A calorimeter combines two independently measured temperature differences into an…

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

Scientific Computing for Physicists, Ch The uncertainty of a simulated number: inputs, sensitivity and correlated output

Problem

A calorimeter combines two independently measured temperature differences into an energy estimate

y = c_1 x_1 + c_2 x_2

, with fixed calibration coefficients

c_1 = 3.0\,\mathrm{J\,K^{-1}}

and

c_2 = -2.0\,\mathrm{J\,K^{-1}}

. The readings are

x_1 = 12.0 \pm 0.5\,\mathrm{K}

and

x_2 = 8.0 \pm 1.0\,\mathrm{K}

, independent, each evaluated Type A from repeated readings of the probe. ((a)) Find

y

and its linearly propagated uncertainty

u_y

. ((b)) Compute the first-order sensitivity index of each input. ((c)) State which reading should be measured more precisely to reduce

u_y

most.

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