In the article Measurements of the Thermal Conductivity and Thermal Diffusivity of
Chapter 3, Problem 13(choose chapter or problem)
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
\(\lambda=\frac{V I A}{\pi l a}\)
where \(\lambda\) 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: \(V, 0.01 \% ; I, 0.01 \% ; I, 1 \% ; A, 0.1 \% ; a, 1 \%\)
a. Find the relative uncertainty in \(\lambda\)
b. Which would reduce the relative uncertainty more: reducing the relative uncertainty inl to \(0.5 \%\) or reducing the relative uncertainties in V, I, and A each to 0?
Equation Transcription:
Text Transcription:
\lambda=VIA over la
\lambda
V,0.01%; I, 0.01%; I, 1%; A, 0.1%;a, 1%
\lambda
0.5%
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