Question

The initial temperature of the body is ${80}^{\circ }C$. If its temperature falls to ${64}^{\circ }C$ in $5$ minutes and in $5$ minutes to ${52}^{\circ }C$ then the temperature of surrounding will be nearly _________.

• A. ${26}^{\circ }C$
• B. ${50}^{\circ }C$
• C. ${35}^{\circ }C$
• D. ${16}^{\circ }C$

Answer 1

The correct option is D ${16}^{\circ }C$

Let the initial temperature be ${\theta }_1$ and final temperature is ${\theta }_2$

According to Newton's law of cooling.

$\frac{{\theta }_1-{\theta }_2}{t}=K[\frac{{\theta }_1+{\theta }_2}{2}-{\theta }_0]$

In case first ,It is $\frac{80-64}{5}=K[\frac{80+64}{2}-{\theta }_0]$

or, $3.2=K[72-{\theta }_0]$ ....(i)

In Second case, $\frac{64-52}{5}=K[\frac{64+52}{2}-{\theta }_0]$

or, $2.4=K[58-{\theta }_0]$ ....(ii)

Solving (i) and (ii), we get ${16}^{\circ }C$