Question

The temperature of a body falls from $40 \,{}^\circ C$ to $36 \,{}^\circ C$ in $4 \, minutes$ , when placed in a constant ambient temperature of $20 \,{}^\circ C$ . The time it takes for the temperature to fall from $36 \,{}^\circ C$ to $32 \,{}^\circ C$ in the same ambient temperature is

• A. $5.1 \, min$
• B. $6.8 \, min$
• C. $9 \, min$
• D. $7.2 \, min$

Answer 1

Answer: (A)

Let $\theta $ be instantaneous temperature, $\theta $
For $40 \,{}^\circ C \rightarrow 36 \,{}^\circ C$
$\frac{36 - 40}{4}=-k\left(\right.38-20\left.\right) \, ...\left(\right.i\left.\right)$
$\theta _{a v g}=38 \,{}^\circ C$
For $36 \,{}^\circ C \rightarrow 32 \,{}^\circ C$
$\frac{32 - 36}{t}=-k\left(\right.34-20\left.\right) \, ...\left(\right.ii\left.\right)$
$\theta _{a v g}=34 \,{}^\circ C$
$\frac{\left(\right. i \left.\right)}{\left(\right. ii \left.\right)}$ Gives
$t=4\left(\frac{18}{14}\right)\Rightarrow t=5.1 \, min$