Question

A body cools from ${50}^{\circ }$C to ${40}^{\circ }$C in 5 minutes. The surrounding temperature is ${20}^{\circ }$C . By how many${}^{\circ }$C does the temperature decrease in the next 5 minutes? Round your answer to the nearest integer.

Answer 1

As per Newton's law of cooling,

$T=T_s+(T_0-T_s)e^{-kt}$

Hence, $\frac{T-T_s}{T_0-T_s}=constant$ for constant time intervals

$\frac{40-20}{50-20}=\frac{T-20}{40-20}$

$\frac{2}{3}=\frac{T-20}{20}$

$T={\frac{100}{3}}^{0}C$