Introduction:
In this scenario, we have an ideal gas that undergoes expansion in both reversible and irreversible processes in an isolated system. We need to determine the relationship between the final temperature (Tf) and the initial temperature (Ti) for both processes.

Reversible Process:
In a reversible process, the system is in equilibrium at every stage of the expansion. The gas expands slowly and infinitesimally, allowing the system to maintain thermal equilibrium with the surroundings. This process is considered to be quasi-static.

Irreversible Process:
In an irreversible process, the system is not in equilibrium at every stage of the expansion. The gas expands rapidly and does not allow the system to adjust to the changes. This process is considered to be non-quasi-static.

Analysis:
Now, let's analyze the relationship between the final and initial temperatures for both reversible and irreversible processes.

Reversible Process:
During a reversible expansion, the gas expands slowly and is able to exchange heat with the surroundings at each stage. This implies that the system remains in thermal equilibrium with the surroundings throughout the process. Therefore, the change in temperature (ΔT) is relatively small.

Irreversible Process:
During an irreversible expansion, the gas expands rapidly and does not have enough time to exchange heat with the surroundings at each stage. This causes the system to deviate from thermal equilibrium. Consequently, the change in temperature (ΔT) is relatively large.

Conclusion:
Based on the above analysis, we can conclude that:
(a) (Tf)irrev > (Tf)rev – The final temperature (Tf) in an irreversible expansion is higher than in a reversible expansion because the gas does not have enough time to exchange heat with the surroundings.
(b) Tf > Ti for reversible process but Tf = Ti for irreversible process – In a reversible process, the gas expands and cools down, resulting in Tf < ti.="" however,="" in="" an="" irreversible="" process,="" the="" gas="" expands="" rapidly="" and="" does="" not="" exchange="" heat="" effectively,="" leading="" to="" tf="" ≈="" />
(c) (Tf)rev > (Tf)irrev – The final temperature in a reversible expansion is lower than in an irreversible expansion since the gas is allowed to exchange heat slowly and maintain thermal equilibrium.
(d) Tf = Ti for both reversible and irreversible processes – This statement is incorrect as the final and initial temperatures are different for both types of processes, as explained above.

In summary, the correct statement is: (a) (Tf)irrev > (Tf)rev.

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