Question

2. A red wine is brought up from the wine cellar, which is a cool 10°C, and left to breathe in : room of temperature 23°C. If it takes 10 min for the wine to reach 15°C, when will the temperature of the wine reach 18°C?

Answer 1

By Newton's law of cooling a l a TR-TW T. where To = Room Tw = wine time temperature temperature in minutes at = 5 -K (TR-Tw) -k is proportionality consta Criven, TR = 234 710)=10°c , M10) = 15c . de -K(23-1) seperative variables and integrating - ln/23-T1 = -kt-c -c is integration Constant en 123-11= kt+c uslup initical condition, Tlo) = 10 = ln (23-10) = K = ln (13) /

en (23-7) = kt + ln (13) en (23-T) - ln (13) = xt " en ( 2357) - Kt 13 using another initial condition T(10) = 15 13 en ( 23:15) - 10% en %) - 10.6. ► or Ikat en To find time, when T=18. So kt = in | 23-18 13 to en ( ) ta en (2350) = en ) a t = lo · In atz) en( - 10x 1.968 119.68 mins . It will take around 19.60 mins to reach 18°C

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