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 10\,s $