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)

$\ln \left(\frac{T_f-T_0}{T-T_0}\right)=Kt$
If $\theta$ is the instantaneous temperature than
$\ln \left(\frac{{\theta }_i-{\theta }_0}{\theta -{\theta }_0}\right)=Kt$
${\theta }_i⟶$ initial temperature
${\theta }_0⟶$ temperature of surrounding
$\ln \left({\theta }_i-{\theta }_0\right)-\ln \left(\theta -{\theta }_0\right)=KT$
$\ln \left(\theta -{\theta }_0\right)=-Kt+\ln \left({\theta }_i-{\theta }_0\right)$
Comparing to
$y=mx+C$
We get a negative slope, so graph will be a straight line with decreasing slope.