Thermodynamics

To correctly match the thermodynamic parameters from List I with their corresponding descriptions in List II, we need to analyze each case based on the Gibbs free energy equation: Where:

• : Change in Gibbs free energy
• : Change in enthalpy
• : Change in entropy
• : Temperature in Kelvin

The spontaneity of a reaction depends on the sign of :

• If , the reaction is spontaneous.
• If , the reaction is non-spontaneous.

Additionally, the effect of temperature on spontaneity varies based on the signs of and :

• Exothermic ( ) and Decreasing Entropy ( ):
  - Spontaneous at low temperatures.
  - Non-spontaneous at high temperatures.
• Exothermic ( ) and Increasing Entropy ( ):
  - Spontaneous at all temperatures.
• Endothermic ( ) and Increasing Entropy ( ):
  - Spontaneous at high temperatures.
  - Non-spontaneous at low temperatures.
• Endothermic ( ) and Decreasing Entropy ( ):
  - Non-spontaneous at all temperatures.

Now, let’s analyze each item in List I and match it with the appropriate description in List II.

1. List I Item A:
   Interpretation: - Since and , the reaction is spontaneous ( ) at low temperatures and non-spontaneous ( ) at high temperatures.
   - Matching Description: The reaction is spontaneous at low temperature.
   - Corresponding List II Item: III. Reaction will be spontaneous at low temperature.
2. List I Item B:
   Interpretation: - Given , the reaction is non-spontaneous.
   - With and , the reaction becomes non-spontaneous at high temperatures.
   - Matching Description: Reaction will be non-spontaneous at high temperature.
   - Corresponding List II Item: I. Reaction will be non-spontaneous at high temperature.
3. List I Item C:
   Interpretation: - Given , the reaction is non-spontaneous.
   - With and , the reaction is non-spontaneous at low temperatures and becomes spontaneous at high temperatures.
   - Matching Description: Reaction will be spontaneous at high temperature.
   - Corresponding List II Item: IV. Reaction will be spontaneous at high temperature.
4. List I Item D:
   Interpretation: - With and , the reaction is spontaneous at high temperatures and non-spontaneous at low temperatures.
   - Matching Description: Reaction will be non-spontaneous at low temperature.
   - Corresponding List II Item: II. Reaction will be non-spontaneous at low temperature.

Summary of Matching:
Therefore, the correct matching is:

Step 1: Isothermal Expansion.
For an isothermal process, the temperature remains constant, and the gas follows the ideal gas law. The pressure decreases as the volume increases. The final pressure for an isothermal process can be calculated using .

Step 2: Adiabatic Expansion.
In an adiabatic expansion, there is no heat exchange with the surroundings. As the gas expands, its internal energy decreases, leading to a decrease in temperature. Consequently, for the same volume, the pressure after an adiabatic expansion will be higher than that after an isothermal expansion because the gas has done work on the surroundings. Hence, .

Final Answer: