Two volumes are dispensed from the same burette and added to make a total: and

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Measurement and Method, Ch Propagating uncertainty into the quantity you actually want

Problem

Two volumes are dispensed from the same burette and added to make a total:

V_1 = 15.00\,\mathrm{mL}

and

V_2 = 22.00\,\mathrm{mL}

, total

V = V_1+V_2

. The burette's own scale may be uncertain by a fraction

\kappa

, with

u(\kappa) = 0.20

per cent (one standard deviation), a calibration error that multiplies every volume read from the burette by the same factor

(1+\kappa)

. Apart from this shared calibration error the two readings are exact. Someone argues: "

V_1

and

V_2

come from readings on the same burette taken close together, so I should just treat them as independent, random readings and add their uncertainties in quadrature:

u(V_1) = 0.20\%\times15.00\,\mathrm{mL} = 0.030\,\mathrm{mL}

u(V_2) = 0.20\%\times22.00\,\mathrm{mL} = 0.044\,\mathrm{mL}

, so

u(V) = \sqrt{0.030^2+0.044^2}\,\mathrm{mL} = 0.053\,\mathrm{mL}

." ((a)) Write

V_1

and

V_2

in terms of the true delivered volumes and the shared calibration error

\kappa

, and use this to find the correct

u(V)

. ((b)) Say whether the quoted quadrature calculation is trustworthy, and explain what it leaves out.

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