Constant-pressure conditions heat capacity

Two common experimental paths for heat measurement are conditions of constant volume (qv) or constant pressure (qP). These conditions lead to the corresponding constant-volume (Cv) or constant-pressure (CP) heat capacities... 

Z1 is inlet vapor compressibility factor Fk is ratio of specific heat ratio of vapor to air, see Eq. (16) XT is control valve pressure drop ratio for air at sonic flow k is specific heat ratio of vapor at inlet conditions Cp is vapor (constant pressure) molar heat capacity at inlet conditions, in btu/lb mole- F. 

For pure substances, the heat capacity is often expressed per mole or per gram of substance. The molar heat capacity at constant pressure (symbol j ) is the quantity of heat required to raise the temperature of one mole of a substance by one degree under the condition of constant pressure. The constant-pressure specific heat capacity (symbol, Cp), sometimes called the specific heat is the quantity of heat required to change the temperature of one gram of a substance by one degree at constant pressure. Here are the values for water at 25 °C. 

The expression for heat capacity brings out the fact that it is an indefinite quantity even when mass is specified, since 8q is so. This is no longer the case when certain conditions, particularly constant volume or constant pressure conditions, are specified. The heat capacity then becomes a definite quantity as a consequence of 8q becoming a definite quantity. 

Now let the constant pressure condition be considered. The heat capacity at constant pressure, Cp, is represented by... 

When an explosive is initiated either to burning or detonation, its energy is released in the form of heat. The liberation of heat under adiabatic conditions is called the heat of explosion, denoted by the letter Q. The heat of explosion provides information about the work capacity of the explosive, where the effective propellants and secondary explosives generally have high values of Q. For propellants burning in the chamber of a gun, and secondary explosives in detonating devices, the heat of explosion is conventionally expressed in terms of constant volume conditions Qv. For rocket propellants burning in the combustion chamber of a rocket motor under conditions of free expansion to the atmosphere, it is conventional to employ constant pressure conditions. In this case, the heat of explosion is expressed as Qp. 

The enthalpy change, dH = T dS + V dp, can be described as dH = dq - -V dp, and for a constant-pressure process, c/p = 0, we have dH = dqp. For a finite state change at constant pressure, qp = AH, that is, the heat transferred is equal to the enthalpy change of the system. This relation is the basis of constant pressure calorimetry, the constant-pressure heat capacity being Cp = dqldT)p. The relationship qp = AH is valid only in the absence of external work, w. When the system does external work, the first law must include dw. Then, the heat transferred to the system under constant-pressure conditions is qp = AH -f w. Thus, if a given chemical reaction has an enthalpy change of -50 kJ mol and does 100 kJ mol" of electrical work, the heat transferred to the system is —50 + 100 = 50 kJ mol". ... 

The comments regarding units on Cy also apply to Cp (that is, you should keep track of whether a specific amount, in units of grams or moles, is specified or if it is actually part of the calculation). We can also define a molar heat capacity Cp for a process that occurs under constant pressure conditions. 

Liquid Heat Capacity The two commonly used liqmd heat capacities are either at constant pressure or at saturated conditions. There is negligible difference between them for most compounds up to a reduced temperature (temperature/critical temperature) of 0.7. Liquid heat capacity increases with increasing temperature, although a minimum occurs near the triple point for many compounds. 

The specific heat of a substance must always be defined relatively to a particular set of conditions under which heat is imparted, and it is here that the fluid analogy is very liable to lead to error. The number of heat units required to produce unit rise of temperature in a body depends in fact on the manner in which the heat is communicated. In particular, it is different according as the volume or the pressure is kept constant during the rise of temperature, and we have to distinguish between specific heats (and also heat capacities) at constant volume and those at constant pressure, as well as other kinds to be considered later. 

As explained in Section 6.5, the heat capacity of a substance is the constant of proportionality between the heat supplied to a substance and the temperature rise that results (q = CAT). However, the rise in temperature and therefore the heat capacity depend on the conditions under which the heating takes place because, at constant pressure, some of the heat is used to do expansion work rather than to raise the temperature of the system. We need to refine our definition of heat capacity. 

For one mole of an ideal gas, dH = Cp dT + Md(f>, where Cp is the constant pressure heat capacity per mole. Now the adiabatic condition implies that... 

