Question

The initial temperature of a body is $80^{\circ }C$. If its temperature falls to $64^{\circ }C$ in 5 minutes and in 10 minutes to $52^{\circ }$. Find the temperature of surrounding.

• A. $26^{\circ }C$
• B. $60^{\circ }C$
• C. $36^{\circ }C$
• D. $49^{\circ }C$

Answer 1

Answer: (D)

According to Newton's law $\frac{{\theta }_1-{\theta }_2}{t}=k\left[\frac{{\theta }_1+{\theta }_2}{2}-{\theta }_0\right]$
Initially, $\frac{(80-64)}{5}=K\left(\frac{80+64}{2}-{\theta }_0\right)$.
$\Rightarrow 3.2=K\left[72-{\theta }_0\right]$ ...(i)
Finally, $\frac{(64-52)}{10}=K\left[\frac{64+52}{2}-{\theta }_0\right]$
$\Rightarrow 1.2=K\left[58-{\theta }_0\right]$ ...(ii)
On solving equation
(i) and (ii) ${\theta }_0=49^{\circ }C$