Liquids heat capacity ratios

The reactor system in a pilot plant contains stock tanks that are 24 in in diameter and 36 in high. A relief system must be designed to protect the vessel in the event of fire exposure. The vessel contains a flammable polymer material. What rupture disc diameter is required to relieve the vessel properly Assume a discharge pressure of 10 psig. The molecular weight of the liquid is 162.2, its boiling point is 673°R, the heat of vaporization is 92.4 Btu/lb, and the heat capacity ratio of the vapor is 1.30. 

Next, we eliminate K from Equation (g) by replacing K with a function of P so that n becomes a function of P. The performance ratio (with constant liquid heat capacity at 347°F) is defined as... 

To look into this further, we show in Fig 4, in part (a), the behavior of the heat capacity of polypropylene, in units of J/K.(mol of -CH2-CH2(CH3)- repeat units) (35,36) in comparison with that of the molecular liquid 3-methyl pentane (37) (divided by 2 to have the same mass basis as the polymer repeat unit) (38). It is seen that the liquid heat capacity of the hexane isomer (x 0.S) falls not much above the natural extrapolation to lower temperatures of the heat capacity per repeat unit of the polymer. This implies that the main effect of polymerization, as far as the change in heat capacity at Tg is concerned, is to postpone the glass transition until a much higher vibrational heat capacity has been excited. This not only reduces the value of ACp but has a disproportionate effect on the ratio Cp,i/Cp,g at Tg. This happens despite a lower glassy heat capacity in the polymer than in the molecular liquid at the same temperature. The latter effect is a direct consequence of the lower Debye temperature (and lower vibrational anharmonicity) at a given temperature for in-chain interactions in the polymer than for intermolecular interactions in the same mass of molecules. 

For each relief case, list following information relief load (vapor in Ib/hr, liquid in gpm), relief conditions (pressure and temperature), relief fluid physical properties (for vapor, provide molecular weight (M), compressibility factor (2), ideal gas heat capacity ratio (k) for liquid, provide specific gravity, viscosity (in centipoise))... 

The heat capacity of a subshince is defined as the quantity of heat required to raise tlie temperature of tliat substance by 1° the specific heat capacity is the heat capacity on a unit mass basis. The term specific heat is frequently used in place of specific heat capacity. This is not strictly correct because traditionally, specific heal luis been defined as tlie ratio of the heat capacity of a substance to the heat capacity of water. However, since the specific heat of water is approxinuitely 1 cal/g-°C or 1 Btiiyib-°F, the term specific heal luis come to imply heat capacity per unit mass. For gases, tlie addition of heat to cause tlie 1° tempcniture rise m iy be accomplished either at constant pressure or at constant volume. Since the mnounts of heat necessary are different for tlie two cases, subscripts are used to identify which heat capacity is being used - Cp for constant pressure or Cv for constant volume. Tliis distinction does not have to be made for liquids and solids since tliere is little difference between tlie two. Values of heat capacity arc available in the literature. ... 

For a thermometer to react rapidly to changes in the surrounding temperature, the magnitude of the time constant should be small. This involves a high surface area to liquid mass ratio, a high heat transfer coefficient and a low specific heat capacity for the bulb liquid. With a large time constant, the instrument will respond slowly and may result in a dynamic measurement error. 

Results in Table I illustrate some of the strengths and weaknesses of the ST2, MCY and CF models. All models, except the MCY model, accurately predict the internal energy, -U. Constant volume heat capacity, Cv, is accurately predicted by each model for which data is available. The ST2 and MCY models overpredict the dipole moment, u, while the CF model prediction is identical with the value for bulk water. The ratio PV/NkT at a liquid density of unity is tremendously in error for the MCY model, while both the ST2 and CF models predictions are reasonable. This large error using the MCY model suggests that it will not, in general, simulate thermodynamic properties of water accurately (29). Values of the self-diffusion coefficient, D, for each of the water models except the CF model agree fairly well with the value for bulk water. 

Cp - Cy equals [P + (dU/dV)T](dV/dT)p. The dUldV term is often referred to as the internal pressure and is large for liquids and solids (See Internal Pressure). Since ideal gases do not have internal pressure, Cp - Cy = nP for ideal gases. The ratio of the heat capacities, Cp/Cy, is commonly symbolized by y. 

Heat transfers are measured by using a calibrated calorimeter. The heat capacity of an object is the ratio of the heat supplied to the temperature rise produced. Molar heat capacities of liquids are generally greater than those of the solid phase of the same substance. Molar heat capacities increase as molecular complexity increases. 

The initiation step could also be positively affected by the above-mentioned transport properties, as the efficiency factor f assumes higher values with respect to conventional liquid solvents due to the diminished solvent cage effect One further advantage is constituted by the tunability of the compressibility-dependent properties such as density, dielectric constant, heat capacity, and viscosity, all of which offer additional possibilities to modify the performances of the polymerization process. This aspect could be particularly relevant in the case of copolymerization reactions, where the reactivity ratios of the two monomers, and ultimately the final composition of the copolymer, could be controlled by modifying the pressure of the reaction system. 

In these equations, e represents the relative volume increase due to the feed and Rh the ratio of the heat capacities of both liquid phases. By representing the reactivity number as a function of the exothermicity number (Figure 5.3), different regions are obtained. The region where runaway occurs is clearly delimited by a boundary line. Above this region, for a high reactivity, the reaction is operated in the QFS conditions (Quick onset, Fair conversion and Smooth temperature profile) and leads to a fast reaction with low accumulation and easy temperature control (see Section 7.6). 

Cryogen Name Vapor Pressure, MPa Gas Density, g/1 Liquid/Gas Expansion Ratio Heat Capacity Cp, J/(kg K) Heat Capacity Cv, J/(kg K) Thermal Conductivity x 10-2 w/(m-K) Viscosity Pa-sec x 105 (cP) Solubility in Water, 0°C, v/v... 

An explicit expression relating kinetic fragility to thermodynamic behavior of supercooled liquids was accomplished for the first time by Mohanty and coworkers [55,56] and independently by Speedy [54], These authors derived an expression for the steepness parameter, a measure of kinetic fragility, from the temperature variation of the relation time or viscosity, with the ratio of excess entropy and heat capacity changes at the glass transition temperature [54-56]. A detailed description of this work will be provided later in the review chapter. 

In a countercurrent packed column, n-butanol flows down at the rate of 0.25 kg/m2 s and is cooled from 330 to 295 K. Air at 290 K, initially free of n-butanol vapour, is passed up the column at the rate of 0.7 m3/m2 s. Calculate the required height of tower and the condition of the exit air. Data Mass transfer coefficient per unit volume, hDa = 0.1 s 1. Psychrometric ratio, (h/hDpAs) = 2.34. Heat transfer coefficients, hL = 3hG. Latent heat of vaporisation of n-butanol, A = 590 kJ/kg. Specific heat capacity of liquid n-butanol, Cl = 2.5 kJ/kg K. Humid heat of gas , s = 1.05 kJ/kg K. 

From Eqs. (8.60) and (8.61) it is possible to derive the foam expansion ratio from the heat capacity of the foam and the heat capacities of its constituents, liquid and gas phases... 

In Chapter 8, along with tables of measured thermophysical data, we saw some fairly simple techniques for estimating these values when experimental results are not available. Among these techniques were Kopp s Rule for the heat capacity of both liquids and solids, and Trouton s ratio for latent heats of fusion and vaporization, along with Kistiakowski s temperature correction for the latter. 

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