Question

A pan filled with hot food cools from ${94}^{o}C$ to ${86}^{o}C$ in$2$ minutes when the room temperature is at ${20}^{o}C$. The time taken to cool it from ${71}^{o}C$ to ${69}^{o}C$ is

• A. $12s$
• B. $22s$
• C. $32s$
• D. $42s$

Answer 1

The correct option is D $42s$

For approximate calculation of the time taken,

$\frac{T_i-T_f}{\Delta t}=k[\frac{T_i+T_f}{2}-T_o]$

where,

$T_o⟶$room temperature

$T_i⟶$initial temperature

$T_f⟶$final temperature

$\Delta t⟶$time taken

$k⟶$constant

$⟹\frac{94-86}{2}=k[\frac{94+86}{2}-20]⟹4=k[90-20]=k\left[70\right]\therefore k=\frac{4}{70}⟹\frac{71-69}{\Delta t}=\frac{4}{70}[\frac{71+69}{2}-20]⟹\frac{2}{\Delta t}=\frac{4}{70}[70-20]⟹\frac{2}{\Delta t}=\frac{4}{70}\times 50\therefore \Delta t=\frac{70}{2\times 50}=0.7min=42sec$