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Grand canonical ensemble | Statistical mechanics | L-9

Grand canonical ensemble Grand canonical ensemble Microcanonical ensemble is a collection of independent assemblies in which energy (E), volume (V), and number of particles (N) remain constant. Canonical ensemble is a collection of independent assemblies in which temperature (T), volume (V), and number of particles (N) remain constant. It mean a microcanonical ensemble ⟶ Canonical ensemble, if we ignore the condition E = constant. Therefore the energy exchange takes place in this ensemble. Actually in chemical process, the number of particles N varies and it is very difficult to keep the number of particles constant in various phenomenon like radioactive decay process. Thus grand canonical ensemble is an ensemble in which the exchange of energy as well as the number of particles takes place with the heat reservoir. The grand canonical ensemble is a collection of essentially independent assemblies having the same temperature T, volume V, and a chemical potential µ....

Liquid helium as a Boson system | Statistical physics

Liquid helium as a Boson system Ordinary helium consists almost entirely of neutral atom of the isotope 2 He 4 . Since the total angular momentum of these atom is zero, so it follow the Bose-Einstein statistics. Properties of helium at low temperature The helium gas at atmospheric pressure condenses at 4.3K temperature into a liquid helium having critical temperature 5.2K, and the density of this liquid helium is very low (ρ = 0.124 g/cm 3 ). On further cooling the helium to about 0.82K, it does not freeze, and the liquid helium remains into liquid state up to absolute zero temperature i.e., T = 0K. It means the helium does not solidified at atmospheric pressure. To get the solid state of helium, it is subjected to an external pressure of at least 23atm. Phase transition of liquid He For He 4 in liquid phase, there is another phase transition (λ-transition), which divides the liquid state into two phases HeI and HeII. While liquefying He at...

Rectangular Cavity Resonator | Microwave electronics

Rectangular cavity resonator A rectangular cavity resonator is a piece of rectangular waveguide of dimension a, b, and c. In figure a rectangular cavity resonator of sides a, b, c is shown. TE waves in a rectangular cavity resonator Here we will consider about two transverse electric waves, out of two one moves in +z direction and another in -z direction. Let the transverse component of electric field for TE waves propagating along +z direction be This equation give the resonant frequencies for different sets of m, n, p for different cavity modes. If two or more independent cavity modes have the same resonant frequencies then it is known as degenerate frequency. It is found that the modes TE 000 , TE 001 , TE 010 and TE 100 do not exist in the cavity. The lowest modes (dominant mode), which are possible in TE mode are TE 101 , TE 011 etc. The allowed frequencies corresponding to dominant modes is fundamental frequency. To know more about...

Determination of size of lycopodium power | Second year practical physics

Determination of size of lycopodium power by forming diffraction fringes Sample reading Table for first order diffraction ring Table for second order diffraction ring Note: Above readings are only for reference, students should perform the practical in their laboratory and get their own readings.

de Broglie hypothesis | Quantum mechanics | Physical basis of quantum mechanics

de Broglie hypothesis According to de-Broglie, a wave is always associated with every moving particle. This wave is known as de-Broglie wave or matter wave. It means a matter wave have particle nature as well as wave nature i.e., dual nature. From quantum theory of radiation, energy of photon, E = h𝝂, where 𝝂 = frequency of incident photon . From Einstein’s theory of relativity E = √(m 0 2 c 4 + p 2 c 2 ) If m 0 = 0, then E = pc, p = momentum and c = velocity of light Now E = h𝝂 and E = pc ∴ h𝝂 = pc or p = h𝝂/c ∵ c = 𝝂λ or λ = c/𝝂 ∴ p = h/λ or λ = h/p This is known as de-Broglie wavelength This wavelength is always associated with a photon Since momentum is the characteristic of particles, and the wavelength is characteristic o...

