AIIMS 2005 Physics Phase Diagrams Assertion Reason Question

To address the question regarding the assertion and reason related to the pressure-temperature (P-T) phase diagram of water, we will break down both elements and evaluate their validity.

Explanation of the Assertion and Reason

1. Assertion: "In pressure-temperature (P-T) phase diagram of water, the slope of the melting curve is found to be negative."

   • This statement is true. In the P-T phase diagram, the melting curve (the line that separates the solid phase from the liquid phase) for water indeed has a negative slope. This implies that increasing the pressure lowers the melting point of ice. In other words, if you apply pressure to ice, it will melt at a lower temperature than it would at standard atmospheric pressure. This phenomenon is primarily due to the unique properties of water and the fact that ice is less dense than liquid water.

2. Reason: "Ice contracts on melting to water."

   • This statement is also true. When ice melts, it transitions into water, and this process does involve a decrease in volume. Ice has a hexagonal crystalline structure that takes up more space than the molecules in liquid water, resulting in a lower density for ice compared to water. Therefore, when ice melts, it does contract to form water.

Evaluation of the Options

• Option A: Both assertion and reason are true, and reason is the correct explanation of assertion.

  • This option is correct. The negative slope of the melting curve is due to the fact that ice contracts upon melting into water. Therefore, the reason provided directly supports and explains the assertion.

• Option B: Both assertion and reason are true but reason is not the correct explanation of assertion.

  • This option is incorrect because the reason does indeed explain why the melting curve has a negative slope.

• Option C: Assertion is true but reason is false.

  • This option is incorrect as both the assertion and reason are true.

• Option D: Both assertion and reason are false.

  • This option is incorrect since both the assertion and reason are true.

Summary

In conclusion, the correct answer is A because both the assertion about the negative slope of the melting curve in the P-T diagram of water and the reason that ice contracts on melting are true. The reason is also a valid explanation for the assertion. This unique behavior of water is crucial in understanding phase changes and is a fundamental concept in thermodynamics and material science.

Additional Concept

To understand the implications of the negative slope in a P-T diagram, we can refer to the Clapeyron equation, which relates the change in pressure with temperature during phase transitions:

$\frac{dP}{dT} = \frac{L}{T \Delta V}$

Where:

• $\frac{dP}{dT}$ is the slope of the phase boundary in the P-T diagram.
• $L$ is the latent heat of the phase change.
• $T$ is the temperature.
• $\Delta V$ is the change in volume between the two phases.

For ice melting into water, $\Delta V$ is negative (since ice is less dense than water), which results in a negative slope $\frac{dP}{dT}$. This reinforces the assertion that the melting curve of water has a negative slope.