1. Tardigrade
  2. Question
  3. Physics
  4. 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).

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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).

JIPMERJIPMER 2010Thermal Properties of Matter

Solution:

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) \longrightarrow 2 \end{array} $
(2) $\div(1)$
$ \begin{aligned} \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 & =5 sec . \end{aligned} $