Sandy manages a ceramics shop and uses a 650ºF kiln to fireceramic green-ware. A

Question

Sandy manages a ceramics shop and uses a 650ºF kiln to fireceramic green-ware. After turning off her kiln, she must wait untilits temperature gauge reaches195ºF before opening it andremoving the ceramic pieces. If room temperature is 80ºF andthe gauge reads 500ºF in 11 minutes, how long must she waitbefore opening the kiln? Round your answer to the nearest wholeminute.

Assume the kiln cools according to Newton's Law of Coolingwhere, is the temperature of the room, is the initial temperatureof the kiln, and t is the time, in minutes.

T(t)=Ta +(To - Ta)e kt

Explanation / Answer

Ta=80 To=650 500= 80+570ek11 420/570=ek11 ln(420/570)/11=t t=-0.0278 195=80+570e-0.278t 115/570 = e-0.278t ln (115/570)/-.278=t t=57.658 min until she can open the oven

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