A chemical synthesis apparatus monitors two reactant volumes, A_k and B_k (in liters), acr… — GMAT

A chemical synthesis apparatus monitors two reactant volumes, $A_k$ and $B_k$ (in liters), across three sequential stages ( $k = 1, 2, 3$ ). At the initial state ( $k = 0$ ), the apparatus contains $A_0 = 100$ liters and $B_0 = 40$ liters.

For each subsequent stage

k

, the volumes are updated sequentially according to the following state transition equations:

A_k = A_{k-1} - B_{k-1} + 40

B_k = B_{k-1} + \frac{A_{k-1}}{2} - 20

Based on the process above, which of the following statements regarding the reactant volumes are correct? Select all that apply.

At the end of Stage 2 ( $k = 2$ ), the volume of reactant A ( $A_2$ ) is 70 liters.Cevap
At the end of Stage 3 ( $k = 3$ ), the volume of reactant B ( $B_3$ ) is 115 liters.Cevap
C
At the end of Stage 2 ( $k = 2$ ), the volume of reactant B ( $B_2$ ) is 70 liters.
D
At the end of Stage 3 ( $k = 3$ ), the volume of reactant A ( $A_3$ ) is 70 liters.
E
At the end of Stage 1 ( $k = 1$ ), the volume of reactant B ( $B_1$ ) is 100 liters.

Cevap

The correct statements are that at the end of Stage 2, the volume of reactant A is 70 liters, and at the end of Stage 3, the volume of reactant B is 115 liters.

Evaluating the process iteratively stage by stage shows that at

k=2

A_2 = 70

liters, and at

k=3

B_3 = 115

liters. Both of these statements match the calculated values.

Adım Adım Çözüm

Calculate state values at the end of Stage 1 (

k=1

)

A_1 = 100 - 40 + 40 = 100

liters;

B_1 = 40 + \frac{100}{2} - 20 = 70

liters.

Apply state equations using initial inputs

A_0 = 100

and

B_0 = 40

Calculate state values at the end of Stage 2 (

k=2

)

A_2 = 100 - 70 + 40 = 70

liters;

B_2 = 70 + \frac{100}{2} - 20 = 100

liters.

Apply state equations using inputs

A_1 = 100

and

B_1 = 70

Calculate state values at the end of Stage 3 (

k=3

)

A_3 = 70 - 100 + 40 = 10

liters;

B_3 = 100 + \frac{70}{2} - 20 = 115

liters.

Apply state equations using inputs

A_2 = 70

and

B_2 = 100

Evaluate the proposed options against calculated values

The statement specifying

A_2 = 70

liters is correct. The statement specifying

B_3 = 115

liters is correct.

Match calculated state outputs with the offered statements.

Anahtar Kavram

Sequential Process Execution and Coupled State Transitions

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru