very short time, he will win, i.e., he has more power than other. What means here? time is the factor with in which he has completed his work.
If you take any two engines, then the task completed by the one engine than other engine will have certainly more power.
So, we can define power is rate of doing work by a force.
Generally, we take power in terms of horse power to express output of machine in engineering subject.
Power is scalar even force and velocity are vectors

Concept of work in physical meaning

Generally, we mean work is muscular power, but in physics the term 'work' has different meaning.
i.e., when a constant force is applied on the object, then it moves some distance, then it has work to be done. Suppose the force is F and the distance moved is S, then the work done by the object is
W=F.S
This formula is applicable when force is applied in the direction its moved. But sometimes the force is applied making some angle 'O' with the direction of moving of the object. At the time, we take
force component along the direction of object moved i.e., FCosO
Then the work done by the object is W=(FCosO).S
For example, when a road roller moves along the horizontal direction, the force is applied in a direction of pulling that makes some angle with horizontal direction that roller moved.
Here is one point to remember is when O=90 degrees, then the work done by the object W=0.
This is the fact in case of electron moves around the nucleus, i.e., the centripetal force is along the radius vector towards the centre of circle, the motion of the body is along the direction of the tangent of circle, between these two the angle is 90 degrees.
It is surprised that when a man is holding a suitcase in air, according to physiological sense, he works hard, but according to physics, he is not yet doing any work because the force which applied on the suitcase causes no displacement.

conservation of linear momentum during collision

Let us consider two particles of masses m1 and m2 which are collided with each other with velocities u1 and u2 respectively. After collision, they get the velocities v1 and v2 respectively.
When there is no external force, the momenta of two particles p1 and p2 respectively and the total momentum of the system remains constant. i.e.,p=p1+p2
From above equation, we can say that algebraic sum of momenta of a system of particles before collision is equal to the algebraic sum of momenta of a system of particles after collision.

Law of conservation of linear momentum

From Newton's second law, it tells about rate of change of momentum is equal to force applied on the body.

Apparent weight in a lift

When a man of 'mg' is in the lift, then the floor of the lift exerts the force R on the person. If the lift is in rest position, then R=mg, i.e., there is no resultant force occurs in this matter.
When the lift to move upwards with acceleration a, then
the force applied on the lift is F=ma
ma=R-mg
R=m(g+a)
R=mg(1+a/g)
i.e., apparent weight of the person increases a/g times when the lift is to move upwards.
When the lift to mover downwards with acceleration a, then
the force applied on the lift is F=ma
ma=mg-R
R=m(g-a)
R=mg(1-a/g)
i.e., apparent weight of the person decreases a/g times when the lift is to move downwards. So we have to understand that mass of the person does not change but weight of the person changes when he moves vertically upwards and downwards.

impulsive force

Impulse is the new concept of dynamics. In order to understand this one, we have to approach the example i.e., the force experienced by the ball when hit by the bat during very little time.
Mainly, the linear momentum of ball changes substantially during this little time.

A large force acting very short interval of time is called impulsive force.
Above figure shows the impulsive force with constant direction varying during short interval of time(between t1 and t2) because of collision.
Suppose a body mass of 'm' moves with velocity 'u' ,during collision, it is acted by impulsive force 'F', with in very short interval of time 'delta t' and changes its velocity to 'v', then
This equation shows the impulsive force during small time t(the product of applied force and time) which equals to the change in momentum of the body.
Above equations can be expressed mathematically as
Mainly, impulse is deformation effect to objects. Shock observers are used to increase the time of action of impulsive force.

continuation of resultant force

Above figure shows the heavy box suspended by a rope.

When a body is put on the table, the body exerts the force on the table, at the same time the table exerts the force on the body. Suppose a heavy box is suspended by the rope, there are two forces to keep the box suspended, i.e., the tension in the rope and the weight of the heavy box. The rope exerts the force on the box to hold it, while the weight of the box tight the rope to stretch which causes the tension in the rope.
When the system is in equilbrium, then the resultant force
Fr=T-W=0
If the weight of the heavy box is greater than tension in the rope, the box falls down on the ground from the rope.
i.e., there is the resultant force Fr=W-T=+Ve

Resultant force

Actually, there are many types of forces in nature for example, gravitational forces, electrostatic forces and nuclear forces. But in case of mechanics, we have other three forces are there, i.e., frictional forces, elastic force and force due to surface tension.
Force is a vector quantity, if more than one force applied on the body, we can find the resultant force using the laws of vector addition.
There are two case of moving the body along the direction of motion. One is the resultant force acting on the body along the direction of motion of the body, when its get accelerated. Another one is resultant force acting on the body along opposite direction of the body, when its get deaccelrated. Above figure shows the forces acting on the body.

