Osm Physics by Ashish

The second law of thermodynamics states that the entropy of an isolated system never decreases; it either stays the same (in reversible processes) or increases (in irreversible processes). It places fundamental limits on the direction of natural processes and on the efficiency of heat engines and refrigerators. Two classical equivalent formulations are the the Kelvin–Planck (Kelvin) and Clausius statement statement. (i) Kelvin–Planck Statement It is not possible to design an engine which works in a cyclic process and converts all the heat extracted from a heat source into work so that the working substance may remain unaffected. In other words, for the continuous production of work, a heat sink is necessary along with the heat source. According to the original statement given by Ke...

A Carnot cycle is a cyclic process consisting of four reversible processes performed in a definite sequence, namely two isothermal processes and two adiabatic processes. Main Parts of a Carnot Engine (i) Heat Source The heat source is a reservoir of effectively infinite heat capacity maintained at a high temperature \(T_1\) K. Its temperature remains constant even when heat is supplied to the working substance. Its upper surface is perfectly conducting. (ii) Mechanical Arrangement and Working Substance A hollow cylinder is used whose walls are perfectly insulating and whose base is perfectly conducting. A frictionless piston made of insulating material is fitted inside the cylinder. An ideal gas is used as the working substance. (iii) Heat Sink The heat sink is a reservoir of effectively infinite heat capacity maintained at a lower temperature \(T_2...

``` Heat Engine, Carnot Cycle and Efficiency of Carnot Engine Heat Engine A heat engine is a device that converts a part of the heat supplied to it into useful mechanical work. A heat engine must contain the following three essential parts: Heat source Mechanical arrangement and working substance Heat sink (i) Heat Source A heat source is a heat reservoir maintained at a high temperature. It has a very large, ideally infinite, heat capacity so that its temperature remains constant even when a large amount of heat is continuously extracted from it. (ii) Mechanical Arrangement and Working Substance To convert heat into mechanical work, a hollow cylinder fitted with a movable piston is used as the mechanical arrangement. The working substance is placed inside the cylinder. The working substance absorbs heat from the heat source and expands, t...

``` (i) Absolute Temperature is Always Positive From the definition of temperature given by Eqs. (12) and (13) of Section 1.4, \[ \beta = \frac{\partial \ln \Omega(E)}{\partial E} = \frac{1}{k_B T} \tag{1} \] where \( \Omega(E) \) represents the number of accessible microstates corresponding to the energy \(E\). For a general system, \( \Omega(E) \) is a rapidly increasing function of energy \(E\). Therefore, \[ \frac{\partial \ln \Omega(E)}{\partial E} > 0. \] Hence, \( \beta \) is positive. Since \[ \beta = \frac{1}{k_B T}, \] and the Boltzmann constant \(k_B\) is positive, the absolute temperature \(T\) is also positive. Therefore, \[ \boxed{T>0} \] for ordinary physical systems. (ii) Magnitude of Absolute Temperature To estimate the magnitude of temperature, the approximate dependence o...

— Statistical Physics According to the principle of equal a priori probability , the probability of the finding a system is directly proportional of the accessible states of the joint system (A*). \( P(E) = C\,\Omega^*(E) \) (1) where the normalisation constant \(C\) is independent of \(E\). Let \(\Omega(E)\) and \(\Omega'(E')\) be the numbers of accessible states of systems \(A\) and \(A'\) respectively. Therefore \( \Omega^*(E) = \Omega(E)\,\Omega'(E') \) (2) Substituting into equation (1) yields \( P(E) = C\,\Omega(E)\,\Omega'(E') \) (3) Taking the natural logarithm of equation (3), \( \ln P(E) = \ln C + \ln\Omega(E) + \ln\Omega'(E') \) (4) The most probable value of \(E\), denoted \({\tilde E}\), is the energy at which \(P...

  The first law of thermodynamics is a statement of the law of conservation of energy applied to thermodynamic systems. When a small amount of heat d Q dQ is supplied to a thermodynamic system, a part of it may be used to increase the internal energy of the system, while the remaining part may be used to do external work . Thus, d Q = d U + d W \boxed{dQ=dU+dW} where d Q dQ = infinitesimal amount of heat supplied to the system, d U dU = infinitesimal change in internal energy, d W dW = infinitesimal work done by the system. If the system performs work d W dW against an external pressure P e x t P_{\rm ext} , d W = P e x t   d V \boxed{dW=P_{\rm ext}\,dV} Therefore, d Q = d U + P e x t   d V \boxed{dQ=dU+P_{\rm ext}\,dV} For a quasi-static process , P e x t = P P_{\rm ext}=P , so d Q = d U + P   d V \boxed{dQ=dU+P\,dV} ​

  Records Light Intensity and Phase: Unlike a regular photograph that only records brightness (amplitude), a hologram records both the intensity and the phase (the relative timing and position) of light waves.   Three-Dimensional (3D) Realism: It recreates full spatial depth, making the reconstructed image look lifelike and tangible.   Motion Parallax: When you change your viewing angle, your perspective shifts. You can peer around the sides of the object just as you would with a real physical item.   Distributed Information: Every small piece of a hologram contains data about the entire recorded object. If a hologram is broken or cut into pieces, each individual piece can still project the entire image (though at a lower resolution or smaller window). Interference Pattern Storage: On the recording medium or film, a hologram does not look like the actual picture. It appears as a complex, unidentifiable microscopic system of light and dark interference fringes, s...