Constant-volume

Except for gases, it is very difficult to detennine Cy. For a solid or liquid the pressure developed in keeping the volume constant when the temperature is changed by a significant amount would require a vessel so massive that most of the total heat capacity would be that of the container. It is much easier to measure the difference... 

Just as one may wish to specify the temperature in a molecular dynamics simulation, so may be desired to maintain the system at a constant pressure. This enables the behavior of the system to be explored as a function of the pressure, enabling one to study phenomer such as the onset of pressure-induced phase transitions. Many experimental measuremen are made under conditions of constant temperature and pressure, and so simulations in tl isothermal-isobaric ensemble are most directly relevant to experimental data. Certai structural rearrangements may be achieved more easily in an isobaric simulation than i a simulation at constant volume. Constant pressure conditions may also be importai when the number of particles in the system changes (as in some of the test particle methoc for calculating free energies and chemical potentials see Section 8.9). 

Fig. 3.23 The Gibbs ensemble Monte Carlo simulation method uses one box for each of the two plwses. Three types < move are permitted translations within either box volume changes (keeping the total volume constant) and transfer a particle from one box to the other.

Naphthaleneamine is a dye intermediate and is used as the starting material in the manufacture of the rodenticide, Antii (8), l-naphthalenethiourea/5 %< < -4/, which is prepared by heating a mixture of 1-naphthylamine hydrochloride, NH SCN, and a large amount water for 14—16 h while keeping its volume constant by a dding an additional amount of water, to give a 97% yield. Its LD q is 600 mg in squirrels (46). 

Hydroxy-1,2,3,4-tetrahydrocrysene (2) A mixture of 4-keto-1,2 3 4-tetrahydrocrysene 1 (2 75 g, 11 mmol) and aluminium isopropoxide (8 2 g, 40 mmol) in PhMe (25 mL) was refluxed for 1 h After cooling, iPrOH (25 mL) was added and the formed acetone was distilled slowly maintaining the volume constant by addition of iPrOH After all acelone was distilled, the solution was acidified with 0% H2SO4 The separated toluene solution was evaporated to gwe 2 1 g of 2 (76%), mp 156-158 C... 

Dehumidification only Decreased moisture content and specific volume constant dry-bulb temperature decreased wet-bulb temperature, specific enthalpy, and % saturation Not practical... 

In an all-air system, the indoor temperature can be controlled either by a constant air volume (CAV) system, which varies the temperature of the air but keeps the volume constant, or by a variable air volume (VAV) system, which maintains a constant temperature and varies the volume of the air supplied to internal spaces. 

With the exception of piston-type pumps, most of the common positive-displacement pumps utilize rotating elements to provide a constant-volume, constant-pressure output. As a result, these pumps can be monitored with the following parameters hydraulic instability, passing frequencies, and running speed. 

Gas thermometers that employ equation (1.10) can be constructed to measure either pressure while holding the volume constant (the most common procedure) or volume while holding the pressure constant. The (pV) product can be extrapolated to zero p. but this is an involved procedure. More often, an equation of state or experimental gas imperfection data are used to correct to ideal behavior. Helium is the usual choice of gas for a gas thermometer, since gas imperfection is small, although other gases such as hydrogen have also been used. In any event, measurement of absolute temperature with a gas thermometer is a difficult procedure. Instead, temperatures are usually referred to a secondary scale known as the International Temperature Scale or ITS-90. 

The ODEs governing the unsteady CSTR are obtained by adding accumulation terms to Equations (4.1). The simulation holds the volume constant, and... 

Solution The component balance for component A (styrene) for a first-order reaction in a constant-volume, constant-density CSTR is... 

The general case treats time-dependent volumes, flow rates, and inlet concentrations. The general case must be used to for most startup and shutdown transients, but some dynamic behavior can be effectively analyzed with the constant-volume, constant-flow rate version of Equation (14.2) ... 

Example 14.1 Consider a first-order reaction occurring in a CSTR where the inlet concentration of reactant has been held constant at uq for f < 0. At time f = 0, the inlet concentration is changed to Up Find the outlet response for t > 0 assuming isothermal, constant-volume, constant-density operation. 

