When ice at $0^\circ\text{C}$ is heated and converted into steam at $100^\circ\text{C}$, which graph correctly represents the variation of temperature with heat supplied?
Show Hint
Remember that the length of the horizontal segments depends on the latent heats. Since the latent heat of vaporization of water is much larger than the latent heat of fusion, the boiling horizontal line is actually much longer than the melting horizontal line!
Step 1: Understanding the Concept:
The process of heating ice at $0^\circ\text{C}$ all the way to steam at $100^\circ\text{C}$ involves three distinct thermodynamic stages.
It involves a phase change from solid to liquid, a pure temperature increase of the liquid, and finally a phase change from liquid to gas. Step 2: Key Formula or Approach:
During a phase change, heat is strictly supplied as latent heat ($Q = mL$), and the absolute temperature remains entirely constant, leading to a horizontal line on a Temperature vs. Heat graph.
During a single-phase temperature rise, heat goes into specific heat capacity ($Q = mc\Delta T$), causing the temperature to rise linearly with a constant positive slope. Step 3: Detailed Explanation:
Let's trace the correct physical sequence of the heating curve:
Stage 1: Ice at $0^\circ\text{C}$ melts into liquid water at $0^\circ\text{C}$. The temperature strictly remains constant at $0^\circ\text{C}$ as heat is continuously supplied. This produces a horizontal line segment starting right from the origin along the heat axis.
Stage 2: The liquid water is then heated from $0^\circ\text{C}$ up to $100^\circ\text{C}$. The temperature continuously rises linearly as more heat is supplied, creating a diagonal straight line moving upward.
Stage 3: The water at $100^\circ\text{C}$ begins to boil and convert entirely into steam. The temperature remains completely constant at $100^\circ\text{C}$ during this entire process, forming a second horizontal line segment.
Looking strictly at the provided visual options, Graph B is the only graph that perfectly depicts this exact "horizontal-diagonal-horizontal" sequence starting from the origin. Step 4: Final Answer:
Graph B correctly represents the exact variation of temperature with the heat supplied.
