A thermocouple's output emf is recorded at eleven junction temperatures set with an…

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Data analysis and model fitting in the laboratory · Data analysis and model fitting in the laboratory

Measurement and Method, Ch Graphs, straight lines and least squares

Problem

A thermocouple's output emf

\varepsilon

is recorded at eleven junction temperatures

\theta

set with an oil bath whose reference thermometer has standard uncertainty

u(\theta) = 0.5\ \mathrm{K}

. Repeated readings give a vertical uncertainty

u(\varepsilon) = 2\ \mu\mathrm{V}

at each temperature. The calibration slope is

40\ \mu\mathrm{V\,K^{-1}}

. A least-squares line through the eleven points, with every point given the

2\ \mu\mathrm{V}

vertical uncertainty alone, gives

\chi^2 = 200

. ((a)) Calculate the horizontal-axis contribution to each point's error bar from the bath's temperature uncertainty, in microvolts, and state whether it may be neglected next to the

2\ \mu\mathrm{V}

vertical bar. ((b)) The fit has

\nu = 9

. Calculate

\chi^2_\nu

as the fit reports it. ((c)) Recompute

\chi^2_\nu

with each point's full uncertainty, the vertical bar and the horizontal contribution of part (a) combined in quadrature, and say whether the line deserves belief.

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