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

Answer: (D)

$1.8^{\circ} C/\min$

Answer 2

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