Question

Two bodies $A$ and $B$ of equal masses, area and emissivity, cooling from the same temperature, following Newton's law of cooling, are represented by the graph. If $\theta$ is the instantaneous temperature of the body and ${\theta }_0$ is the temperature of surroundings, then the relationship between their specific heats is

• A. $s_A=s_B$
• B. $s_A>s_B$
• C. $s_A<s_B$
• D. None of the above

Answer 1

The correct option is B $s_A>s_B$

We know that, rate of loss of temperature is inversely proportional to specific heat.
i.e $\frac{d\theta }{dt}\propto \frac{1}{s}.$

So, for a graph plot between the rate of change of temperature and time, we can say that, if the slope of the graph is more, specific heat is less.
From the given graph, we can deduce that slope of $B$ is greater than the slope of $A$
Thus, $s_A>s_B$
Hence, option (b) is the correct answer.