Question

During the melting of a slab of ice at \(273K\) at atmospheric pressure

• A. Positive work is done by the ice-water system on the atmosphere
• B. Positive work is done on the ice-water system by the atmosphere
• C. Negative work is done on the ice-water system by the atmosphere
• D. The internal energy of the ice-water system decreases

Hint:

When volume decreases, surroundings do positive work on the system.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question deals with the thermodynamics of a phase change, specifically the melting of ice. We need to consider the change in volume during this process and its implication for the work done, as well as the change in internal energy based on the first law of thermodynamics.
Step 2: Key Formula or Approach:
1. Volume Change: Ice has a lower density (and thus larger specific volume) than liquid water. When ice melts into water, its volume decreases. 2. Work Done: The work done by a system on its surroundings at constant pressure is $W = P\Delta V = P(V_{final} - V_{initial})$. - If the system expands ($\Delta V>0$), work is done by the system ($W>0$). - If the system contracts ($\Delta V<0$), work is done on the system ($W<0$). 3. First Law of Thermodynamics: $\Delta U = Q - W$, where $\Delta U$ is the change in internal energy, $Q$ is the heat added to the system, and $W$ is the work done by the system.
Step 3: Detailed Explanation:
1. Volume Change: When ice melts, it turns into liquid water. Due to the unique crystalline structure of ice, it is less dense than liquid water. Therefore, upon melting, the volume of the system decreases. \[ V_{final} (\text{water})<V_{initial} (\text{ice}) \implies \Delta V = V_{final} - V_{initial}<0 \] 2. Work Done: The work done by the system (the ice-water mixture) on the atmosphere is: \[ W_{by} = P \Delta V \] Since $\Delta V$ is negative, the work done by the system is negative ($W_{by}<0$). The work done on the system by the atmosphere is the negative of the work done by the system: \[ W_{on} = -W_{by} = -P \Delta V \] Since $\Delta V$ is negative, $W_{on}$ is positive. So, positive work is done on the system by the atmosphere as it compresses the system. This makes option (B) correct. Option (A) is incorrect because work done by the system is negative. Option (C) is equivalent to option (A), as "negative work done on the system" means "positive work done by the system", which is false. 3. Internal Energy Change: According to the first law of thermodynamics, $\Delta U = Q - W_{by}$. - To melt ice, heat must be supplied to the system, so the heat added, $Q$, is positive (latent heat of fusion). - We found that the work done by the system, $W_{by}$, is negative. - Therefore, the change in internal energy is: \[ \Delta U = Q - (\text{a negative value}) = Q + |\text{negative value}| \] Since Q is positive, $\Delta U$ must be positive. This means the internal energy of the ice-water system increases. Option (D) is incorrect. Step 4: Final Answer:
Since the volume decreases during melting, the atmosphere does positive work on the system. Therefore, option (B) is correct.