Page 228 - Modelling in Transport Phenomena A Conceptual Approach

208 CHAPTER 7. UNSTEADY-STATE MACROSCOPIC BALANCES

Substitution of the numerical values gives

(12)(8.314 x 10-5)(50 + 273)(5)
P=7- = 3.78 bar
0.5
The amount of heat supplied by the heating coils is determined from the inventory
rate equation for energy, Eq. (7.5-5). Simplification of this equation is

Since the process is isothermal, UsYs wmains constant. Substituting Eq. (17) into
Eq. (21) and using the fact that Hout = Hsys yields

Qint = 12 (kys - Usys) = 12'RTsys
= (12)(8.314)(50 + 273) = 32,225 J/min
Therefore, the amount of heat transfew-ed is

Qint = Qint t = (32,225)(5) = 161) 125 J

7.5.1 Unsteady-State Energy Balance Around a
Continuous Stirred Tank Reactor
An unsteady-state energy balance in a continuous stirred tank reactor (CSTR)
follows the same line as the steady-state case given in Section 6.3.2.2. Using the
same assumptions, the resulting energy balance becomes

(7.5-10)
SYS
On the other hand, the macroscopic mole balance for species i, Eq. (7.2-5), is

(7.511)

Multiplication of Eq. (7.5-11) by &(T) and summation over all species gives

= [?&(T)%] (7.512)

SYS