Question

The excess temperature of a body falls from ${12}^{o}C$ to $6^{o}C$ in $5$ minutes, then the time to fall the excess temperature from $6^{o}C$ to $3^{o}C$ is (assume the Newton's cooling is valid)

• A. $10minutes$
• B. $7.5minutes$
• C. $5minutes$
• D. $2.5minutes$

Answer 1

The correct option is C $5minutes$

The excess temperature of a body falls from ${12}^{0}C$ to $6^{0}C$ in $5$ min

To using Newton's law of cooling

$\frac{dQ}{dt}=K(\theta -{\theta }_1)$

or, $\frac{{\theta }_1-{\theta }_f}{dt}=C(12-6)$

or, $\frac{12-6}{5}=C\left(6\right)$

or, $C=\frac{6}{5}\times \frac{1}{6}$

or, $C=\frac{1}{5}$

Now 2nd Case,

$\frac{dQ}{dt}=K(\theta -{\theta }_1)$

or, $\frac{6-3}{dt}=\frac{1}{5}(6-3)$

or, $dt=\frac{3}{3}\times 5$

or, $t=5$ minute.