Condensate fraction and momentum distribution in the ground state of liquid 4He

Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no regular arrangement (no fixed shape); in a gas, they are far apart with no regular arrangement (no fixed shape). Particles in a solid vibrate about fixed positions (cannot flow) and do not generally move in relation to one another; in a liquid, they move past each other (can flow) but remain in essentially constant contact; in a gas, they move...

A pressure-composition phase diagram explicitly describes the behavior of an ideal solution of two volatile liquids under varying pressures and compositions. A pressure-composition diagram has two main curves. The bubble point curve represents the plot of pressure versus liquid mole fraction. It indicates the pressure at which the first bubble of vapor forms from the liquid phase as the system pressure decreases.The dew point curve is the pressure versus vapor mole fraction. It indicates the...

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...

The internal energy of a substance—the total kinetic energy of all its molecules and the potential energy of their associated forces—depends on the strength of the intermolecular forces in the condensed phases and the pressure exerted on the substance. The internal energy of a substance is the highest in the gaseous state, the lowest in the solid state, and intermediate in the liquid state. Phase transitions are caused by changes in physical conditions, such as temperature and pressure, that...

The equilibrium vapor pressure of a liquid is the pressure exerted by its gaseous phase when vaporization and condensation are occurring at equal rates: Dissolving a nonvolatile substance in volatile liquid results in a lowering of the liquid’s vapor pressure. This phenomenon can be explained by considering the effect of added solute molecules on the liquid's vaporization and condensation processes. To vaporize, solvent molecules must be present at the surface of the solution. The presence of...

The number of independent ways a gas molecule can move along straight line, rotate, and vibrate is called its degrees of freedom. Supposing d represents the number of degrees of freedom of an ideal gas, the molar heat capacity at constant volume of an ideal gas in terms of d is