The Biot–Savart law

Ø   The Biot–Savart law is used for computing the megneic field generated by an elecric current.It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current.The law is valid in the magnetostatic approximation.

                           Electric currents (along closed curve)

Ø   The Biot–Savart law is used for computing the resultant magnetic field B at position r generated by a steady current I, a continual flow of charges which is constant in time and the charge neither accumulates nor depletes at any point.

                                           
Ø   Where

dl is a vector whose magnitude is the length of the differential element of the wire,

μ0 is the magnetic constant,

 is the unit vector of r

Ørsted`s observation

Ø   Ørsted noticed a compass needle deflected from magnetic north when an electric current from a battery was switched on and off, confirming a direct relationship between electricity and magnetism On 21 April 1820.

Ø   According to its his initial interpretation the magnetic effect create from all the side the electric wire.

Ø     After three years he published his finding which is show that an electric current produces a circular magnetic field as it flows through a wire.

Carnot cycle

Ø   The Carnot cycle is a theoretical thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded by others in the 1830s and 1840s.

Ø   This is most efficient cycle for converting a thermal energy into work or creating a temperature different by doing a given amount of work.

Ø   Every thermodynamics process exits in different state when a system is taken through these series of different state and then returned its final state a thermodynamics cycle is said to have occurred.

Ø   In the process of going through this cycle the system may perform work on its surrounding, thereby acting as a heat engine.

Ø   Although such a perfect engine is only a theoretical limit and cannot be built in practices.

1. Reversible isothermal expansion of the gas at the "hot" temperature, T₁ (isothermal heat addition or absorption)

Ø    During this step ( In the Figure A to B )  the gas is allowed to expand and it does work on the surroundings.

Ø   The temperature of the gas does not change during the process, thus it is an isothermal expansion.

Ø   The gas expansion is propelled by absorption of heat energy Q₁ and of entropy ΔS = Q₁  from the higher
                                                   T₁
temperature reservoir.

    
2.Isentropic (reversible adiabatic) expansion of the gas (isentropic work output).

Ø    For this step ( In the Figure B to C ) the mechanisms of the engine are assumed to be thermally insulated, thus they neither gain nor lose heat.

Ø   The gas continues to expand, doing work on the surroundings, and losing an equivalent amount of internal energy.

Ø   The gas expansion causes it to cool to the "cold" temperature, T₂. The entropy remains unchanged.

3.Reversible isothermal compression of the gas at the "cold" temperature, T₂. (isothermal heat rejection)

Ø     ( In Figure C to D) Now the surroundings do work on the gas, causing an amount of heat energy Q₂ and of entropy ΔS = Q₂  to flow

                           T₂

out of the gas  to the low temperature reservoir..

Ø   ΔS = Q₁ = Q₂  ( Clausius ineqality )
         T₁     T₂

4.Isentropic compression of the gas (isentropic work input).

Ø    (In Figure D to A) Once again assumed thermally insulated mechanisms of the engine.

Ø   During this step, the surrounding do work on the gas, increasing its internal energy and compressing it causing the temperature to rise T₁.

Ø   The entropy remain unchanged At this point the gas is in the same state as at the start if step 1.

Work done is given by W = Q₁ – Q₂

Efficiency η = W = Q₁ – Q₂ = T₁ – T₂

                       Q₁        Q₁             T₁

Thermal Efficiency of a heat engine

Ø    It is very obvious that higher the conversion of heat energy to mechanical energy by an engine, the higher its efficiency.

Ø   Let Q₁ = heat absorbed by an engine

          Q₂ = unutilized heat, i.e rejected heat

Then efficiency of heat engine is defined as,

η =        heat supplied – heat rejected

                               heat supplied

   =         converted heat

             heat supplied

  

   =       Q₁ – Q₂

                 Q₁

                 

   =          1 – Q₂

Q₁

Heat engine

Ø   A heat engine is designed to convert heat energy into mechanical energy which can be used to do mechanical work.

Ø    This engine made up of tree parts.

1 Source ( which provide Heat energy )

2 Working substance ( as a vapor of gas )

3 Sink (cold body )

Ø    In the overall system, the hot body is the source of heat and sink is cold body.

Working:

Ø    Heat engine gained heat energy from the source via Working substance, does some mechanical work and reject the heat into the sink.

Ø    If the complete two revolutions per unit time then its known as four stroke engine.

Ø    While the revolutions will be one per unit time then its known as two stroke engine.

First law of thermodynamics

Ø   The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems.

Ø   According to this, the energy can neither be created nor destroyed but just can be converted from one form to another.

    In thermodynamic way we can say that

Ø   “The law of conservation of energy states that the total energy of an isolated system is constant.”

Ø   The first law is often formulated by stating that the change in the internal energy of a closed system is equal to the amount of heat supplied to the system.

Ø   When we supply heat to any thermodynamic system, a part of it is used to change its internal energy while rest is converted into work.

Ø   Suppose U_i and U_f are the initial and final energy of the system, W the work done and Q is the heat energy absorbed, then the first law can be represented as under

Q = ( U_f  - U_i ) + W

Ø   Above eqn. is the mathematical representation of this law.

Ø   For a process taking place at constant pressure, if the volume change is dV, then W = PdV

dQ = dU + PdV

Ø   It should be noted that

1.   If the system gained heat, then dQ is +Ve and if lost then –Ve.

2.   Work done by a system is taken as positive, while work done on the system is taken as negative.

Second law of thermodynamics

Second law of thermodynamics

Ø    The second law of thermodynamics states that the entropy of an isolated system never decreases.

Ø   It retains the energy conservation between mechanical work and heat. But it does not state the condition of conversion as well as direction of heat transferred.

The statement of this law can be given in number of ways.

1.Clausius statement

Ø    Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.

2.Kelvin statement

Ø    It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects.

3.Planck's proposition

 

Ø    It is impossible to construct an engine which will work in a complete cycle, and produce no effect except the raising of a weight and cooling of a heat reservoir.

 

4.Planck's statement 

Ø    Every process occurring in nature proceeds in the sense in which the sum of the entropies of all bodies taking part in the process is increased. In the limit, i.e. for reversible processes, the sum of the entropies remains unchanged.

Zeroth law

Zeroth law of thermodynamics states that if two thermodynamics system are each in thermal equilibrium with third, then all three are in thermal equilibrium with each other.

We can also say that…

“ If a body A, be in thermal equilibrium with body B and body C then B and C are in thermal equilibrium with one another. ”

Thermal equillibrum

Two physical systems are in thermal equilibrium if no heat flows between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the Zeroth Law of Thermodynamics. A system is said to be in thermal equilibrium with itself if the temperature within the system is spatially and temporally uniform.

When the system should in thermally, chemically and physically equilibrium then we can say that the system are in thermodynamic equilibrium so systems in thermodynamic equilibrium are always in thermal equilibrium but it is not necessary that system in thermal equilibrium are always in thermodynamic equilibrium.