A gas is expanded from volume `V_(1)` to `V_(2` through three different process:
a. Reversible adiabatic
b. Reversible isothermal
c. Irreversible adiabatic (against a constant external pressure `P_(ex))`
The correct option is

Options

A. `[(T_(f))_(Gas)]_("Reversible isothermal") gt [(T_(f))_(GaS)]_("Reversible adiabatic") gt [(T_(f))_(Gas)]_("Irreversible adiabatic")`
B. `[(T_(f))_(Gas)]_("Reversible isothermal") gt [(T_(f))_(GaS)]_("Irreversible adiabatic") gt [(T_(f))_(Gas)]_("Reversible adiabatic")`
C. `w_("Reversible isothermal ")gtw_("Irreversible adiabatic") gt w_("Reversible adiabatic")`
D. `(P_(f))_("Reversible isothermal")gt (P_(f))_("Reversible adiabatic") gt (P_(f))_("Irreversible adiabatic")`

Explanation

To solve the problem of determining the correct order of work done during the expansion of a gas from volume \( V_1 \) to \( V_2 \) through three different processes (reversible adiabatic, reversible isothermal, and irreversible adiabatic), we can follow these steps:

### Step 1: Understand the Processes
- **Reversible Adiabatic Process**: In this process, the gas expands without heat exchange with the surroundings (Q = 0). The work done is related to the change in internal energy.
- **Reversible Isothermal Process**: In this process, the gas expands at a constant temperature. The work done is maximized because the gas can absorb heat from the surroundings to maintain its temperature.
- **Irreversible Adiabatic Process**: In this process, the gas expands against a constant external pressure. The work done is less than that in the reversible adiabatic process because the process is not carried out in equilibrium.

### Step 2: Analyze Work Done in Each Process
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