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

Question

Given $C_p = a + bT$
$a = 19.5$, $b = 0.042$, $n = 1$ mole
Temperature changes from $27^\circ C$ to $327^\circ C$.
Find $\Delta H$.

Answer 1

To address the query concerning the melting of an ice slab at 273 K and atmospheric pressure, a step-by-step analysis is required.

The key considerations when ice melts at 273 K and atmospheric pressure are:

Phase Transition: The ice transforms from solid to liquid at a constant temperature of 273 K. This is an isothermal process.
Thermodynamic Principles: The first law of thermodynamics states: $dU = \delta Q - \delta W$, where $dU$ is the change in internal energy, $\delta Q$ is heat added, and $\delta W$ is work done by the system.
Internal Energy of the Ice-Water System: During isothermal melting, internal energy changes due to absorbed latent heat. However, because the temperature is constant, this change is primarily associated with the phase transition, not significant shifts in kinetic energy.
Work Exchange: As ice melts into water, the volume decreases slightly because water is denser than ice. At atmospheric pressure, this volume reduction means the atmosphere performs positive work *on* the ice-water system.

Evaluation of the provided options:

Option 1: "Internal energy of ice-water system remains unchanged." Incorrect, as latent heat absorption affects internal energy, despite constant temperature.
Option 2: "Positive work is done by the ice-water system on the atmosphere." Incorrect; work is done *on* the system.
Option 3: "Internal energy of the ice-water system decreases." Incorrect for melting, which involves energy absorption.
Option 4: "Positive work is done on the ice-water system by the atmosphere." Correct, due to the volume decrease during melting at atmospheric pressure.

Therefore, the accurate conclusion is that positive work is performed on the ice-water system by the atmosphere, corresponding to Option 4.

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