Question

During the melting of a slab of ice at 273 K at atmospheric pressure:

• A. Internal energy of ice-water system remains unchanged.
• B. Positive work is done by the ice-water system on the atmosphere.
• C. Internal energy of the ice-water system decreases.
• D. Positive work is done on the ice-water system by the atmosphere.

Hint:

Apply the first law of thermodynamics and consider the sign conventions for work and heat. Melting ice results in a decrease in volume, indicating work done on the system.

Answer 1

The Correct Option is D

To solve the given question regarding the melting of a slab of ice at 273 K and atmospheric pressure, let's analyze the situation step by step.

When ice melts at 273 K and under atmospheric pressure, the following points are important:

1. Understanding the Phase Change: During the melting process, the ice transitions from a solid state to a liquid state at constant temperature (273 K). This is an isothermal process, meaning temperature remains constant while the phase changes.
2. Thermodynamic Concepts: The first law of thermodynamics can be expressed as: \(dU = \delta Q - \delta W\), where:
   • \(dU\) = Change in internal energy
   • \(\delta Q\) = Heat added to the system
   • \(\delta W\) = Work done by the system
3. Internal Energy of the Ice-Water System: Since the melting process is isothermal and involves a phase change from solid to liquid, the internal energy \((U)\) changes due to the latent heat absorbed. However, since the temperature remains constant, the internal energy change is often related to the phase change itself and depends on the latent heat of fusion rather than significant change in internal kinetic energy.
4. Work Done by or on the Ice-Water System: During the melting process at atmospheric pressure, the volume of the system decreases slightly as water is denser than ice. This means that atmospheric pressure does positive work on the system. Hence, positive work is done on the ice-water system by the atmosphere, which correlates with the correct answer choice.

Let's evaluate the given options:

• Option 1: "Internal energy of ice-water system remains unchanged." This is not entirely correct as internal energy relates to the energy absorbed for the phase change, despite the absence of temperature change.
• Option 2: "Positive work is done by the ice-water system on the atmosphere." This is incorrect, as positive work is done on the system rather than by the system.
• Option 3: "Internal energy of the ice-water system decreases." This is incorrect for a melting process, where typically energy is absorbed due to latent heat.
• Option 4: "Positive work is done on the ice-water system by the atmosphere." This is correct for the reasons explained above.

Thus, the correct answer is that positive work is done on the ice-water system by the atmosphere, which aligns with Option 4.

Answer 2

Volume decreases during melting of ice so positive work is done on ice water system by atmosphere. 
Heat absorbed by ice water so \( \Delta Q \) is positive, work done by ice water system is negative. 
Hence by first law of thermodynamics \( \Delta U = \Delta Q + \Delta W = \) Positive So internal energy increases.