Question

Q4. A metal bar whose temperature is 20°C is placed in boiling water. How long does it take to heat the bar to practically 100°C, say, to 99.9°C, if the temperature of the bar after 1 min of heating is 51.5°C"?

Answer 1

AR at Ict TG) denole the temperature of the metal bar any time t after placing the boon in boiling water. by Newton's Law of cooling : T*(+) x (To-T) have To=100°c = kodt • dT. 100-T -In 1100-1) = kt-Inc In/100-71 = - kt+ lnc -Kt 100-T= Cie -kt :: T(+) = 100-c.e given intitial condition : TO) = 20 → 20 = 100-c.eo G= 80 :. TCU) = 100-80€ lekt gillen Condition T(1)=51-5 51.5 = 100-30ek ek .48.5 80 K= In 180 = 0-50046 -48.5 -0.500467 :. TCH)= 100-90€ now TC4) = 99.9 → 99.9 = 100-80 e -0.500465 -0.500465 е = 0o! 80

in ta 1 In (800) 0.50046 E 13.3569 : the metal boor Coill attain temperature of 99-9°C after (13-4 min Thank you