Question

A body cools from 50°C to 49°C in 5 seconds. How long will it take to cool from 40°C to 39°C? (Assume temperature of surrounding to be 30°C and Newton’s law of cooling is valid).

• A. 2.5 s
• B. 5.0 s
• C. 10.0 s
• D. 20.0 s

Answer 1

Answer: (B)

Newtons law of cooling:
Case : $\left(\frac{{\theta }_1-{\theta }_2}{t}\right)\alpha \left(\frac{{\theta }_1+{\theta }_2}{2}-{\theta }_s\right)$
$\begin{array}{c}\left(\frac{50-49}{5}\right)\propto (49.5-30)\\ \left(\frac{1}{5}\right)\propto (19.5)=\text{ (1). }\end{array}$
Pase 2:
$\begin{array}{c}\left(\frac{40-39.5}{t}\right)\propto (39.75-30)\\ \left(\frac{0.5}{t}\right)\propto (9.75)⟶2\end{array}$
(2) $÷(1)$
$\begin{array}{rl}\frac{(0.5/t)}{(1/5)}& =\frac{9.75}{19.5}\\ \frac{0.5}{t}& =\frac{1}{5}\left(\frac{1}{2}\right)\\ t& =0.5\times 10\\ t& =5sec.\end{array}$