According to Newtons law of cooling, the temperature T of a body at time t is given by T

Chapter 3, Problem 11

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According to Newton's law of cooling, the temperature  of a body at time  is given by \(T=T_{a}+\left(T_{o}-T_{a}\right) e^{-k t}\), where \(T_{a}\) is the ambient temperature, \(T_{0}\) is the initial temperature, and  is the cooling rate constant. For a certain type of beverage container, the value of  is known to be 0.025 \mathrm{~min}^{-1}\)

a. Assume that \(T_{a}=36^{\circ} \mathrm{F}\) exactly and that \(T_{0}=72.0 \pm 0.5^{\circ} \mathrm{F}\). Estimate the temperature  at time \(t=10 \mathrm{~min}\), and find the uncertainty in the estimate.

b. Assume that \(T_{o}=72^{\circ} \mathrm{F}\) exactly and that \(T_{a}=36.0 \pm 0.5^{\circ} \mathrm{F}\). Estimate the temperature  at time \(t=10 \mathrm{~min}\), and find the uncertainty in the estimate.

Equation Transcription:

     

   

     

     

   

 

     

 

Text Transcription:

T=T_{a}+\left(T_{o}-T_{a}\right) e^{-k t}

T_{a}

T_{0}

0.025 min^{-1}

T_{a}=36^{\circ} F

T_{0}=72.0 \pm 0.5^{\circ}{F}

t=10 min

T_{o}=72^{\circ}{F}

T_{a}=36.0 \pm 0.5^{\circ}{F}

t=10 min