The magnitudes of enthalpy changes for irreversible adiabatic expansion of a gas from 1L to 2L is `∆H_(1)` and for reversible adiabatic expansion for the same expansion is `∆H_(2)`. Then

Options

A. `∆H_(1) gt ∆H_(2)`
B. `∆H_(1) < ∆H_(2)`
C. `∆H_(1)= ∆H_(2)` enthalpy being a state function
D. `∆H_(1)= ∆E_(1) "&" ∆H_(2)= ∆E_(2) " where" ∆E_(1) "&" ∆E_(2)` are magnitude of change in internal energy of gas in these expansions respectively.

Answer

To solve the question regarding the enthalpy changes for irreversible and reversible adiabatic expansion of a gas, we will analyze the relationship between work done, temperature change, and enthalpy change in both processes.

### Step-by-Step Solution:

1. **Understanding Adiabatic Processes**:
- An adiabatic process is one in which no heat is exchanged with the surroundings. For both irreversible and reversible adiabatic expansions, the system does work on the surroundings, and the internal energy of the gas changes.

2. **Work Done in Reversible vs. Irreversible Processes**:
- In a reversible process, the work done (W) is maximized because the system is in equilibrium at every stage. In contrast, for an irreversible process, the work done is less than that in a reversible process.
- Therefore, we can state:
\[ W_{\text{reversible}} > W_{\text{irreversible}} \]

3. **Temperature Changes**:
- The temperature change (∆T) in an adiabatic process is related to the work done. Since the work done is greater in the reversible process, the final temperature of the gas after reversible expansion will also be higher than that after irreversible expansion.
- Thus, we can conclude:
\[ T_{\text{final, reversible}} > T_{\text{final, irreversible}} \]

4. **Enthalpy Changes**:
- The change in enthalpy (∆H) for a process is related to the change in temperature (∆T). For an ideal gas, the change in enthalpy can be expressed as:
\[ \Delta H \propto \Delta T \]
- Since the temperature change is greater in the reversible process, we can infer that:
\[ \Delta H_{\text{reversible}} > \Delta H_{\text{irreversible}} \]

5. **Conclusion**:
- Given that the enthalpy change for irreversible adiabatic expansion is denoted as ∆H₁ and for reversible adiabatic expansion as ∆H₂, we can conclude:
\[ \Delta H_1 < \Delta H_2 \]
- Therefore, the correct statement is that the magnitude of enthalpy change for irreversible expansion is less than that for reversible expansion.

### Final Answer:
\[ \Delta H_1 < \Delta H_2 \]