Question

A body takes $10$ minutes to cool from ${60}^{\circ }C$ to ${50}^{\circ }C$. The temperature of surroundings is constant at ${25}^{\circ }C$. Then, the temperature of the body after the next $10$ minutes will be approximately:

• A. ${47}^{\circ }C$
• B. ${45}^{\circ }C$
• C. ${41}^{\circ }C$
• D. ${43}^{\circ }C$

Answer 1

The correct option is C ${41}^{\circ }C$

Let the temperature of thr body after 10 minute be 'T'

$10=\frac{1}{k}loge\left(\frac{T-25}{50-25}\right)=\frac{1}{k}loge\left(\frac{T-25}{25}\right)---\left(II\right)$

Divide equation (I) by (II)

$\frac{10}{10}=\frac{\frac{1}{k}loge\left(\frac{5}{7}\right)}{\frac{1}{k}loge\left(\frac{T-25}{25}\right)}$

$T={44.86}^{\circ }c\approx {45}^{\circ }c.$

The answer is option (2).