Question

A body cools from $50{}^{\circ }C$ to $49.9{}^{\circ }C$ in 5 s. How long will it take to cool from $40{}^{\circ }C$ to $39.9{}^{\circ }C$ ? [Assume the temperature of the surroundings to be $30{}^{\circ }C$ and Newtons law of cooling to be valid]

• A. 2.5s
• B. 5s
• C. 20s
• D. 10s

Answer 1

Answer: (D)

From Newtons law of cooling $E=\left(\frac{{\theta }_1+{\theta }_2}{2}-\theta \right)t$ $\left(\frac{50+49.9}{2}-30\right)5=\left(\frac{40+39.9}{2}-30\right)t$ $t=\frac{19.95\times 5}{9.95}$ $=\frac{99.75}{9.95}\approx 10s$