Chapter 2, Problem 2.29P

(a)

Interpretation Introduction

Interpretation:

The equation predicts that the time at which $\text{50\%}$ of micro pipets remain within specifications is two years should be given.

Concept introduction:

Fraction within specifications:

In the micro pipette specification, the relationship between fraction specifications with time is given by blow equation,

$\text{Fraction within specification}\text{=}{\text{e}}^{{\text{-t(ln2)/t}}_{\text{m}}}$

Where,

${\text{t}}_{\text{m}}$ is time between failure time to correct time.

Answer to Problem 2.29P

Fraction within specifications is ${\text{e}}^{\text{-ln2}}$

Explanation of Solution

To give the equation predicts that the time at which $\text{50\%}$ of micro pipets remain within specifications is two years.

Given,

${\text{t}}_{\text{m}}\text{=2}\text{Yr}$

The equation predicts that the time at which $\text{50\%}$ of micro pipets remain within specifications is two years with ${\text{t}}_{\text{m}}\text{=2}\text{Yr}$ is,

$\begin{array}{l}\text{Fraction within specification}\text{=}{\text{e}}^{{\text{-t(ln2)/t}}_{\text{m}}}\\ ={\text{e}}^{\text{-2(ln2)/2}}\\ ={\text{e}}^{\text{-ln2}}\\ =\frac{1}{2}\end{array}$

The given ${\text{t}}_{\text{m}}$ is plugged in above equation to give an equation to amount of micro pipets remain within specifications

Conclusion

The true mass of ${\text{KNO}}_{\text{3}}$ should be determined.

(b)

Interpretation Introduction

Interpretation:

The time to recalibrated micro pipets should be calculated.

Concept introduction:

Fraction within specifications:

In the micro pipette specification, the relationship between fraction specifications with time is given by blow equation,

$\text{Fraction within specification}\text{=}{\text{e}}^{{\text{-t(ln2)/t}}_{\text{m}}}$

Where,

${\text{t}}_{\text{m}}$ is time between failure time to correct time.

Answer to Problem 2.29P

The time to recalibrated micro pipet is $\text{54}\text{days}$

Explanation of Solution

To determine the time to recalibrated micro pipette.

Given,

${\text{t}}_{\text{m}}\text{=2}\text{Yr}$

The percentage for pipette are within the specifications is $\text{95\%}$

$\begin{array}{l}\text{Fraction within specification}\text{=}{\text{e}}^{{\text{-t(ln2)/t}}_{\text{m}}}\\ 0.95={\text{e}}^{\text{-2(ln2)/2}}\end{array}$

Take ln to both side.

$\begin{array}{l}\text{ln(0}\text{.95)}\text{=}\text{-t(ln2)/2}\\ \text{t}\text{=}\text{-2ln(0}\text{.95)/ln2}\\ \text{=}\text{0}\text{.148}\text{yr}\\ \text{=}\text{8}\text{weeks}\\ \text{=}\text{54}\text{days}\end{array}$

The percentage for pipette are within the specifications is plugged in above equation to give a time to recalibrated micro pipette.

The time to recalibrated micro pipet is $\text{54}\text{days}$

Conclusion

The time to recalibrated micro pipet was calculated.