Chapter 1, Section 1.2, Additional Question 02 owton\'s law of cool Sis --k(, wh

Question

Chapter 1, Section 1.2, Additional Question 02 owton's law of cool Sis --k(, where ao)sthe temperature of an oe-t hoen Tson teraletagentt anak..poatie Suppose a building loses heat in sccondance with Newton's lns of cooling.Suppose that the rate constant k has the vahe 0.23 hr Ame that the interr tempernature dt T72F, when the heatng sye fals. external temperature T-11. F. how long wat take for the "tenor temperature to fal to Ti-32P Round your anser to two decimal places The interior temperature will fall to 32 F the absolute tolerance i +0 0 show Wark is REQUEREo for this question Sh Wr

Explanation / Answer

du/dt = -k(u-T) => du/(u-T)= -kdt

Integrate both sides we get ln(uf-T)/(ui - T) = -k(t-0)

=> ln(32-11)/(72-11) = -0.23*t

=> ln(21/61)/-0.23 = t => t = 4.63 hours

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