A metal bar at a temperature of 100F is placed in a room at a constant temperatu

Question

A metal bar at a temperature of 100F is placed in a room at a constant temperature of 0F. If after 20 minutes the temperature of the bar is 50F, (a) find the time it will take the bar to reach 25F and (b) the temperater of the bar after 10 minutes. I saw the same questions asked before but the answers had a lot of missed steps and I could not figure it out. A detailed answer would help a lot

Explanation / Answer

by using newton/s law of cooling we get dE/dt= -k(To-T) whre T0 is the temp of body and T is temp of surrounding..... thus we have the formulae T(t)=Ta+(Th-Ta)e^-kt where........ T(t) = Temperature at time t, TA = Ambient temperature (temp of surroundings), TH = Temperature of hot object at time 0, k = positive constant and t = time.,............. putting the initial value we get K=in2/20=0.346/min .................................................... a> .thus time taken to reach 25 F will be 25=0+(50-0)e^0.34*t /................on solving we get t=40 min ........ so it will take another 40 min ......... b>. putting the value in given formulae we get T(10)=70.7 F

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