Page 225 - Modelling in Transport Phenomena A Conceptual Approach

7.5. CONSERVATION OF ENERGY 205

Solution
a) System: Contents of the tank

Assumptions
1. Properties of the tank contents are uniform, ie., Hout = Hsys.

2. Heat transfer between the system and its surroundings is almost zero. Note
that the insulation around the tank does not necessarily imply that Qint = 0.
Since the tank wall is in the surroundings, there will be heat transfer between
the tank wall and air remaining in the tank during the evacuation process.
Heat transfer may be considered negligible when (i) the mass of the wall is
small, (ii) process takes place rapidly (remember that heat transfer is a slow
process).
Analysis

Since nin = nint = 0 and there is no chemical reaction, Eq. (7.3-2) reduces to

Integration of Eq. (1) yields
nsYs = no - 12t (2)

where no is the number of moles of air initially present in the tank, i.e.,

no=-- POV - (7)(0*5) = 130.3mol
RT, (8.314 x 10-5)(50 + 273)
On the other hand, the inventory rate equation for energy, Eq. (7.5-5), takes the
form

Substitution of Eqs. (1) and (2) into Eq. (3) gives
-
fays
- 12 (flout - Us,,) = (no - 12 t) - (4)
I
dt
Since H = U+Pv = O+RT, the use of the first assumption enables us to express
the left-hand side of Eq. (4) as