Question

A metallic sphere cools from $50 \,{}^\circ C$ to $40 \,{}^\circ C$ in $300 \, s$ . If the room temperature is $20 \,{}^\circ C$ , then its temperature in the next $5 \, min$ will be

• A. $38^\circ C$
• B. $33.3^\circ C$
• C. $30^\circ C$
• D. $36^\circ C$

Answer 1

Answer: (B)

According to Newton's law of cooling
$\frac{\theta _{1} - \theta _{2}}{t}=K \, \left[\frac{\theta _{1} - \theta _{2}}{t} - \theta _{0}\right]$
$\frac{50 - 40}{300}=K\left[\frac{50 + 40}{2} - \, 20\right] \, \, or \, K= \, \frac{1}{25 \times 30}$
$\frac{40 - \theta }{300}=K\left[\frac{40 + \theta }{2} - \, 20\right]=\frac{K \theta }{2}=\frac{\theta }{1500}$
Or $300 \, \theta =60000-1500 \, \theta $ ,
$\theta =\frac{60000}{1800}=33.3℃$