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Q: Newton's Law of Cooling ( Answered ,   2 Comments ) Question
 Subject: Newton's Law of Cooling Category: Science > Physics Asked by: tralcva-ga List Price: \$35.00 Posted: 18 Aug 2006 21:56 PDT Expires: 17 Sep 2006 21:56 PDT Question ID: 757539
 ```When an object is removed from a furnace and placed in an environment with a constant temperature of 80F, its core temperature is 1500F. One hour after it is removed, the core temperature is 1120F. What is the core temperature 5 hours after the object is removed from the furnace?``` Subject: Re: Newton's Law of Cooling Answered By: livioflores-ga on 19 Aug 2006 06:23 PDT Rated: ```Hi!! According to the Newton's Law of Cooling we have that: T(t) = Ts + (To - Ts)*e^(-k*t) ; where: t is the time in the preferred units (seconds, minutes, hours, etc.) T(t) is the temperature of the object at time t Ts is the sorrounding constant temperature To is the initial temperature of the object k is a constant to be found According to the given data: T(t) = 80 + (1500-80) * e^(-k*t) = 80 + 1420*e^(-k*t) We know that 1 hour after it is removed, the core temperature is 1120F, then: T(1) = 80 + 1420 * e^(-k) = 1120 ==> e^(-k) = (1120-80)/1420 = 0.7324 ==> k = -ln(0.7324) = 0.3114 Now we have completed the object's cooling equation: T(t) = 80 + 1420 * e^(-0.3114*t) So we are able to find the object's temperature at time t=5 hours: T(5) = 80 + 1420 * e^(-0.3114*5) = = 80 + 1420 * e^(-1.557) = = 80 + 1420 * 0.21 = = 378.2°F For references about the derivation of the Cooling equation according the Newton's Law of Cooling see: "Newton's Law of Cooling": http://www.sosmath.com/diffeq/first/application/newton/newton.html "Newton's Law of Cooling -- from Eric Weisstein's World of Physics": http://scienceworld.wolfram.com/physics/NewtonsLawofCooling.html Search strategy: "Newton's Law of Cooling" I hope this helps you in the understanding of this topic, if you find something unclear and/or incomplete please do not hesitate to request for a clarification before rate this answer. Regards, livioflores-ga```
 tralcva-ga rated this answer: ```Well explained answer and really helps me with my final exam study guide.....that stressful time is rolling around again``` `I see that the new school semester has commenced.`
 ```I am so glad that the service offered by us, the Google Answers' researchers, is helpful to you. Thank you so much for the good rating and comments. Sincerely, livioflores-ga``` 