Melting Ice Process Analysis

The question concerns the physical changes occurring during the melting of ice into water at a constant temperature ($T = 273 \ K$) and atmospheric pressure ($P$). This involves understanding work done and internal energy changes during a phase transition.

Work Done During Phase Change

Work done ($W$) in thermodynamics is typically calculated as $W = P \Delta V$, where $P$ is the external pressure and $\Delta V$ is the change in volume.

• Volume Change: Ice is less dense than water at $273 \ K$. The density of ice ($\rho_{ice}$) is approximately $917 \ kg/m^3$, while the density of water ($\rho_{water}$) is approximately $1000 \ kg/m^3$. Since mass ($m$) is conserved, $V = m/\rho$. As ice melts into water, the density increases, causing the volume to decrease. Therefore, the change in volume $\Delta V$ is negative ($\Delta V < 0$).
• Work Calculation: Work done *by* the system is $W_{by\_system} = P \Delta V$. Since $P$ (atmospheric pressure) is positive and $\Delta V$ is negative, $W_{by\_system}$ is negative ($W_{by\_system} < 0$). This signifies that work is done *on* the system by the surroundings (atmosphere). The work done *on* the system is $W_{on\_system} = -W_{by\_system} = -P \Delta V$. Since $\Delta V < 0$, $W_{on\_system}$ is positive.

Therefore, positive work is done on the ice-water system by the atmosphere.

Internal Energy Change During Melting

Internal energy ($U$) comprises the kinetic and potential energies of the molecules within the system. The First Law of Thermodynamics states $\Delta U = Q - W_{by\_system}$, where $Q$ is the heat added to the system.

• Heat Transfer: Melting is an endothermic process. Heat energy must be supplied (latent heat of fusion) to overcome the intermolecular forces holding the ice structure together, increasing the potential energy component of the internal energy. Thus, $Q$ is positive ($Q > 0$).
• Internal Energy Calculation: Substituting the values into the First Law: $\Delta U = Q - W_{by\_system}$. Since $Q > 0$ and $W_{by\_system} < 0$, we have $\Delta U = (\text{positive value}) - (\text{negative value}) = (\text{positive value}) + (\text{positive value})$. This clearly indicates that $\Delta U$ is positive ($\Delta U > 0$). The internal energy of the ice-water system increases during melting.

Conclusion

Based on the analysis:

• Positive work is done on the system because the volume decreases.
• Internal energy increases because heat is absorbed for the phase change.

Comparing with the options, Option 1 correctly states that positive work is done on the ice-water system by the atmosphere.