Question

Ice at \( -5^\circ C \) is heated to become vapor with temperature of \( 110^\circ C \) at atmospheric pressure. The entropy change associated with this process can be obtained from:

• A. \( \int_{268 \, \text{K}}^{383 \, \text{K}} C_p \, dT + \frac{\Delta H_{\text{melting}}}{273} + \frac{\Delta H_{\text{boiling}}}{373} \)
• B. \( \int_{268 \, \text{K}}^{273 \, \text{K}} \frac{C_{p,m}}{T} \, dT + \frac{\Delta H_m \, \text{fusion}}{T_f} + \frac{\Delta H_m \, \text{vaporisation}}{T_b} \)
• C. \( \int_{268 \, \text{K}}^{373 \, \text{K}} C_p \, dT + q_{\text{rev}} \)
• D. \( \int_{268 \, \text{K}}^{273 \, \text{K}} C_p \, dT + \frac{\Delta H_m \, \text{fusion}}{T_f} + \frac{\Delta H_m \, \text{vaporisation}}{T_b} + \int_{373 \, \text{K}}^{383 \, \text{K}} C_p \, dT \)

Hint:

When calculating entropy change in heating processes, remember to account for both temperature changes and phase transitions. Use the appropriate heat capacities and latent heats at each step.

Answer 1

The Correct Option is B

We are given the following steps in the process: \[ \text{Ice} \to \text{Ice} \xleftrightarrow{\text{Water}} \to \text{Water} \xrightarrow{\text{Water vapor}} \text{Water vapor} \] We need to calculate the total entropy change \( \Delta S_{\text{overall}} \) for this process: \[ \Delta S_{\text{overall}} = \Delta S_1 + \Delta S_2 + \Delta S_3 + \Delta S_4 + \Delta S_5 \] Where:
\( \Delta S_1 \) corresponds to the ice being heated from \( 268 \, \text{K} \) to \( 273 \, \text{K} \),
\( \Delta S_2 = \frac{\Delta H_m \, \text{fusion}}{273} \) corresponds to the melting of the ice at \( 273 \, \text{K} \),
\( \Delta S_3 = \int_{273 \, \text{K}}^{373 \, \text{K}} \frac{C_{p,m}}{T} \, dT \) corresponds to the heating of the water from \( 273 \, \text{K} \) to \( 373 \, \text{K} \),
\( \Delta S_4 = \frac{\Delta H_m \, \text{vaporisation}}{373} \) corresponds to the vaporisation of water at \( 373 \, \text{K} \),
\( \Delta S_5 = \int_{373 \, \text{K}}^{383 \, \text{K}} C_p \, dT \) corresponds to the heating of water vapor from \( 373 \, \text{K} \) to \( 383 \, \text{K} \).
Therefore, the correct answer is option (2).