Q. A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next of 10 minutes will be
A) $\frac{7}{4}T$
B) $\frac{3}{2}T$
C) $\frac{4}{3}T$
D) T
Explanation
[Solution] Using the average form: $\frac{T}{10} = k(1.5T)$ gives k = 1/15; then $\frac{2T - x}{10} = k\left(\frac{2T + x}{2} - T\right)$ gives $x = \frac{3}{2}T$. (Exponential cooling also halves the excess, 2T → T → T/2, giving 3T/2.) Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.