Question

A metal sphere cools at the rate of $ 3^{\circ} C/\min $ when its temperature is $ 50^{\circ} C $ . Its rate of cooling when its temperature is $ 40^{\circ} C $ and the temperature of surrounding is $ 25^{\circ} C $ is

• A. $ 1.3^{\circ} C/\min $
• B. $ 1.4^{\circ} C/\min $
• C. $ 1.5^{\circ} C/\min $
• D. $ 1.8^{\circ} C/\min $

Answer 1

The Correct Option is D

$\left(\frac{d \theta}{d t}\right)_{1}= K \left(\theta_{1}-\theta_{0}\right) \ldots$ (i) $\left(\frac{d \theta}{d t}\right)_{2}= K \left(\theta_{2}-\theta_{0}\right) \ldots$ (ii) $\therefore \frac{(d \theta / d t)_{1}}{(d \theta / d t)_{2}}=\frac{\theta_{1}-\theta_{2}}{\theta_{2}-\theta_{0}}$ $=\frac{50-25}{40-25}$ $\frac{3}{(d \theta / d t)_{2}} \frac{25}{15}$ $ \Rightarrow\left(\frac{d \theta}{d t}\right)_{2}=1.8^{\circ} C / \min$