$6.$A model for a CSTR is developed that contains two differential equations $($shown below$).$ In this

model, the following variables are used:

$C_A=$ concentration of A leaving reactor

$C_{Ai}=$ concentration of A entering reaction

$Q=$ heat rate

$F_i=$ flow rate

$V=$ volume

$UA=$ heat transfer coefficient $x$ heat transfer area

$=$ density

$c_p=$ heat capacity

$E_A=$ activation energy

$k^0=$ pre$-$exponential factor

$T_i,T=$ inlet temperature and exit temperature

$R=$ ideal gas constant

$\frac{d{C}_A}{dt}=\frac{F_i}{V}(C_{Ai}-C_A)-k$exp$(\frac{-E_A}{RT})C_A$

$\frac{dT}{dt}=UA(T-T_i)+\frac{Q}{V{c}_P}$

For a state$-$space model:

a$)$ List the state variables:

b$)$ List the input variables: