Question

Instantaneous temperature difference between 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

Answer: (B)

$\ln \left(\frac{T_{f}-T_{0}}{T-T_{0}}\right)=K t$
If $\theta$ is the instantaneous temperature than
$\ln \left(\frac{\theta_{i}-\theta_{0}}{\theta-\theta_{0}}\right)=K t$
$\theta_{i} \longrightarrow $ initial temperature
$\theta_{0} \longrightarrow $ temperature of surrounding
$\ln \left(\theta_{i}-\theta_{0}\right)-\ln \left(\theta-\theta_{0}\right)=K T $
$\ln \left(\theta-\theta_{0}\right)=-K t+\ln \left(\theta_{i}-\theta_{0}\right)$
Comparing to
$y=m x+C$
We get a negative slope, so graph will be a straight line with decreasing slope.