The equilibrium state is generated by minimizing the Gibbs free energy of the system at a given temperature and pressure. In [57], the method is described as the modified equilibrium constant approach. The reaction products are obtained from a data base that contains information on the enthalpy of formation, the heat capacity, the specific enthalpy, the specific entropy, and the specific volume of substances. The desired gaseous equation of state can be chosen. The conditions of the decomposition reaction are chosen by defining the value of a pair of variables (e.g., p and T, V and T). The requirements for input are ... 

A tubular flow reactor is used for the gas phase reaction, A => 2B, under adiabatic conditions with a constant pressure of 2 atm. Pure A is charged at 600 R. The heat of reaction is AHr = -2000 Btu/lbmol of A. Heat capacities are 20 and 15 Btu/(Ibmol)(R) for A and B and the specific rate is... 

Constant conduction heat pipes, 13 227 Constant failure rate, 13 167 Constant-field scaling, of FETs, 22 253, 254 Constant-modulus alloys, 17 101 Constant of proportionality, 14 237 Constant pressure heat capacity, 24 656 Constant rate drying, 9 103-105 Constant rate period, 9 97 23 66-67 Constant retard ratio (CRR) mode, 24 103 Constant slope condition, 24 136-137 Constant stress test, 13 472 19 583 Constant-voltage scaling, of FETs, 22 253 Constant volume heat capacity, 24 656 Constant volume sampling system (CVS), 10 33... 

The physical properties of solvents greatly influence the choice of solvent for a particular application. The solvent should be liquid under the temperature and pressure conditions at which it is employed. Its thermodynamic properties, such as the density and vapor pressure, temperature and pressure coefficients, as well as the heat capacity and surface tension, and transport properties, such as viscosity, diffusion coefficient, and thermal conductivity, also need to be considered. Electrical, optical, and magnetic properties, such as the dipole moment, dielectric constant, refractive index, magnetic susceptibility, and electrical conductance are relevant, too. Furthermore, molecular... 

Under isentropic conditions and with constant heat capacities, the pressure-volume relation is... 

Enthalpy-Temperature Relation and Heat Capacity When heal is adsorbed by a substance, under conditions such that no chemical reaction or slate transition occur and only pressure-volume work is done, the temperature. T, rises and the ratio of the heat adsorbed, over the differential temperature increase, is by definition the heat capacity. For a process at constant pressure (following Equation (2)). this ratio is equal to the partial derivative of the enthalpy, and it is called the hear capacity at constant pressure. C,. (usually in calories/degree-mole) ... 

A catalytic hydrogenation is performed at constant pressure in a semi-batch reactor. The reaction temperature is 80 °C. Under these conditions, the reaction rate is lOmmolT s-1 and the reaction may be considered to follow a zero-order rate law. The enthalpy of the reaction is 540 kj moT1. The charge volume is 5 m3 and the heat exchange area of the reactor 10 m2. The specific heat capacity of water is 4.2kJkg 1K 1. 

The transitions between phases discussed in Section 10.1 are classed as first-order transitions. Ehrenfest [25] pointed out the possibility of higher-order transitions, so that second-order transitions would be those transitions for which both the Gibbs energy and its first partial derivatives would be continuous at a transition point, but the second partial derivatives would be discontinuous. Under such conditions the entropy and volume would be continuous. However, the heat capacity at constant pressure, the coefficient of expansion, and the coefficient of compressibility would be discontinuous. If we consider two systems, on either side of the transition point but infinitesimally close to it, then the molar entropies of the two systems must be equal. Also, the change of the molar entropies must be the same for a change of temperature or pressure. If we designate the two systems by a prime and a double prime, we have... 

Duration of a cycle of HHP operation is defined as time required for reaction hydrogenation/dehydrogenation in pair hydride system. This time determines heat capacity of HHP. Duration of a cycle depends on kinetics of hydrogenation reactions, a heat transfer between the heated up and cooling environment, heat conductivities of hydride beds. Rates of reactions are proportional to a difference of dynamic pressure of hydrogen in sorbers of HHP and to constants of chemical reaction of hydrogenation. The relation of dynamic pressure is adjusted by characteristics of a heat emission in beds of metal hydride particles (the heat emission of a hydride bed depends on its effective specific heat conductivity) and connected to total factor of a heat transfer of system a sorber-heat exchanger. The modified constant of speed, as function of temperature in isobaric process [1], can characterize kinetics of sorption reactions. In HHP it is not sense to use hydrides with a low kinetics of reactions. The basic condition of an acceptability of hydride for HHP is a condition of forward rate of chemical reactions in relation to rate of a heat transmission. 

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