Chapter 10, Problem 10.3P

Interpretation Introduction

(a)

Interpretation:

Calculate an expression for $m_w(t)$ letting $t=0$ signify the time at which $m_w(t)=750kg/h$, and incorporate it into a differential methanol balance, letting $M(kg)$ be the mass of methanol in the tank at any time.

Concept introduction:

Material balance

$Accumulation=Input–Output+Generation–Consumption$

Interpretation Introduction

(b)

Interpretation:

Integrate the balance equation to obtain an expression for $M(t)$ and check the solution two ways. For now, assume that the tank has an infinite capacity.

Interpretation Introduction

(c)

Interpretation:

Calculate how long it will take for the mass of methanol in the tank to reach its maximum value, and calculate that value. Then calculate the time it will take to empty the tank.

Concept introduction:

For a maximum value of a function of $M$ ,

$\frac{dM}{dt}=0$

Interpretation Introduction

(d)

Interpretation:

Suppose the tank volume is $3.4m^3$ .Draw a plot of $Mvst$, covering the period from $t=0$ to an hour after the tank is empty. Write expressions for $M(t)$ in each time range when the time changes.