Arrange the following in order of magnitude of work done by the system / on the system at constant temperature : (a) |mathrmw_mathrmreversible|$|\mathrm{w}_{\mathrm{reversible}}|$ for expansion in infinite stage. (b) |mathrmw_mathrmirreversible|$|\mathrm{w}_{\mathrm{irreversible}}|$ for expansion in single stage. (c) |mathrmw_mathrmreversible|$|\mathrm{w}_{\mathrm{reversible}}|$ for compression in infinite stage. (d) |mathrmw_mathrmirreversible|$|\mathrm{w}_{\mathrm{irreversible}}|$ for compression in single stage. Choose the correct answer from the options given below:

### Related Formula w_textrev = -nRT lnleft(fracV_mathrmfV_mathrmiright)$$w_{\text{rev}} = -nRT \ln\left(\frac{V_{\mathrm{f}}}{V_{\mathrm{i}}}\right)$$ w_textirrev = -P_textext left(V_mathrmf - V_mathrmiright)$$w_{\text{irrev}} = -P_{\text{ext}} \left(V_{\mathrm{f}} - V_{\mathrm{i}}\right)$$ ### Core Logic For isothermal reversible and irreversible steps: 1. **Reversible Path**: Since a reversible compression path retraces the exact coordinates of the reversible expansion path, the magnitudes of work are equal: |w_textrev, expansion| = |w_textrev, compression| implies a = c$$|w_{\text{rev, expansion}}| = |w_{\text{rev, compression}}| \implies a = c$$

2. **Isothermal Expansion**: Reversible work magnitude is the maximum possible work. Hence, for expansion: |w_textrev, expansion| > |w_textirrev, expansion| implies a > b$$|w_{\text{rev, expansion}}| > |w_{\text{irrev, expansion}}| \implies a > b$$

3. **Isothermal Compression**: Irreversible compression requires more work than reversible compression because of sudden pressure adjustments against the surroundings: |w_textirrev, compression| > |w_textrev, compression| implies d > c$$|w_{\text{irrev, compression}}| > |w_{\text{rev, compression}}| \implies d > c$$

### Step 1: Combine the inequalities Combining the results: - We have a = c$a = c$ - We have d > c$d > c$ - We have a > b$a > b$ This leads to the strict inequality sequence: d > c = a > b$d > c = a > b$ ### Pattern Recognition Thermodynamics Principle: Reversible expansion is the most efficient (gives maximum work magnitude), whereas reversible compression is the most efficient (requires minimum work magnitude). Single-stage irreversible compression is always the least efficient, demanding the absolute highest work input. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Chemical Thermodynamics