Practical Physics II Year

Dear students you can get your physics practical assignment for the B.Sc. II year from here. The links of the notes of different practical objects are given below: Practical Physics II Object 1 Determination of band gap of a given pn junction diode https://cutt.ly/flVYxwG

Verification of Malus law | Third Year Practical Physics

Verification of law of malus Sample reading Determination of P Angle of incidence Photo electric current Photo electric current P (θ) (I max ) (I min ) (I max - I min ) / (I max + I min ) 0 219 360 10 272 67 20 278 72 30 256 28 40 271 30 50 330 21 60 337 44 Determination of 123 Position of Nicol prism (β) Observed value of current (µA) 0 243 10 194 20 176 30 164 40 219 50 232 60 220 70 146 80 122 90 190 100 125 110 243 120 202 130 220 140 265 150 226 160 226 170 216 180 274 190 268 200 252 210 260 220 250 230 236 240 206 250 162 260 124 270 105 280 98 290 110 300 250 310 187 320 264 330 250 340 273 350 224 360 225 Note: Above readings are only for reference, students should perform the practical in their laboratory and get their own readings. Students can also note voltage in place of current as an intensity. Object 4 Inverting and non-inverting Operational amplifier https://cutt.ly/gkarhFk

Electric quadrupole | Electrostatics

Electric field The space around a charged particle in which another charge experience a force is known as electric field. Electric field due to a circular loop of charge This is a linear charge distribution in which the charge is distributed along the circumference of the ring or circular loop. If observation point lies on the centre of the loop, then the electric field internsity at this point i.e., at the centre of the loop will be zero. If observation point lies very far from the centre of the loop then the value of electric field will be same as the electric field due to a point charge. It means in this case the circular loop behaves as a point charge for the observation point. Electric field due to an infinitely long straight uniformly charged wire In this article the charge is distibuted along the length of the wire. The electric field at any point due to infinitely long straight wire varies inversely with distance from the wire. NOTE The present lecture is a biling...

Dipole in electric field | Electrostatics

Electric dipole | Electrostatics

Characteristics of pn junction diode | Second year practical physics

Study of characteristic curve of a pn junction diode Sample reading Table for forward characteristic The space around a charged particle in which another charge experience a force is known as electric field. Table for reverse characteristic Note These readings are only for reference. Students should perform the practical in laboratory and obtain their own readings.

Van der Waals equation

Andrews experimental PV curve and state of continuity The slope of tangent drawn on critical point is opposite on either side of this point. The isothermal curve touching the critical point is critical isothermal. The temperature, pressure and volume corresponding to critical point are known as critical temperature (T c ), critical pressure (P c ) and critical volume (V c ) respectively. P c , V c and T c are combindly known as critical constants. Conclusion of Andrews experimental curve Any gas can be liquified below its critical temperature. Every gas has a critical temperature above which the gas can not be liquified by increasing pressure. At critical temperature, the density of liquid and its saturated vapour are equal. Above this temperature we can not distinguish between the two states. Near critical temperature, the compressibility of gas is very high and it become infinitive at critical temperature. Above critical temperature, the gas behaves as permanent gas....

Virial equation of state and Boyle temperature

Ideal gas An ideal gas is a gas which satisfy Boyles’ and Charles’ law for all the values of pressure, volume and temperature completely. Equation of state of an ideal gas for 1 gm molecule or 1 mole is PV = RT. In deriving this equation it was assumed that The size of gaseous molecules are infinitely small, so they do not occupy any space. There is no attractive or repulsive force between the gaseous molecules, so they have only kinetic energy, not potential energy. Deviation from perfect gas equation No gas is ideal or perfect, because no gas follow the ideal gas equation PV = RT at all conditions. The gases which liquified easily show more deviation from the ideal gas equation. For every gas there is a temperature at which the value of PV remain almost constant with increase in P and the value of PV increases at very high pressure. This particular temperature is known as Boyle temperature (T B ). Below T B , PV first decreases with increase in P, reaches to a minimum v...

Electric field due to an infinitely long straight uniformly charged wire | Electromagnetics | Electrostatics

Electric field due to an infinitely long straight uniformly charged wire The space around a charged particle in which another charge experience a force is known as electric field. The electric field at any point due to infinitely long straight wire varies inversely with distance from the wire. Electric field at P due to charge dq of length dy The charge on length dy, dq = λ dy This electric field will be along MP Total electric field at P Due to symmetry ...

Field effect transistor | FET | Third Year Practical Physics

Characteristic of FET and determination of mutual inductance, output resistance and voltage gain Sample reading Table for output characteristic S.No. V DS in volt Drain current I D (mA) for V GS = 0 V V GS = 0.5 V V GS = 1 V 1 0 0 0 0 2 0.5 2.5 2.25 1.5 3 1 5.25 3.75 2.75 4 1.5 6.75 5 3.5 5 2 7.25 6 3.75 6 2.5 8.25 6.5 4.25 7 3 8.75 6.75 4.5 8 3.5 9.25 ...

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