Question

If the time taken. by a hot body to cool from ${50}^{o}C$ to ${40}^{o}C$ is 10 min when the surrounding temperature is ${25}^{o}C$, then the time taken for it to cool from ${40}^{o}C$ to ${30}^{o}C$ when the surrounding temperature is ${15}^{o}C$, is

• A. 40 min
• B. 10 min
• C. 4 min
• D. 15 min
• E. 20 min

Answer 1

The correct option is B 10 min

Avg temperature in first case = $(50+40)/2={45}^{0}C$
Avg temperature in second case = $(40+30)/2={35}^{0}C$
As from Newton law of cooling,
$dT/dt=-k(T-T_0)$
${\int }^{}dT=-20k{\int }^{}dt$
$10=-20k\times 10$
$k=1/20$
For 2nd case:
$dT/dt=-k(T-T_0)$
${\int }^{}dT=-45k{\int }^{}dt$
$10=-20k\times t$
$t=10min$