Question

A body cools form ${50}^{0}C$ to ${40}^{0}C$ in 6 minute .When its surrounding temperature is ${30}^{0}C$, what will be its temperature 12 min after the start of the experiment? surrounding temperature remains the same?

• A. ${32}^{0}C$
• B. ${45}^{0}C$
• C. ${55}^{0}C$
• D. ${30}^{0}C$

Answer 1

The correct option is A ${32}^{0}C$

From Neuron law of cooling,

$ln\left(\frac{T_1-T_0}{T_2-T_0}\right)=kt$ Body cool from $T_1$ to $T_2$ in time t.

To : surrounding temperature.

(i) when it cools from $T_1{50}^{\circ }c$ to $T_2={40}^{\circ }C$ln $\pm =6min,$at $T_0={30}^{\circ }C$

$\Rightarrow ln\left(\frac{50-30}{40-30}\right)=k.6$

$\Rightarrow k=\frac{ln2}{6}$

(ii) now, after 12 min it cools to temp. T from $T_1={40}^{\circ }C$

$\Rightarrow ln\left(\frac{40-30}{T-30}\right)=\frac{ln2}{6}\times 12=2c{m}^2$

$\Rightarrow ln\left(\frac{10}{T-30}\right)=ln4$

$\Rightarrow \frac{10}{T-30}=4\Rightarrow T={32.5}^{\circ }C.$ (Ans)