Animated Solution for Physics - Properties of Solids and Liquids: The variation of temperature of a material as heat is given to it at a constant rate as shown in the figure. The material is in solid state at the point $O$. The state of the material at the point $P$ is …… .

Understanding Phase Transitions

Welcome to this beautiful problem on calorimetry! At first glance, a graph might just look like a bunch of lines, but in thermodynamics, every slope and every flat plateau tells a fascinating physical story. Let's look at the graph provided. We are plotting the temperature of a material on the y-axis against the heat added to it at a constant rate on the x-axis. The material starts its journey at point $O$.

In any heating curve, we observe two distinct behaviors. When the temperature rises as heat is added, the material is in a single phase (like pure solid, pure liquid, or pure gas), and its specific heat capacity dictates the slope of the line.

The problem explicitly states that at point $O$, the material is in a solid state. As we continuously add heat from $O$ to $A$, the temperature steadily increases. This means the material is simply a solid getting hotter. So, the entire sloped region $O$ to $A$ represents the solid phase.

But what happens when the temperature remains stubbornly constant despite us pumping in more heat? A phase change is occurring! The heat energy is no longer increasing the kinetic energy of the molecules (which would raise the temperature); instead, it is being used as latent heat to break the intermolecular bonds holding the current phase together.

Now, look at the horizontal line segment $A$ to $B$. Here, the solid has reached its melting point. The heat added is the latent heat of fusion, which is actively melting the solid into a liquid. Throughout this entire horizontal segment, the material exists in a state of coexistence.

Our point of interest, $P$, lies exactly on this horizontal line $A$ to $B$. Since the melting process is actively ongoing between $A$ and $B$, the material is in the middle of its transition. It hasn't fully melted yet, nor is it completely solid anymore.

Therefore, at point $P$, the material exists in a mixed state—it is partly solid and partly liquid! Just to complete the picture, once all the solid melts at $B$, the temperature rises again from $B$ to $C$ (pure liquid), and at $C$, it starts boiling (liquid and gas mixture). Understanding every segment of this curve gives you absolute mastery over phase diagrams!