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College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.4: Composition Of Functions
Problem 97SE: The number of bacteria in a refrigerated food product is given by N(T)=23T256T+1,3T33 ,where T is...
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The resistance (R) of silicon as a function of temperature (T) is given by the relationship R = Ro exp(E,/ 2kT) where Ro is a constant, Eg is the energy gap between the valance band and conduction band of silicon and k is Boltzmann's constant (k=1.3807×10 2³JK-!) A student measures the resistance of a silicon sample as a function of temperature and obtains the following data. T(K) R(N) 148.1 570.6 555.9 202.6 549.4 227.1 544.1 255.1 527.3 362.0 522.2 406.1 513.1 502.5 497.6 750.1 484.9 1026.7 The uncertainties in the measured temperature are negligible, but the manufacturer of the multimeter used to measure the resistance quotes the uncertainty in any measurement as +1% of the measured value. (i) Linearise the above equation relating R and T so that the student's data can be plotted in a linear form Plot a graph, in the approved style, showing the linearised data and the appropriate uncertainties (ii)
Transcribed Image Text:The resistance (R) of silicon as a function of temperature (T) is given by the relationship R = Ro exp(E,/ 2kT) where Ro is a constant, Eg is the energy gap between the valance band and conduction band of silicon and k is Boltzmann's constant (k=1.3807×10 2³JK-!) A student measures the resistance of a silicon sample as a function of temperature and obtains the following data. T(K) R(N) 148.1 570.6 555.9 202.6 549.4 227.1 544.1 255.1 527.3 362.0 522.2 406.1 513.1 502.5 497.6 750.1 484.9 1026.7 The uncertainties in the measured temperature are negligible, but the manufacturer of the multimeter used to measure the resistance quotes the uncertainty in any measurement as +1% of the measured value. (i) Linearise the above equation relating R and T so that the student's data can be plotted in a linear form Plot a graph, in the approved style, showing the linearised data and the appropriate uncertainties (ii)
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