Question

A body cools from $60^{o}C$ to $50^{o}C$ in 10 minutes. If the room temperature is $25^{o}C$ and assuming Newton's law of cooling to hold good, the temperature of the body at the end of the next 10 minutes will be

• A. $38.5^{o}C$
• B. $40^{o}C$
• C. $42.85^{o}C$
• D. $45^{o}C$

Answer 1

Answer: (C)

$42.85^{o}C$

Answer 2

$\frac{60 - 50}{10} = K\left( \frac{60 + 50}{2} - 25 \right)$ …..(i)

$\frac{50 - \theta}{10} = K\left\lbrack \frac{50 + \theta}{2} - 25 \right\rbrack$ …..(ii)

On dividing, we get

$\frac{10}{50 - \theta} = \frac{60}{\theta} \Rightarrow \theta = 42.85^{o}C$