Duduli

The partition function is a fundamental quantity in statistical mechanics that describes how a system is distributed among its possible energy states. For a system in thermal equilibrium: Z = Σ e⁻ᴱⁱ/ᵏᴮᵀ where Eᵢ is the energy of the ith state, kB is the Boltzmann constant, and T is the absolute temperature. The partition function is useful because many thermodynamic quantities, such as internal energy, entropy, and Helmholtz free energy, can be calculated from it.

Proof:-

Brewster’s Law states that when unpolarized light is incident on a transparent surface at the polarizing angle i_B, the reflected and refracted rays are perpendicular to each other.       tan i_B=μ where i_B is the Brewster angle and μ is the refractive index of the medium. Key point: At Brewster angle, the reflected light is completely plane polarized.

Stars appear to twinkle because their light passes through Earth’s atmosphere. Different layers of air have different temperatures and densities, so they continuously bend the starlight in slightly different directions. Stars are extremely far away and appear as point sources of light, so these changes make their brightness seem to fluctuate. Planets are much closer and appear as tiny disks rather than point sources. Light comes from many points across the disk, and the fluctuations from different parts tend to cancel each other out.

According to Einstein’s special relativity , a massive object cannot reach the speed of light (c). As its velocity approaches (c), its relativistic energy increases enormously: E = γmc², where γ = 1/√(1 − v²/c²) When (v tends to c), γ → ∞, so an infinite amount of energy would be required to reach (c). Light can travel at (c) because photons have zero rest mass. Key idea : A massive object can approach the speed of light, but can never reach it.

A capacitor stores electric charge and allows current only while its voltage is changing. ●DC: The voltage becomes constant after the capacitor is fully charged, so dV/dt = 0. Hence, current becomes zero. Therefore, a capacitor blocks DC. ●AC: The voltage continuously changes with time, so dV/dt ≠ 0. The capacitor continuously charges and discharges, allowing current to flow. Therefore, a capacitor allows AC.

During a phase change, the heat supplied to a substance is used to overcome intermolecular forces and change its molecular arrangement, rather than increasing its temperature. This energy is called latent heat. For example, while ice melts at 0°C, its temperature remains 0°C until all the ice has melted.  So, even though temperature remains constant, internal energy changes.

Entropy(S) is a thermodynamic state function that measures the degree of energy dispersal or randomness/disorder of a system. Unit:- J K-¹ For Specific entropy  Unit :- J Kg K-¹   ●                         dS=dQ/T For reversible process ds=0 For irreversible process ds>0 Examples :- ●Ice melting → entropy increases. ●Water evaporating → entropy increases. ●Gas expanding freely → entropy increases. ●Heat naturally flowing from hot to cold → total entropy increases.

Electromagnetic induction is the phenomenon of production of an induced emf (electromotive force) in a closed circuit whenever the magnetic flux linked with the circuit changes. The induced emf is given by e=-dΦ/dt For a coil of N-turns e=-NdΦ/dt where magnetic flux is Φ=BAcosθ Lenz's law:- The induced current always flows in such a direction that it opposes the change in magnetic flux that produces it.

Resonance is the phenomenon in which a system oscillates with maximum amplitude when the frequency of the external periodic force equals its natural frequency.

A wave function (ψ) is a mathematical function that describes the quantum state of a particle. Its squared magnitude gives the probability density of finding the particle at a particular position. |ψ|² = Probability density In short : The wave function tells us what we can know about a quantum particle and where it is likely to be found.

Quantum tunneling is a phenomenon where a quantum particle can pass through a potential barrier even when its energy is less than the barrier height. In classical physics: ❌ Impossible In quantum physics: ✅ Possible Example : It is responsible for α-decay and is used in scanning tunneling microscopes (STM).

The Doppler effect is the apparent change in frequency of a wave when there is relative motion between the source and the observer. ●Source approaching → frequency increases → higher pitch ●Source moving away → frequency decreases → lower pitch Example :-The pitch of an ambulance siren sounds higher as it approaches you and lower as it moves away.

Chemical potential is the change in the Gibbs free energy of a system when one mole of a substance is added at constant temperature and pressure.                     μ=(∂G/∂n)ₜ,ₚ where G is Gibbs free energy and n is the number of moles. ● Chemical potential represents the driving.     force for the movement of particles. ☆  Particles naturally move from higher.             chemical potential to lower  chemical potential. ☆  At equilibrium, the chemical potential is.       the  same throughout the system.

Even though billions of stars emit light, space appears dark because most of the universe is empty.Light travels in straight lines and doesn’t illuminate empty space unless it interacts with matter. So, between stars and galaxies, there is very little material to scatter the light toward our eyes.

The polarizability of a hydrogen atom describes how easily it's electron cloud can be distorted by an external electric field.

The rank of the tensor is the number of suffixes or indices(without counting an index which appears once as a subscript) in the symbol representing tensor.

It is a device which is used to produce the plane polarised light. It is based on the principle of selective absorption and more effective than the tourmaline crystal. Polaroid allows the light oscillations parallel to the transmission axis to pass through them. The crystal or polaroid on which the unpolarised light is incident is called polariser. Crystal or polaroid on which polarised light is incident is called analyser.