Problem 110 - Master Resource Book in JEE Main Physics

Question

A solid material is supplied with heat at constant rate and the temperature of the material changes as shown. From the graph, the false conclusion drawn is (a) \(A B\) and \(C D\) of the graph represent phase changes (b) \(A B\) represents the change of state from solid to liquid (c) Latent heat of fusion is twice the latent heat of vaporization (d) \(C D\) represents change of state from liquid to vapour [e) Latent heat of vaporization is twice the latent heat of fusion

Step-by-Step Solution

Answer

The false conclusion is (c) because typically latent heat of vaporization is more than latent heat of fusion.

Step 1: Understand the Graph and Stages

The problem involves a graph that shows temperature changes over time as a material is heated. Typically, these graphs have sections where temperature remains constant, indicating phase changes (latent heat) and sections where temperature changes, indicating heating within a phase. Identify these sections to analyze what phase changes they correspond to.

Step 2: Analyze Statements

Review each option given in the problem: (a) Across a phase change, temperature remains constant while heat is absorbed. (b) During A to B, temperature constant suggests a phase change. (c) and (e) compare latent heats: analyze the slopes/flat sections to deduce accurate energy relationships. (d) During C to D, temperature constant, likely a phase change.

Step 3: Validate Each Statement

For statement (a), both sections A B and C D are likely to be correct phase changes as temperature remains constant. For statement (b), A B depicts a constant temperature, likely indicating melting from solid to liquid, so it's likely true. For statement (d), C D also depicts a constant temperature, indicating vaporization, hence it also appears true. Statements (c) and (e) need calculation based on graph: measure lengths or given values (not available here) for latent heat determination.

Step 4: Evaluate Relationship Between Latent Heats

Latent heat relationships are judged from horizontal lengths (or given energies if quantified). Argument is: if latent heat for AB is half CD (say 1:2), and given comparison is opposite (e.g., option e), you're finding the contradiction. Compare AB vs. CD latent heat given or deduced.

Step 5: Identify the False Statement

From previous analysis, latent heat measurements or directly the statement about false comparison (usually straightforward visually) informs this. Option (e) considers specific ratio mentioned in (c) or calculated from balance.

Key Concepts

Latent Heat of Fusion

When a solid turns into a liquid, it undergoes a phase change that requires energy input without a change in temperature. This energy required is known as the latent heat of fusion. It is the energy needed to break the bonds holding the molecules in a solid state so they can move freely past each other as a liquid.
For example, when ice melts, it absorbs heat without temperature change until it completely transitions into water. This is why the graph section during melting remains flat, indicating constant temperature as heat is absorbed.

• The concept is important because it explains why ice does not raise the temperature of water until it has fully melted.
• The latent heat of fusion is crucial for calculating the energy needed to melt a given mass of a material.

Understanding this concept helps explain why the horizontal part of the heating curve remains constant during phase change from solid to liquid.

Latent Heat of Vaporization

The latent heat of vaporization is the energy required to transform a liquid into a gas, again without changing temperature. Much like with fusion, when a liquid undergoes vaporization, it remains at a constant temperature until the process is complete. This is because all heat energy is used to overcome the molecular forces keeping the liquid together.
During boiling, for instance, water remains at 100°C until all of it has changed to steam. The flat line in the heating curve graph corresponds to this process, indicating that energy input only changes the phase, not the temperature.

• Latent heat of vaporization is higher than latent heat of fusion because turning liquid into gas requires breaking more molecular bonds than melting.
• Understanding this helps in designing processes involving boiling and condensation, as precise energy calculations are essential.

Thus, knowing the latent heat of vaporization aids in visualizing and interpreting graphs showing phase changes accurately.

Heat Transfer Graph Analysis

Heat transfer graphs, such as the one presented in the original exercise, effectively depict how energy impacts the temperature of a material over time. These graphs are invaluable for visualizing phase changes. They typically have segments where temperature remains constant due to latent heat and others where temperature rises with continuous heat application.

• The flat sections on the graph indicate a phase change occurring at a constant temperature.
• The slopes or temperature changing sections suggest the material is within a single phase and energy increases temperatures.

Analyzing such a graph helps determine the correct phase change points and the relationships between the energies involved.
For example, by inspecting the length of the flat portions, one can infer the relative amounts of latent heat needed for different phase changes like melting or boiling. A discrepancy or unusual ratio inferred from these graphs, as noted in options from the exercise, requires deeper evaluation of energy relationships.