Page 179 - Modelling in Transport Phenomena A Conceptual Approach

6.3. CONSERVATION OF ENERGY 159

6.3.1 Energy Equation Without Chemical Reaction
In the case of no chemical reaction, Eqs. (6.3-9) and (6.3-16) are used to determine
energy interactions. If kinetic and potential energy changes are negligible, then
these equations reduce to Eqs. (6.3-15) and (6.3-17), respectively. The use of the
energy equation requires the enthalpy change to be known or calculated. For some
substances, such as steam and ammonia, enthalpy values are either tabulated or
given in the form of a graph as a function of temperature and pressure. In that case
enthalpy changes can be determined easily. If enthalpy values are not tabulated,
then the determination of enthalpy depending on the values of temperature and
pressure in a given process are given below.

6.3.1.1 Constant pressure and no phase change

Since dP = 0, integration of &. (6.3-12) gives
fi = lve, (6.3-18)
T
dT
CP
in which fi is taken as zero at TTef. Substitution of Eq. (6.3-18) into Eq. (6.3-15)
gives

If Cp is independent of temperature, Eq. (6.3-19) reduces to
&neP(Tin - T'ef) &utep(Tat - TLf) + Qint + J@s = 0 (6.3-20)

Example 6.3 It is required to cool a gas composed of 75 mole % Nz, 15% C02 and
10% 02 from 800 "C to 350 "C. Determine the cooling duty of the heat exchanger
if the heat capacity expressions are in the form

ep(J/mol.K)=~+bT+~T~+dT~ [=] K
T
where the coeficients a, b, c and d are given by

Species a bx lo2 cx lo5 d x lo5
N2 28.882 - 0.1570 0.8075 - 2.8706

02 25.460 1.5192 - 0.7150 1.3108
COz 21.489 5.9768 -3.4987 7.4643