Multiple choice

A body originally at 60°C cools down to 40°C in 15 minutes when kept in air at a temperature of 25°C. What will be the temperature of the body at the end of 30 minutes?

  1. 35.2°C

  2. 31.5°C

  3. 28.7°C

  4. 15°C
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Newton's Law of Cooling: T(t) = Ta + (T0 - Ta)e^(-kt). First interval: 40 = 25 + (60-25)e^(-15k) => 15 = 35e^(-15k) => e^(-15k) = 15/35 = 3/7. Second interval (30 min): T = 25 + (60-25)e^(-30k) = 25 + 35(e^(-15k))^2 = 25 + 35(3/7)^2 = 25 + 35(9/49) = 25 + 45/7 = 25 + 6.43 = 31.43 degrees C.

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