Question

A body cools from ${62}^0$C to ${50}^0$C in $10$ minutes. How long will it take to cool to ${42}^0$C, if room temperature is ${26}^0$C?

• A. $5$ min
• B. $7.5$ min
• C. $10$ min
• D. $12.5$ min

Answer 1

The correct option is C $10$ min

$\frac{dT}{dt}=-k(T-26)$

Solving this equation for two situations we get,

$e^{-k{t}_1}=\frac{50-26}{62-26}=\frac{2}{3}$

$e^{-k{t}_2}=\frac{42-26}{50-26}=\frac{2}{3}$

Hence, $t_1=t_2=10$ minutes