Page 180 - Modelling in Transport Phenomena A Conceptual Approach

160 CHAPTER 6. STEADY-STATE MACROSCOPIC BALANCES

Solution

Assumptions

1. Ideal gas behavior.

2. Changes in kinetic and potential energies are negligible.

3. Pressure drop in the heat exchanger aS negligible.

Analysis

System: Gas stream in the heat exchanger
Since nint = 0 and there is no chemical recsction, Eq. (6.2-3) reduces to

ni, = nmt = n

Therefore, Eq. (6.3-19) becomes

where Qint = Q;,t/n, Ti, = 1073K, and Tout = 623K.
The molar heat capacity of the gas stream, 6p, can be calculated by multiplying
the mole fraction of each component by the respective heat capacity and adding
them together, i.e.,
3
C'p = xi (u; + biT + ciT2 + 4T3)
i=l
= 27.431 + 0.931 x T + 0.009 x T2 - 0.902 x lo-' T3 (4)
Substitution of Eq. (4) into Eq. (3) and integration gives

Qint = - 15,662 J/mol

The minus sign indicates that heat must be removed jbm the gas stream.