The reactor operates at constant volume, constant density, constant flow rate, and isothermally. The only difference between the two products is the addition of component C to the feed when Product II is made. 

These equations of motion can be integrated by many standard ensembles constant energy, constant volume, constant temperature and constant pressure. More complex forms of the extended Lagrangian are possible and readers are referred to Ref. [17] for a Lagrangian that allows intermolecular charge transfer. 

The expression in Equation (3.6) is really a.partial differential the value of U depends on both T and V, the values of which are connected via Equation (1.13). Accordingly, we need to keep one variable constant if we are unambiguously to attribute changes in Cy to the other. The two subscript V terms tell us C is measured while maintaining the volume constant. When the derivative is a partial derivative, it is usual to write... 

We call Cy the heat capacity at constant volume . With the volume constant, we measure Cy without performing any work (so w = 0), so we can write Equation (3.6) differently with dq rather than dU. 

M. Ducros, H. Tachoire. Calorimetrie de Combustion a Volume Constant dans TOxygene (lere Partie). L Actualite Chim. 1978, 9. 

MSE.2. 1. Prigogine et S. Raulier, Chaleur specifique a volume constant des liquides mono-atomiques (Constant volume specific heat of monoatomic liquids), Physica 396 04 (1942). 

Make calculations on unknown gases based on a determined temperature-volume constant. 

Observing and Inferring Why was it necessary to keep the volume constant during this experiment ... 

The request that no ND4 should be within the cube is represented by n = 0. The inter-centre distance increases here so fast with x that the behaviour of the system cannot be explained with ND4 clean cubes. Since the density of nucleation centres should not increase drastically on increasing x, we have either to reduce the clean volume with x, or to allow for some stray ND4 keeping the volume constant. The latter possibility is shown in Fig. 14. The open circles correspond to the values where n is increased by one when x is increased by 0.05, starting with n = 0 for x = 0.15. It should be noted that these points still correspond to Rb-rich areas. This can be seen in Fig. 14 where the minima of the curves indicate the average concentration x = n/32. The spoiling of the nucleation centres has, of course, to be paid with a lower local transition temperature, which is indeed observed in the real system. Going along with this procedure, we would obtain cluster sizes of about 100 formula units for D-RADP-25 and of 80 formula units for D-RADP-30, i.e. of about 2 nm in... 

Louis Gay-Lussac continued the ballooning exploits initiated by Charles, ascending to over 20,000 feet in a hydrogen balloon in the early 1800s. Gay-Lussac s law defines the relationship between the pressure and temperature of an ideal gas. If the temperature of the air in the syringe increases while keeping the volume constant, the gas particles speed up and make more collisions with the inside walls of the syringe barrel. As we have seen, an increase frequency in the number of collisions of the gas particles with a container s wall translates into an increase in pressure. Gay-Lussac s law says that pressure is directly... 

Preparation of Sodium Hydroxide from Sodium Carbonate. Dissolve 14 g of anhydrous sodium carbonate in 100 ml of water. Pour the solution into a 250-300-ml round-bottomed flask. Put pieces of broken chamotte crucible on the bottom of the flask (for what purpose ). Fasten the flask in a stand so that a small space remains between the gauze and the bottom of the flask. Heat the solution in the flask up to boiling and add 8-10 g of triturated calcium hydroxide (in small portions). Insert a funnel into the neck of the flask (for what purpose ) and boil the solution during one hour, adding water from time to time to keep the volume constant. After cooling, filter the solution and measure its volume and density. Use the density value to determine the percentage of sodium hydroxide in the solution. Hand in the alkali solution to the laboratory assistant. 

Finally, the diffusion of a chemical may be influenced by another diffusing compound or by the solvent. The latter effect is known as solute-solvent interaction it may become important when solute and solvent form an association that diffuses intact (e.g., by hydration). This may be less relevant for neutral organic compounds, but it plays a central role for diffusing ions. But even for noncharged particles the diffusivities of different chemicals may be coupled. The above example of the glycerol diffusing in water makes this evident in order to keep the volume constant, the diffusive fluxes of water and glycerol must be coupled. 

---