A gaseous system is initially characterised by 500 mL volume and 1 atm pressure at 298 K. This system is allowed to do work as
In isobaric conditions it expands to 800 mL resulting a decrease in pressure and temperature to 0.6 atm and 273 K respectively.
(ii) In adiabatic conditions it is allowed to expand upto 800 mL and results a decrease in pressure and temperature to 0.6 atm and 273 K respectively.
If Gibbs energy change in (i) is `DeltaG_(a)` and in (ii) is `DeltaG_(b)`, then what will be the ration of `(DeltaG_(a))/(DeltaG_(b))`? (a) 0 (B) 1 (C) between 0 -1 (D) more than 1

Options

A. 0
B. 1
C. between 0 -1
D. gt 1

Explanation

To solve the problem, we need to analyze the changes in Gibbs free energy (ΔG) for both the isobaric and adiabatic processes.

### Step-by-Step Solution:

1. **Identify Initial and Final States:**
- Initial state (for both processes):
- Volume (V1) = 500 mL
- Pressure (P1) = 1 atm
- Temperature (T1) = 298 K
- Final state (for both processes):
- Volume (V2) = 800 mL
- Pressure (P2) = 0.6 atm
- Temperature (T2) = 273 K

2. **Understanding the Processes:**
- **Isobaric Process:** The system expands at constant pressure. Here, the pressure decreases from 1 atm to 0.6 atm, and the temperature decreases from 298 K to 273 K.
- **Adiabatic Process:** The system expands without heat exchange with the surroundings. Again, the pressure and temperature decrease to the same final values as in the isobaric process.

3. **Gibbs Free Energy Change (ΔG):**
- Gibbs free energy is a state function, which means its change (ΔG) depends only on the initial and final states, not on the path taken to get there.
- Since both processes start from the same initial state and end at the same final state, we can conclude that:
\[ \Delta G_a = \Delta G_b \]

4. **Calculating the Ratio:**
- Since ΔG_a = ΔG_b, the ratio of the changes in Gibbs free energy is:
\[ \frac{\Delta G_a}{\Delta G_b} = \frac{\Delta G_b}{\Delta G_b} = 1 \]

5. **Conclusion:**
- Therefore, the ratio of the Gibbs energy change in isobaric conditions to that in adiabatic conditions is:
\[ \frac{\Delta G_a}{\Delta G_b} = 1 \]
- The correct answer is (B) 1.