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# In the article “Measurements of the Thermal Conductivity

ISBN: 9780073401331 38

## Solution for problem 13SE Chapter 3

Statistics for Engineers and Scientists | 4th Edition

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Problem 13SE

In the article “Measurements of the Thermal Conductivity and Thermal Diffusivity of Polymer Melts with the Short-Hot-Wire Method”(X. Zhang, W. Hendro, et al., International Journal of Thermophysics, 2002:1077-1090), the thermal diffusivity of a liquid measured by the transient short-hot-wire method is given by

where λ is the thermal diffusivity; V and I are the voltage and current applied to the hot wire, respectively; l is the length of the wire; and A and a are quantities involving temperature whose values are estimated separately. In this article, the relative uncertainties of these quantities are given as follows: V, 0.01%; I, 0.01%; l;1%; A, 0.1%; a, 1%. ,

a. Find the relative uncertainty in λ.

b. Which would reduce the relative uncertainty more: reducing the relative uncertainty in l to 0.5% or reducing the relative uncertainties in V, I, and A each to 0?

Step-by-Step Solution:

Step 1 of 3 :

Given,

The thermal diffusivity of a liquid by the transient short-hot-wire method is given by

=

Where, = thermal diffusivity, V and I are the Voltage and Current applied to the hot wire.

L = length of the wire, A and a are the quantities involving temperature whose values are estimated separately

Let, V=0.01% , I = 0.01%, l = 1%, A = 0.1% and a = 1%.

Step 2 of 3 :

The claim is to find the relative uncertainty in

Relative uncertainty : the relative uncertainty is a unitless quantity. It is frequently expressed as a percent. In practice is unknown. So, if the bias is negligible, we estimate the relative uncertainty with  .

Similarly, the relative uncertainty for  is   =

The given relative uncertainties are = 0.01%/100

= 0.0001

= 0.0001, = 0.01,  = 0.001 and = 0.01.

ln = lnV + lnI + lnl + lnA + lna

Then, =

=

= 0.141

= 1.41%

Therefore, = 1.41%

Step 3 of 3

##### ISBN: 9780073401331

The full step-by-step solution to problem: 13SE from chapter: 3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 13SE from 3 chapter was answered, more than 243 students have viewed the full step-by-step answer. The answer to “In the article “Measurements of the Thermal Conductivity and Thermal Diffusivity of Polymer Melts with the Short-Hot-Wire Method”(X. Zhang, W. Hendro, et al., International Journal of Thermophysics, 2002:1077-1090), the thermal diffusivity of a liquid measured by the transient short-hot-wire method is given by where ? is the thermal diffusivity; V and I are the voltage and current applied to the hot wire, respectively; l is the length of the wire; and A and a are quantities involving temperature whose values are estimated separately. In this article, the relative uncertainties of these quantities are given as follows: V, 0.01%; I, 0.01%; l;1%; A, 0.1%; a, 1%. ,a. Find the relative uncertainty in ?.________________b. Which would reduce the relative uncertainty more: reducing the relative uncertainty in l to 0.5% or reducing the relative uncertainties in V, I, and A each to 0?” is broken down into a number of easy to follow steps, and 140 words. This full solution covers the following key subjects: relative, Wire, Thermal, hot, Diffusivity. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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