Question

Two identical pressure cookers, Cooker A and Cooker B, each having a total internal capacity of 6 litres are available. Cooker A is filled with 2 litres of liquid water at 110°C and Cooker B is filled with 4 litres of liquid water at 110°C. The remaining space in both the cookers is filled with saturated water vapour in equilibrium with the liquid water. If \( g \) represents the specific Gibbs free energy, and subscripts \( v \) and \( l \) represent the saturated vapour and the saturated liquid phases, respectively, which of the following expressions is correct? 
 

• A. \( g_{v,A} > g_{l,B} \)
• B. \( g_{v,A} < g_{l,B} \)
• C. \( g_{v,A} = g_{l,B} \)
• D. \( g_{l,B} = 2 g_{l,A} \)

Hint:

When two phases are in equilibrium, the specific Gibbs free energies of the two phases are equal at the same temperature and pressure.

Answer 1

The Correct Option is C

Step 1: Understand the situation in both cookers.
Both cookers are filled with liquid water at the same temperature (110°C), but with different amounts of liquid. Cooker A has 2 litres of liquid, while Cooker B has 4 litres of liquid. The remaining space in both cookers is filled with saturated water vapour.

Step 2: Consider the relationship between Gibbs free energy.
In each cooker, the vapour and liquid phases are in equilibrium. At equilibrium, the specific Gibbs free energy for the liquid and vapour phases are equal. However, the amounts of liquid and vapour are different in the two cookers. Since both cookers are at the same temperature and pressure, and the vapour is in equilibrium with the liquid, the Gibbs free energies of the vapour in Cooker A and the liquid in Cooker B must be equal. That is, \( g_{v,A} = g_{l,B} \).

Step 3: Conclusion.
Thus, the correct expression is \( g_{v,A} = g_{l,B} \), making option (C) the correct answer.

Final Answer: (C) \( g_{v,A} = g_{l,B} \)