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You taken ice-cream out of the freezer,kept at - 18°C. Outside it is 32°C After one minute, the ice cream has warmed to - 8°C what is the temperature of ice cream ofter five minutes |
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Answer» tion:Let T be the temperature of the ice-cream (in ∘C) after t minutes out of the freezer. Then Newton's law givesdTdt=−k(T−32)=−kT+32k.Remembering that k is a CONSTANT, solving this DIFFERENTIAL equation gives a general solution ofT=Ce−kt+32.Since T=−18 when t=0, we OBTAIN −18=C+32, so C=−50. Since T=−8 when t=1, we have −8=−50e−k+32, which gives k=loge54. We obtainT=−50e−(loge54)t+32=−50(45)t+32.(Here we used some INDEX laws.) Hence, when t=5, we haveT=−50(45)5+32=1952125≈15.6 ∘C.Your ice-cream has well and truly melted! Note that we have effectively assumed that the ice-cream is a block of a single temperature — not very realistic. |
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