Internal enthalpy

Table 2.3 lists the molar internal enthalpies of black powder reaction products such as CO2 where Cp values are the molar heat capacities of the products at constant pressure. Using these, it is possible to estimate the heat of reaction at a particular temperature by assuming two temperature values and summing up the internal enthalpies for the reaction products multiplied by their corresponding number of moles as in Table 2.4. 

Table 2.3 Molar internal enthalpies of reaction products Cp T — Tq) Tq = 25°C 300K.

Table 36. Molar internal enthalpies of reaction products c (T-T0) T0 = 25... 

G = Gibbs molar free energy S = molar entropy F = Helmholtz free molar energy H = molar enthalpy U = molar internal energy... 

References D. D. Wagman, et ah, The NBS Tables of Chemical Thermodynamic Properties, in J. Phys. Chem. Ref. Data, 11 2,1982 M. W. Chase, et ah, JANAF Thermochemical Tables, 3rd ed., American Chemical Society and the American Institute of Physics, 1986 (supplements to JANAF appear in J. Phys. Chem. Ref. Data) Thermodynamic Research Center, TRC Thermodynamic Tables, Texas A M University, College Station, Texas I. Barin and O. Knacke, Thermochemical Properties of Inorganic Substances, Springer-Verlag, Berlin, 1973 J. B. Pedley, R. D. Naylor, and S. P. Kirby, Thermochemical Data of Organic Compounds, 2nd ed.. Chapman and Hall, London, 1986 V. Majer and V. Svoboda, Enthalpies of Vaporization of Organic Compounds, International Union of Pure and Applied Chemistry, Chemical Data Series No. 32, Blackwell, Oxford, 1985. 

Equation (3.16) shows that the force required to stretch a sample can be broken into two contributions one that measures how the enthalpy of the sample changes with elongation and one which measures the same effect on entropy. The pressure of a system also reflects two parallel contributions, except that the coefficients are associated with volume changes. It will help to pursue the analogy with a gas a bit further. The internal energy of an ideal gas is independent of volume The molecules are noninteracting so it makes no difference how far apart they are. Therefore, for an ideal gas (3U/3V)j = 0 and the thermodynamic equation of state becomes... 

Enthalpy. Enthalpy is the thermodynamic property of a substance defined as the sum of its internal energy plus the quantity Pv//, where P = pressure of the substance, v = its specific volume, and J = the mechanical equivalent of heat. Enthalpy is also known as total heat and heat content. 

Base point (zero values) for enthalpy, internal energy, and entropy are 0 K for the ideal gas at 101.3 kPa (1 atm) pressure. 

Fig. 3. Enthalpy (bolded line) and internal energy of (-) water and ( " ) steam. To convert kj to kcal, divide by 4.184.

Hea.t Ca.pa.cities. The heat capacities of real gases are functions of temperature and pressure, and this functionaHty must be known to calculate other thermodynamic properties such as internal energy and enthalpy. The heat capacity in the ideal-gas state is different for each gas. Constant pressure heat capacities, (U, for the ideal-gas state are independent of pressure and depend only on temperature. An accurate temperature correlation is often an empirical equation of the form ... 

Cp = specific heat e = specific internal energy h = enthalpy k =therm conductivity p = pressure, s = specific entropy t = temperature T = absolute temperature u = specific internal energy [L = viscosity V = specific volume f = subscript denoting saturated hquid g = subscript denoting saturated vapor... 

Themodynamic State Functions In thermodynamics, the state functions include the internal energy, U enthalpy, H and Helmholtz and Gibbs free energies, A and G, respectively, defined as follows ... 

Note that under choked conditions, the exit velocity is V = V = c = V/cKTVM not V/cKT(/M, . Sonic velocity must be evaluated at the exit temperature. For air, with k = 1.4, the critical pressure ratio p /vo is 0.5285 and the critical temperature ratio T /Tq = 0.8333. Thus, for air discharging from 300 K, the temperature drops by 50 K (90 R). This large temperature decrease results from the conversion of internal energy into kinetic energy and is reversible. As the discharged jet decelerates in the external stagant gas, it recovers its initial enthalpy. 

Thermodynamic paths are necessary to evaluate the enthalpy (or internal energy) of the fluid phase and the internal energy of the stationary phase. For gas-phase processes at low and modest pressures, the enthalpy departure function for pressure changes can be ignored and a reference state for each pure component chosen to be ideal gas at temperature and a reference state for the stationarv phase (adsorbent plus adsorbate) chosen to be adsorbate-free solid at. Thus, for the gas phase we have... 

Turbine design Turbine tp Internal efficiency, % Exhaust enthalpy, Btu/lb A/i," Btu/lb Steam rate... 

The material balance table can be supplemented with temperatures, pressures, phases, and stream enthalpies (or internal energies). Utility flows and conditions should be added to the process information. 

For isentropic flow, the energy equation can be written as follows, noting that the addition of internal and flow energies can be written as the enthalpy (h) of the fluid ... 

AA is sometimes referred to as the change in work function. This equation simply states that energy will be available to do work only when the heat absorbed exceeds the increase in internal energy. For proeesses at constant temperature and pressure there will be a rise in the heat content (enthalpy) due both to a rise in the internal energy and to work done on expansion. This can be expressed as... 

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