Question

A body cools from ${60}^{o}C$ to ${50}^{o}C$ in $2min$ when it is placed in a room maintained at ${30}^{o}C$. The time taken by the same body in the same room to cool further from ${50}^{o}C$ to ${40}^{o}C$ will be

• A. Less than $2min$
• B. Approximately $2min$
• C. Greater than $2min$
• D. $2min$

Answer 1

The correct option is C Greater than $2min$

Sir Newton's law of cooling states that rate of cooling of a body is directly proportional to the difference in temperatures of body ($T$) and surrounding ($T_0$).

$E\propto (T-T_0)$

Case-1 --when body cools from ${60}^{o}C$ to ${50}^{o}C$ , the difference in temperature is , $T-T_0=60-30={30}^{o}C$

Case-2 --when body cools from ${50}^{o}C$ to ${40}^{o}C$ , the difference in temperature is , $T-T_0=50-30={20}^{o}C$

In second case, the difference in temperatures decreases hence rate of cooling also decreases therefore in second case the time of cooling will increase i.e. will be greater than $2min$.