Osm Physics by Ashish

When the vapour of a substance is in thermodynamic equilibrium with its liquid or solid phase at a given temperature, the pressure exerted by the vapour is called the saturated vapour pressure . The dependence of saturated vapour pressure on temperature is described by the Clapeyron equation. For two phases in equilibrium, the Clapeyron equation is \[ \boxed{ \frac{dP}{dT} = \frac{L}{T(V_2-V_1)} } \tag{1} \] where \(L\) is the molar latent heat of transition. \(V_1\) is the molar volume of the condensed phase. \(V_2\) is the molar volume of the vapour phase. \(T\) is the absolute temperature. For vaporization or sublimation at sufficiently low pressure, the molar volume of the vapour is much larger than that of the liquid or solid: \[ V_2\gg V_1. \] Therefore, \[ V_2-V_1\approx V_2. \] Equation (1) becomes \[ \frac{dP}{dT} \approx \frac{L}{TV_2}. \tag{2} \] Assuming that the vapour behaves as an ideal gas, the equation of sta...

Thermodynamic Equilibrium and Phase Transitions Triple Point A pure substance may exist in three principal phases: solid, liquid, and vapour. The equilibrium state of a substance is determined by its thermodynamic variables, particularly pressure \(P\) and temperature \(T\). A change in pressure or temperature may cause a phase transition. The equilibrium between different phases can be represented by a pressure–temperature (\(P\)–\(T\)) phase diagram. Consider the phase diagram of water, which contains three phase-equilibrium curves: Solid–liquid equilibrium curve (fusion curve). Liquid–vapour equilibrium curve (vaporization curve). Solid–vapour equilibrium curve (sublimation curve). Pressure–Temperature Phase Diagram of Water Temperature (T) Pressure (P) Critical point Solid Liquid Vapour Fusion curve Vaporization curve Sublimation curve Triple point Tₜ Pₜ Fig. 3.10.1: Schematic pressu...

A change in temperature or pressure may cause a substance to transform from one phase into another. This transformation is called a phase transition . The principal phase transitions are: Melting: Transformation from solid to liquid. Freezing: Transformation from liquid to solid. Vaporization: Transformation from liquid to vapour. Condensation: Transformation from vapour to liquid. Sublimation: Direct transformation from solid to vapour. Deposition: Direct transformation from vapour to solid. During phase equilibrium, two phases coexist without any net transfer of matter from one phase to the other, although molecular exchange may continue in both directions. Thermodynamic Condition for Phase Equilibrium Consider a closed system containing two phases, denoted by phase 1 and phase 2, of the same pure substance. The phases are in thermal and mechanical contact and are allowed to exchange molecules. The system is maintained at ...

Consider a system A in contact with a large reservoir A' , maintained at constant temperature \(T_0\) and pressure \(P_0\). The system and reservoir together form an isolated composite system \(A^*\), which exchanges neither energy nor volume with its surroundings. Isolated Composite System A* Reservoir A' Temperature T₀ Pressure P₀ Large reservoir System A Energy E Entropy S Volume V Heat Work Total energy and total volume remain constant Fig. : A thermodynamic system A in thermal and mechanical contact with a large reservoir A'. The combined system A* is isolated. Let \(E\), \(S\), and \(V\) represent the internal energy, entropy, and volume of system A, respectively. The corresponding quantities for reservoir A' are denoted by \(E'\), \(S'\), and \(V'\). Since the composite system is isolated, its total internal energy remains constant: \[ E^*=E+E...

Absolute zero is the lowest possible temperature on the thermodynamic temperature scale. It corresponds to \[ \boxed{ T=0\,\text{K}=-273.15^\circ\text{C} } \] At absolute zero, a system is in its lowest accessible energy state, called the ground state. However, quantum-mechanical zero-point motion may remain present. The production of extremely low temperatures has been an important objective of experimental physics because many quantum phenomena, including superconductivity, superfluidity, and magnetic ordering, become observable at cryogenic temperatures. Cooling by Evaporation of Liquid Helium Before the development of magnetic refrigeration, one of the principal methods of producing temperatures below 4.2 K was the evaporation of liquid helium at reduced pressure. When the pressure above liquid helium is reduced by pumping, its boiling temperature decreases. The evaporation of the more energetic atoms removes energy from the remaining li...

Superconductivity was discovered by the Dutch physicist Heike Kamerlingh Onnes in 1911 while investigating the electrical resistance of mercury at extremely low temperatures. He observed that the electrical resistance of mercury decreased abruptly to an immeasurably small value when its temperature was lowered below approximately 4.2 K. This sudden disappearance of measurable electrical resistance is called superconductivity . The materials that exhibit superconductivity below a characteristic temperature are known as superconductors . The temperature below which a material enters the superconducting state is called its critical temperature or transition temperature , denoted by \(T_c\). Definition: Superconductivity is the phenomenon in which a material exhibits zero DC electrical resistance and expels magnetic flux from its interior under appropriate conditions when cooled below its critical temperature. The critical temperature depends on th...

Liquid helium is a colourless, transparent, and highly volatile cryogenic liquid. Its density at the normal boiling point is approximately \(0.125\,\text{g cm}^{-3}\). One of the most remarkable properties of helium is that it does not solidify at atmospheric pressure, even when its temperature approaches absolute zero (0 K). This behaviour arises from the exceptionally weak interatomic forces and the large quantum-mechanical zero-point energy of helium atoms. Unlike most substances, helium must be subjected to sufficiently high pressure to undergo solidification. For helium, the minimum solidification pressure is approximately 25 bar at temperatures approaching absolute zero. Another important feature of liquid helium is that it exists in two distinct liquid phases: Liquid Helium I (He I): The normal liquid phase, which exists above the lambda-transition temperature. Liquid Helium II (He II): The superfluid phase, which exists below the lambda-t...

Maxwell's thermodynamic relations are four fundamental equations that establish relationships among temperature (\(T\)), pressure (\(P\)), volume (\(V\)), and entropy (\(S\)). These relations are obtained from the fundamental thermodynamic equations by applying the mathematical properties of exact differentials. According to the first law of thermodynamics, \[ dU=\delta Q-\delta W \] For a reversible process involving only pressure-volume work, \[ \delta Q_{\mathrm{rev}}=T\,dS \qquad\text{and}\qquad \delta W_{\mathrm{rev}}=P\,dV \] Therefore, \[ \boxed{dU=T\,dS-P\,dV} \] (1) Here, \(U\) is internal energy, \(T\) is absolute temperature, \(S\) is entropy, \(P\) is pressure, and \(V\) is volume. Let \(U\), \(S\), and \(V\) be differentiable functions of two independent variables \(x\) and \(y\). Their total differentials are \[ dU= \left(\frac{\partial U}{\partial x}\right)_y dx+ \left(\frac{\partial U}{\partial y}\right)_x dy \] \[ ...