Phase change enthalpy calculations

For non-pure materials, when the phase change temperature is not constant, the phase change enthalpy can be calculated using the following expression, which includes the temperature change (between Tmi and 7m2) during phase change ... 

Section 14.1 examines the liquid and solid states. Section 14.2 discusses changes of phase and concepts related to systems with two phases in contact, such as vapor pressure. In Section 14.3, the measurement of quantities of heat added to or removed from a system is introduced, and the energies involved in phase changes are calculated. Section 14.4 deals with the enthalpies involved in chemical reactions. 

If a phase change occurs in the process stream for which heat duties are being calculated, it is best to perform a flash calculation and determine the heat loss or gain by the change in enthalpy. For a quick hand approximation it is possible to calculate sensible heat for both the gas and liquid phases of each component. The sum of all the latent and sen -i-ble heats is the approximate total heat duty. 

Tlic heat duty is best calculated with a process simulation program hi will account for phase changes as the fluid passes throiigli ilic ctioke. It will balance the enthalpies and accurately predict the change m tcnipcrature across the choke. Heat duty should be checked for vanoits combinations of inlet temperature, pressure, flow rate, and outlet temper ature and pressure, so as to determine the most critical combination. 

Enthalpy-concentration diagrams greatly facilitate the calculation of energy balances involving concentration and phase changes this is illustrated in Example 3.6. 

Calculate and add the enthalpy from any reaction or phase change and add to the stream enthalpies. 

These energies relate to bond rearrangement in gaseous molecules, but calculations are often performed for reactions of condensed phases, by combining the enthalpies of vaporization, sublimation, etc. We can calculate a value without further correction if a crude value of AHr is sufficient, or we do not know the enthalpies of phase changes. 

The Third Law of Thermodynamics postulates that the entropy of a perfect crystal is zero at 0 K. Given the heat capacity and the enthalpies of phase changes, Eq. (12-3) allows the calculation of the standard absolute entropy of a substance, S° = AS for the increase in temperature from 0 K to 298 K. Some absolute entropies for substances in thermodynamic standard states are listed in Table 12-1. 

Equation (16-2) allows the calculations of changes in the entropy of a substance, specifically by measuring the heat capacities at different temperatures and the enthalpies of phase changes. If the absolute value of the entropy were known at any one temperature, the measurements of changes in entropy in going from that temperature to another temperature would allow the determination of the absolute value of the entropy at the other temperature. The third law of thermodynamics provides the basis for establishing absolute entropies. The law states that the entropy of any perfect crystal is zero (0) at the temperature of absolute zero (OK or -273.15°C). This is understandable in terms of the molecular interpretation of entropy. In a perfect crystal, every atom is fixed in position, and, at absolute zero, every form of internal energy (such as atomic vibrations) has its lowest possible value. 

The enthalpy change associated with a chemical reaction or phase change at constant pressure and temperature can be calculated from the enthalpy of each species involved in the process. When species A undergoes the phase transformation from a to p,... 

The heat of reaction method may be slightly easier when only one reaction occurs and the heal of reaction is known. When this method is used, the specific enthalpy of each species in every feed or product stream is calculated by choosing a process path from the reference state to the process stale, calculating AH for each heating and cooling step and each phase change in the path, and summing the enthalpies for the steps. When specific enthalpies have been calculated for all species in all of their inlet and outlet states, AH for a continuous process is calculated as... 

To calculate the change in enthalpy (f/j - Jf j) when the reacting fluid is heated without phase change from its entrance temperature 2(0 to a temperature T, we use Equation (8 19) to write... 

Calculating the enthalpy when phase changes are involved... 

Calculate enthalpy (and internal energy) changes (excluding phase changes) from heat capacity equations, graphs and charts, tables, and computer data bases given the initial and final states of the material. 

We are now equipped to include in the calculation of ah enthalpy change the occurrence of a phase change. Because enthalpy is a state variable, any arbitary path from the initial to the final state will suffice for the actual computation. Simply choose the simplest possible path. 

EXAMPLE 4.18 Calculation of Enthalpy Change Including a Phase Change... 

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