The resultant force Fr=F-(Fv+Fs)
When the resultant force is zero, then the external force balances with the sum of viscous and frictional forces which causes the body moves with uniform velocity.

See the above figure, there are two blocks and they are kept on table with contact each other, then Newton's third law is applicable between two blocks and with table. Here we see external is also applied on the block 'A'. This same force 'F' is also automatically applied on the block 'B' because it contact with block 'A' i.e., force 'F' is applied on (m1+m2). Therefore, acceleration
Between two blocks A and B, we can apply Newton's third law is also applicable, therefore
f2=-f1
If you consider the block A alone, then the net force acting on A is F-f1, therefore, acceleration
If the force applied on the block B, then the common acceleration is same but the contact force will be different.

Atwood's machine principle

Actually, for free falling of body, to determine the acceleration of body we can apply laws of motion, but the time is too short for free falling body.
In Atwood's Machine, mass m2 is considerably retarded by the mass m2, therefore the unbalanced resultant force on the system to be considered as
F=(m2-m1)g------1
The net accelerated mass is M=m1+m2-------2
Therefore the acceleration of the system is
This is the Atwood's principle to determine the acceleration due to gravity

Atwood's machinee

This is the article about the matter of two objects of different masses are suspended by a cable of inextensible over pulley of massless. One thing here we have to remember that two objects are moved vertically with same acceleration. For two objects free body diagram is same that is like below


For the object of mass m1, unbalanced force acting on m1 is T-m1g. i.e.,
T-m1g=m1a--------1
For the object of mass m2, unbalanced force acting on m2 is m2g-T.i.e.,
m2g-T=m2a--------2
Adding equations 1 and 2, we get



From the equation 1,
According to the figure, this tension will be less than m1g and greater than m2g

Two objects connected by a cable

In this article, i would like to give the concern about the two objects moving in horizontal and vertical directions,

In the below diagram is called free body diagram for the object in horizontal direction. There are three forces are there on the object in horizontal direction, i.e., N,T and m1g.

As the object has no vertical direction, N-m1g=0; N=m1g; the object is moved by cable with tension T with acceleration 'a' i.e.,

T=m1a------1

Next consider the object in vertical direction of mass m2, as the pulley is massless, inextensible and has a fixed length, the object of mass m2 moves with the accleration , therefore

m2g-T=m2a------2

Adding eqn 1 and eqn2, then we get

m2g=(m1+m2)a

idea about the single object suspended by a cable

Of course! you know very well about this topic, but i would like some idea particularly about this topic. Please, observe below figure carefully, then we find out that in normal
manner, the tension T in cable is always balanced by the weight of the object so that T-mg=0

T=mg
But when the cable is pulled upwards with some external force 'F' then the new tension T' arises
i.e., T'-mg=ma or T'=m(g+a)
When the cable is lowered down with the same external force 'F' then the new tension T'' arises
i.e., mg-T''=ma or T''=m(g-a)

idea about the laws of motion in kinematics

• when a particle is moving along straight line, then the particle has two entities i.e., distance its moved and then time it completes the given distance. Here, the idea is the distance travelled by the particle is a function of time i.e., X(t). Can you analyse the graph between the distance and time?. If you take the graph between time and distance travelled by the particle, then your graph is like upside down hills because the particle may have different speeds at different points of its path
• One important condition to derive the laws of motion, the acceleration of the particle should be constant throughout its journey.
  
• It is the problem while taking the average velocity of the particle starting from a point along a straight line because the particle can be rest at any point its journey or it reaches to its destination point at rest position. So, it is better to take the change of velocity with time i.e., acceleration, like that acceleration concept comes out.
• By using calculus, we can easily derive the laws of motion. For derivation of the laws of motion, only acceleration remains constant is basic point and concept.