The Question is from neet-physics , and it was created by the author Mr. ANIL KUMAR.G

Question

A real gas undergoes an irreversible isothermal expansion against a constant external pressure.  Which of the following statements is TRUE regarding the work done?

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [C]
## CONCEPT FRAMEWORK
**Primary Concept**: Work done in thermodynamic processes
**Related Topics**: Reversible vs Irreversible processes, Isothermal processes
**Prerequisites**: Understanding of work in thermodynamics, reversible and irreversible processes, isothermal process.
## SOLUTION PATHWAY
**Given Information**:
*   Irreversible isothermal expansion
*   Constant external pressure
**Method & Steps**:
1. **Work done in an irreversible expansion**:  Work done during an irreversible expansion against a constant external pressure ($P_{ext}$) is given by:
    Reasoning: This formula applies to expansions where the external pressure is constant and the change in volume occurs due to this pressure.
   Formula/Rule: $W = -P_{ext}(V_2 - V_1)$
2. **Work done in a reversible isothermal expansion**: Work done during a reversible isothermal expansion is given by:
    Reasoning: The reversible process is performed infinitely slowly, keeping the internal and external pressures nearly equal at each stage. This results in maximum work.
    Formula/Rule: $W_{rev} = -nRT \ln(\frac{V_2}{V_1})$
3. **Comparison of work**: For an expansion ($V_2 > V_1$), the work done is negative (work is done by the system). The magnitude of work done in a reversible isothermal expansion is always greater than that in an irreversible expansion between the same initial and final volumes. This is because in an irreversible expansion, the system does not take full advantage of the pressure difference, and some energy is lost.
    Working:  Since $P_{ext}$ is constant and less than the pressure of the gas during the expansion, the area under the P-V curve for the irreversible process is less than that of the reversible process. Thus, magnitude of work done is less in irreversible process.
    Key Point: Work in thermodynamics is path-dependent, reversible processes represent the maximum theoretical work attainable.
4. **Conclusion**: The work done in an irreversible expansion against constant external pressure is less than the work done in a reversible expansion between the same initial and final volumes.
    Result: The work done in the irreversible process is less than the work done in the reversible process.
    Verification: The nature of irreversible expansion involves loss of energy, and hence less work is done.
## OPTION ANALYSIS
[A] :x: This statement is incorrect because the work done in an irreversible process is not equal to that in a reversible process.
[B] :x: This statement is incorrect. The work done in an irreversible expansion is always less than that in a reversible expansion.
[C] ✓: This statement is correct.  The magnitude of work done in an irreversible process is less than that in a reversible process.
[D] :x: This statement is incorrect. Work is done during the expansion process.
## LEARNING AIDS
**Common Mistakes**:
1. **Confusion between reversible and irreversible work**: Reversible work is the maximum work obtainable, while irreversible work is less due to losses.
2. **Incorrect sign convention**: Work done by the system is negative, while work done on the system is positive.
**Quick Tips**:
1.  **Visualizing P-V diagrams**: The area under the curve represents the work done. The reversible process has a larger area under the curve for expansion.
2. **Remembering the key difference**: Reversible processes are idealized and occur infinitely slowly, while irreversible processes occur in finite time.

Mr. ANIL KUMAR.G · Answer

The work done is equal to the work done in a reversible isothermal expansion between the same initial and final volumes.

Mr. ANIL KUMAR.G · Answer

The work done is greater than the work done in a reversible isothermal expansion between the same initial and final volumes.

Mr. ANIL KUMAR.G · Answer

The correct Option is "The work done is less than the work done in a reversible isothermal expansion between the same initial and final volumes."

Mr. ANIL KUMAR.G · Answer

The work done is zero.

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