Answer to Q.16
Assuming no chemical reaction inside the tank, the following conservation rule holds
No. of moles accumulated inside the tank = No. of moles IN – number. of moles OUT |
(1) |
|
(2) |
Assuming the temperature to be constant throughout the process T1 = T = T2 , and V and R being the contant quantities, eq. (2) can be re-written as
|
(3) |
Using the Taylor series expansion of a function of two variables, as following:
|
(4) |
On 
, we obtain
|
(5) |
Similarly using eq. (4) on 
, we obtain
|
(6) |
Now, using eqs.(5) and (6) on eq.(3), we obtain
|
(7) |
At steady state, eq. (7) takes the form,
|
(8) |
Substracting eq.(8) from eq.(7), we obtain
|
(9) |
Expressing them into deviation variable form,
|
(9) |
Where
|
(10)
(11)
(12) |
Taking Laplace Transform of the eq.(9) and rearranging , we obtain
|
(13) |
Hence the time constant of the system is
|
(14) |
Static gains of the system are
|
(15) |
And
|
(16) |
The block diagram is given as follows:
