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According to Newton’s law of cooling, the temperature T of
Chapter 3, Problem 11E(choose chapter or problem)
According to Newton’s law of cooling, the temperature T of a body at time t is given by \(T=T_{a}+\left(T_{0}-T_{a}\right) e^{-k t}\), where \(T_{a}\) is the ambient temperature, \(T_0\) is the initial temperature, and k is the cooling rate constant. For a certain type of beverage container, the value of k is known to be \(0.025 \min ^{-1}\).
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 T at time \(t=10 \min\), and find the uncertainty in the estimate.
b. Assume that \(T_{0}=72^{\circ} \mathrm{F}\) exactly and that \(T_{a}=36.0 \pm 0.5^{\circ} \mathrm{F}\). Estimate the temperature T at time \(t=10 \mathrm{~min}\), and find the uncertainty in the estimate.
Equation Transcription:
Text Transcription:
T=T_a+(T_0-T_a)e^{-kt}
T_a
T_0
0.025 min^-1
T_a=36^oF
T_0=72.0{+/-}0.5^oF
t=10 min
T_0=72^oF
T_a=36.0{+/-}0.5^oF
t=10 min
Questions & Answers
QUESTION:
According to Newton’s law of cooling, the temperature T of a body at time t is given by \(T=T_{a}+\left(T_{0}-T_{a}\right) e^{-k t}\), where \(T_{a}\) is the ambient temperature, \(T_0\) is the initial temperature, and k is the cooling rate constant. For a certain type of beverage container, the value of k is known to be \(0.025 \min ^{-1}\).
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 T at time \(t=10 \min\), and find the uncertainty in the estimate.
b. Assume that \(T_{0}=72^{\circ} \mathrm{F}\) exactly and that \(T_{a}=36.0 \pm 0.5^{\circ} \mathrm{F}\). Estimate the temperature T at time \(t=10 \mathrm{~min}\), and find the uncertainty in the estimate.
Equation Transcription:
Text Transcription:
T=T_a+(T_0-T_a)e^{-kt}
T_a
T_0
0.025 min^-1
T_a=36^oF
T_0=72.0{+/-}0.5^oF
t=10 min
T_0=72^oF
T_a=36.0{+/-}0.5^oF
t=10 min
ANSWER:
Answer :
Step 1 of 3:
According to the Newton’s law of cooling, the temperature T of a body at time t is given by
Where, is the ambient temperature
is the initial temperature
k is the cooling rate constant.
Here the value of k is 0.025