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) $\theta_{0}=49^{\circ} C$