Question

Instantaneous temperature difference between a cooling body and the surroundings, obeying Newton's law of cooling, is $\theta$. Which of the following represents the variation of ln $\theta$ with time $t$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

From Newtons law of cooling,
$\ln \left(\frac{T_1-T_0}{T_2-T_0}\right)=kt$
Let ${\theta }_i$ be the initial temperature of body and ${\theta }_s$ be the temperature of the surroundings.
Suppose $\theta$ is the instantaneous temperature differerence between the body and surroundings.
Then, $\ln \left(\frac{{\theta }_i-{\theta }_s}{\theta }\right)=kt$
$\Rightarrow \ln ({\theta }_i-{\theta }_s)-\ln \theta =kt$
$\Rightarrow \ln \theta =-kt+\ln ({\theta }_i-{\theta }_0)$
Comparing to $y=mx+C$, option (b) is correct.