TEST

YOURSELF

$($Answers$,$ p$.662)$

Consider the following set of equations:

$x_1+2x_2-x_3^2=0$

$5x_1-x_2^3+4=0$

$($a$)$ How many degrees of freedom does this system possess?

$($b$)$ Which choice of a design variable would lead to an easier procedure to solve for the state variables, $x_1$ or $x_3?$

$2.$ A liquid stream containing species $A,B,C,$ and $D$ enters a vaporizer $($flow rates $n_1,$dots, $n_{4}k\frac{g}{s}).$ Essentially all of the A$,25\%$ of the B$,$ and none of the D is vaporized. The C is distributed between the liquid and vapor products according to a known equilibrium relationship. How many degrees of freedom does this process possess?

$3.$ Consider the equations $($i$)5x-3y=7,($ii$)10x-3y-6z=14,$ and $($iii$)y=2z.$

$($a$)$ Try to solve this system of equations for $x,y,$ and $z,$ and explain why you can't do it$.$

$($b$)$ Prove that the set of equations has one degree of freedom, choose a design variable, specify a value for it$,$ and determine the corresponding state variable values.