The internal energy of a liquid

This force is positive since /(0 s d) 0, and F( d) = 0 since f(s) is an odd function. There is no force on the molecule unless it is within distance d of the surface, on one side or the oflier. The work to remove one molecule from the liquid is therefore 

Since K has the form a/V. (1.7) or (1.11), where the constant a (not to be confused with the capillary constant) is given by 

Here the term in the first bracket is the pressure within the fluid, that is 

The fundamental equations of van der Waals s theory (1.33) survive to this day as a necessary feature of what are now called mean-field 

In a planar liquid-gas surface in which the density is changing only in the z-direction, we can express the energy per molecule at height z by 

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We now derive an important expression for the internal energy of a liquid. Consider a system in the T, V, N ensemble and assume that the total potential energy of the interaction is pairwise additive, namely,... 

The internal energy of a system depends on many things chemical identity, sample size, temperature, pressure, physical state (gas, liquid, or solid), and so forth. What the internal energy does not depend on is the system s past history. It doesn t matter what the system s temperature or physical state was yesterday or an hour ago, and it doesn t matter how the chemicals were made. All that matters is the present condition of the system. Thus, internal energy is said to be... 

Joule s experiments on the free expansion of an ideal gas showed that the internal energy of such a system is a function of temperature alone. For a real gas, this is only approximately true. For condensed phases, which are effectively incompressible, the volume dependence on the change in internal energy is negligible. As a result, the internal energies of liquids and solids are also considered a function of temperature alone. For this reason, the internal energy of a system may loosely be referred to as the thermal energy . 

The internal energy of a system depends almost entirely on the chemical composition, state of aggregation (solid, liquid, or gas), and temperature of the system materials. It is independent of pressure for ideal gases and nearly independent of pressure for liquids and solids. If no temperature changes, phase changes, or chemical reactions occur in a closed system and if pressure changes are less than a few atmospheres, then MJ = 0. 

The internal energy of a solution is very closely related to the interactions between the molecules. The fact that the energy of mixing is zero, that is to say that the internal energy is unaffected by the mixing process, means that the interactions between the different molecules in the solution must be equal to the arithmetic mean of those between the molecules in the two pure liquids cf. chap. XXIV 4). 

In 1933, Hildebrand related the internal energy of a mole of non-polar liquid to the radial distribution function and pair potentials... 

The thermal energy of a liquid particle is defined by the internal energy density, which depends on parameters of local thermodynamic condition. According to the first law of thermodynamics. 

If the work of liquid explosives to the surrounding is done through the adiabatic expansion of high-temperamre and high-pressure gas products, according to the first law of thermodynamics, the decrease in the internal energy of a system is equal to the total released heat and work done to the surroundings. 

If we assume that the internal energy of a crystal in the solid and the liquid states is determined primarily by the binding energy and if we substitute U = V3 U J.j, we find that the conditions sufficient for the validity of the addltlvlly rule can be derived easily from Eq. (4) ... 

The surface energy of a liquid or solid arises from the unsatisfied bonds of the surface atoms. Since these atoms are more strongly bound by internal forces, work (surface free... 

In contrast, the internal temperature of a material does not change as the material undergoes a change of state. (Thus, its internal energy does not change at that point). Therefore, for a chcuige of state between solid and liquid, we would have ... 

The dissolved 02 and N2 are allowed to escape from the liquid phase, decompressed to a negligibly small pressure (p = 0), and finally compressed as an ideal gas mixture to the standard state pressure. The (02 + N2) mixture is treated as if it were pure 02 (the amount of N2 is very small and the internal energies of solution of 02 and N2 are very similar [55]) and the energy changes associated with steps 12 and 13 are... 

Gross calorific value (gross heat of combustion at constant volume) heat produced by combustion of a unit quantity of a solid or liquid fuel when burned at constant volume in an oxygen bomb calorimeter under specified conditions, with the resulting water condensed to a liquid not applied to gaseous fuels and applies to a volatile liquid fuel only if it is suitably contained during the measurement closely related to the internal energy of combustion for the same reaction at constant standard temperature and pressure. 

The change in the energy of immersion as a function of the precoverage pjpa is shown in Figure 11.8. In contrast to the behaviour of kaolinite, a relative pressure of c. 0.75 was required in order to reduce the immersion energy to its final constant level of 12.6 J g-1. By assuming that this corresponds to the immersion of particles coated with liquid water, we obtain a value of 105 m2 g 1 for the external area (since the surface internal energy of pure liquid water is 0.119 J m 2). 

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