Question

A body at ${50}^{o}C$ cools in a surroundings maintained at ${30}^{o}C$. The temperature at which the rate of cooling is half that of the beginning is:

• A. ${16.3}^{o}C$
• B. ${26.3}^{o}C$
• C. ${40}^{o}C$
• D. ${46.3}^{o}C$

Answer 1

The correct option is C ${40}^{o}C$

Rate of cooling $-\frac{dT}{dt}=\frac{K}{ms}(T-T_o)$

$⟹$ $\frac{1}{2}=\frac{T_2-T_o}{T_1-T_o}$

Given : $T_1={50}^o$ $T_o={30}^o$

So, $\frac{1}{2}=\frac{T_2-30}{50-30}$

$⟹T_2={40}^o$