Question

The room temperature is ${25}^{\circ }C$.A body cools from ${60}^{\circ }Cto{50}^{\circ }C$ in 10 minutes. Assuming Newton’s Law of cooling to hold good, the temperature of the body at the end of next 10 minutes will be

• A. $38.{85}^{\circ }C$
• B. ${40}^{\circ }C$
• C. $42.{85}^{\circ }C$
• D. $45.{75}^{\circ }C$

Answer 1

The correct option is C $42.{85}^{\circ }C$

$\frac{{\theta }_1-{\theta }_2}{t}=\alpha [\frac{{\theta }_1+{\theta }_2}{2}-{\theta }_0]\therefore \frac{60-50}{10}=\alpha [\frac{60+50}{2}-25]\Rightarrow \alpha =\frac{1}{30}SIunitsAlso,\frac{50-\theta }{10}=\alpha \left[\frac{50+\theta }{2}\right]or\frac{50-\theta }{10}=\frac{1}{30}\left[\frac{\theta }{2}\right]300-6\theta =\theta \Rightarrow 7\theta =300\Rightarrow \theta =\frac{300}{7}=42.{85}^{\circ }C$