Question

A hot liquid is kept in a big room. The logarithm of the numerical value of the temperature difference between the liquid and the room is plotted against time. The plot will be very nearly

• A. a straight line
• B. a circular arc
• C. a parabola
• D. an ellipse.

Answer 1

The correct option is A a straight line

By newton's law of cooling formula,

$\frac{dT}{dt}=k[T-T_m]\Rightarrow \frac{dT}{T-T_m}=kdt$

On integrating,

$\Rightarrow \int \frac{dT}{T-T_m}=k\int dt\Rightarrow \ln [T-T_m]=kt+C$

So, from above equation; $\ln [T-T_m]\propto t$

If graph is plotted between $\ln [T-T_m]$ and $t$, the graph will be straight line.