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 Thermo-physics, 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?

Transcribed Image Text:

VIA λ= πια