Problem 3: The rate of cooling of a sphere can be given as dT where the temperat

Question

Problem 3: The rate of cooling of a sphere can be given as dT where the temperature of the body is T and ambient temperature Tamb 20°C, 1/r is the proportionality constant. Experimental data has been acquired for a sphere of unknown ?, with an initial temperature of T-1000 C. The temperature profile as a function of time is given as Time sec Temp 13 15 17 63 48 37 29 25 24 23 a) Fit a fourth-order polynomial through the experimental data and estimate the temperature from the results at t - 0 sec and t - 20 sec. How do they compare to the initial temperature, Ti, and the ambient temperature Tamb? b) Plot the time versus experimental data using the markers 'o'. On the same plot, plot the time versus the interpolated temperature, for the span from 0 to 20 seconds in steps of 0.2 seconds The solution to the differential equation, Equation 1, is T-Tamb-t/ Ti-Ta [Eq. 2] L amb If we take the natural log of both sides T-T amb Ti-Tamb we end up with an equation that is linear (y mx + b) with a slope of-1/t c) Use the temperatures that you obtained in part (a) from the interpolation to fit a line through Equation 3 and determine T. d) With t, plot the time versus temperature from Equation 2 by rearranging [Eq. 4] Publish vour results

Explanation / Answer

clear;clc
t=xlsread('book1.xlsx','A1:A8'); %time
T=xlsread('book1.xlsx','B1:B8'); %Temperature
myfit=fit(t,T,'poly4');
plot(t,T,'o')
hold on
T0=feval(myfit,0) % Temperature @time=0
T20=feval(myfit,20)% Temperature @time=20
time=0:0.2:20;
TT=feval(myfit,time);  
plot(time,TT); hold off

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