Specific enthalpy state

The specific enthalpy of a gas is calculated using the principle of corresponding states. The enthalpy of a gas mixture is equal to the sum of the ideal gas enthalpy and a correction term ... 

If appropriate enthalpy data are unavailable, estimates can be obtained by first defining reference states for both solute and solvent. Often the most convenient reference states are crystalline solute and pure solvent at an arbitrarily chosen reference temperature. The reference temperature selected usually corresponds to that at which the heat of crystallization A/ of the solute is known. The heat of crystallization is approximately equal to the negative of the heat of solution. For example, if the heat of crystallization is known at then reasonable reference conditions would be the solute as a soUd and the solvent as a Uquid, both at The specific enthalpies then could be evaluated as... 

Use of equations of state to estimate specific enthalpy and density... 

For the vapour phase, the deviation of the specific enthalpy from the ideal state can be illustrated using the Redlich-Kwong equation, written in the form ... 

The rate constants (/c[and k]) and the stoichiometric coefficients (t and 1/ ) are all assumed to be known. Likewise, the reaction rate functions Rt for each reaction step, the equation of state for the density p, the specific enthalpies for the chemical species Hk, as well as the expression for the specific heat of the fluid cp must be provided. In most commercial CFD codes, user interfaces are available to simplify the input of these data. For example, for a combusting system with gas-phase chemistry, chemical databases such as Chemkin-II greatly simplify the process of supplying the detailed chemistry to a CFD code. 

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 ... 

Throughout the preceding discussion, simplified expressions of stream-specific enthalpy as a function of temperature are used. They have to be updated during process operation to consider changes in steady-state compositions. 

The specific enthalpy and entropy of the conformation transition of proteins from the native to denatured state has an upper limit that is reached above 140°C and seems to be universal for all compact globular proteins (Figs. 4 and S). By enthalpy and entropy of conformational tran-... 

The FEHE achieves significant energy recovery. Hence, the energy flow Hr is of comparable magnitude to Hi, kr = Hr,s/Hi,s = 0(1), and the steady-state specific enthalpies ho and ho of the inlet and outlet streams are of comparable magnitude, ho,s/ho,s = 0(1). 

The specific enthalpy relative to the dead state, 8, is defined as (14, 19,24)... 

When the system is a homogeneous substance of constant composition, the phase rule indicates that fixing the values of two intensive properties establishes its state. The molar or specific enthalpy of a substance may therefore be expressed as a function of two other state variables. Arbitrarily selecting these asrtemperature and pressure, we write... 

This means that the partial specific enthalpy of NaOH at infinite dilution ( at xN.OH 0) is aibirarily set equal to zero at 68(T). The graphical interpretation that the diagram is constructed in such a way that a tangent drawn to the isotherm at xNaOH = 0 intersects the xn oh = 1 ordinate (not shown) at an entl of zero. The selection of ff ttOH as zero at 68(°F) automatically fixes the values the enthalpy of NaOH in all other states. 

Define the terms flow work, shaft work, specific internal energy, specific volume, and specific enthalpy. Write the energy balance for an open process system in terms of enthalpy and shaft work and state the conditions under which each of the five terms can be neglected. Given a description of an open process system, simplify the energy balance and solve it for whichever term is not specified in the process description. 

State why the actual values of U and / can never be known for a given species in a specified state (temperature, pressure, and phase) and define the concept of a reference state. Explain in your own terms the statement, The specific enthalpy of CO(g) at 100°C and 0,5 atm relative to CO(g) at 500°C and 1 atm is -12,141 J/mol. (Your explanation should involve a process in which carbon monoxide gas goes from one state to another.)... 

Given a description of any nonreactive process for which tabulated specific internal energies or specific enthalpies are available at all input and output states for all process species, (a) draw and completely label a flowchart, including Q and W (or Q and for an open system) if their values are either specified or called for in a problem statement (b) perform a degree-of-freedom analysis and (c) write the necessary equations (including the appropriately simplified energy balance) to determine all requested variables. 

A properly drawn and labeled flowchart is essential for the efficient solution of energy balance problems. When labeling the flowchart, be sure to include all of the information you wall need to determine the specific enthalpy of each stream component, including known temperatures and pressures. In addition, show states of aggregation of process materials when they... 

Fortunately, we never need to know the absolute values of H or // at specified states we only need to know AH and AH for specified changes of state, and we can determine these quantities experimentally. We may therefore arbitrarily choose a reference state tor a species and determine AH = 0 - Href for the transition from the reference state to a series of other states. If we set Href equal to zero, then H(= AH) for a specified state is the specific internal energy at that state relative to the reference state. The specific enthalpies at each state can then be calculated from the definition, H = U + PV, provided that the specific volume (V) of the species at the given temperature and pressure is known. 

YOURSELF be zero. Relative to this state, what is the specific enthalpy of liquid water at 75 C and 1 bar. ... 

The reference states may be chosen for computational convenience, since the choice has no effect on the calculated value of A//. You will later learn that Table B.8 lists specific enthalpies of nitrogen relative to N2(g, 25°C. 1 atm), which makes this state a convenient choice for nitrogen. There are no tabulated enthalpy data for acetone in the text, so we will choose one of the process stream conditions, Ac(l, 20°C, 5 atm), as the reference state for this species, which will enable us to set the corresponding H value equal to zero rather than having to calculate it. 

Since the liquid acetone leaving the system is at the reference state, we set its specific enthalpy equal to zero. 

To calculate the four unknown specific enthalpies in the table, we construct hypothetical process paths from the reference states to the states of the species in the process and evaluate AH for each path. This is the part of the calculation you have not yet learned to do. We will show you the calculation of Hi to illustrate the method, give the results of the other calculations, and go into detail about the required procedures in Sections 8.2-8.5. 

If more than one species is involved or if there are several input or output streams instead of just one of each, the procedure given in Section 8.1 should be followed choose reference states for each species, prepare and fill in a table of amounts and specific internal energies (closed system) or species flow rates and specific enthalpies (open system), and substitute the calculated values into the energy balance equation. The next example illustrates the procedure for a continuous heating process. 

The formulas and values of the unknown specific enthalpies are given below. Convince yourself that the formulas represent for the transitions from the reference states to the process states. 

The basis for the construction of the psychrometnc chart is the Gibbs phase rule (Section 6.3a). which states that specifying a certain number of the intensive variables (temperature, pressure, specific volume, specific enthalpy, component mass or mole fractions, etc.) of a system automatically fixes the value of the remaining intensive variables. Humid air contains one phase and two components, so that from Equation 6.2-1 the number of degrees of freedom is... 

In these equations n is the amount (mass or moles) of a species in one of its initial or final states in the process, h is the flow rate (mass or molar) of a species in a continuous stream entering or leaving the process, and 0 and H are respectively the specific internal energy and specific enthalpy of a species in a process state relative to a specified reference state for the same species. 

You can use the formulas given above to determine the specific enthalpy of any spedes in one state relative to that species in any other stale. For example, to calculate H for benzene vapor at temperature 300°C and 15 atm relative to solid benzene at a reference state of -20°C and 1 atm, you would carry out the following steps. 

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