A hot liquid is placed in a large room. The logarithm of the...

According to Newton's law of cooling, the rate of change of temperature is proportional to the temperature difference between the object and its surroundings.

$\dfrac{dT}{dt} = -k(T - T_0)$

Let $\Delta T = T - T_0$ be the temperature difference.

$\dfrac{d(\Delta T)}{dt} = -k \Delta T$

Integrating both sides:

$\int \dfrac{d(\Delta T)}{\Delta T} = -k \int dt$

$\ln(\Delta T) = -kt + C$

This equation is of the form $y = mx + c$, where $y = \ln(\Delta T)$ and $x = t$.

Thus, the plot of the logarithm of the temperature difference versus time is a straight line with a negative slope.