Question

Hot water in a beaker takes $10min$ to cool from ${90}^{o}C$ to ${80}^{o}C$. Then the time taken to cool from ${80}^{o}C$ to ${70}^{o}C$ is

• A. Less than $10min$
• B. More than $10min$
• C. $10min$
• D. More than or less than $10min$ depending upon the nature of the surroundings

Answer 1

Answer: (B)

More than $10min$

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

$E\propto (T-T_0)$

Case-1 --when water cools from ${90}^{o}C$ to ${80}^{o}C$ , the difference in temperature is , $T-T_0=90-T_0$

Case-2 --when body cools from ${80}^{o}C$ to ${70}^{o}C$ , the difference in temperature is , $T-T_0=80-T_0$

It is clear that: $90-T_0>80-T_0$

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 more than 10 minutes .