Question

It takes ten minutes to increase the temperature of a body from ${70}^o$C to ${80}^o$c. Time required to increase the temperature of the body from ${60}^o$ to ${70}^o$ would be.

• A. More than $10$ minutes
• B. Less than $10$ minutes
• C. $10$ minutes
• D. Data is inadequate so can't be determined

Answer 1

The correct option is A More than $10$ minutes

Assuming Room temperature to be $T_s={27}^{\circ }C=300K$

Newton's Law of cooling formula

$(T_f-T_s)={(T_i-T_S)}_e^{-kt}$

$\downarrow$ $\downarrow$

final temperature Initial temperature

Case I - $T_f={80}^{\circ }C\left(353k\right),$ $T_i={70}^{\circ }C\left(343K\right),t=10min$

$\Rightarrow 53=43e^{-k\left(10min\right)}...\left(1\right)$

Case II :- $T_f={70}^{\circ }C\left(343k\right),T_i={60}^{\circ }C\left(333k\right),t=t$

$\Rightarrow 43=33e^{-kt}...\left(2\right)$

(1) - (2)

$\Rightarrow \frac{53}{43}=\frac{43}{33}{e}^{-k(10-t)}$

$\Rightarrow 0.94=e^{kt-10k}$

$\Rightarrow \left(0.94\right)e^{10k}=e^{kt}$

This proves that $t>10min$ (A)