Question

A body cools from $70{}^\circ C$ to $50{}^\circ C$ in 5 min. Temperature of surroundings is $20{}^\circ C$ . Its temperature after next 10 min is

• A. $25{}^\circ C$
• B. $30{}^\circ C$
• C. $35{}^\circ C$
• D. $45{}^\circ C$

Answer 1

Answer: (B)

$30{}^\circ C$

Answer 2

According to Newtons law of cooling, $\frac{{{\theta }_{1}}-{{\theta }_{2}}}{t}=\alpha \left[ \frac{{{\theta }_{1}}+{{\theta }_{2}}}{2}-{{\theta }_{0}} \right]$ For the given conditions $\frac{70-50}{5}=\alpha \left[ \frac{70+50}{2}-20 \right]$ ?(i) Let $\theta$ be the temperature after next 10 min. Then, $\frac{50-\theta }{10}=\alpha \left[ \frac{50+\theta }{2}-20 \right]$ ?(ii) Solving Eqs. (i) and (ii), we get $\theta =30{{\,}^{o}}C$