Work comparison for single-stage compression (no clearance) In a single-stage, single-acting reciprocating air compressor without clearance volume, which compression path results in the maximum indicated work input between the same inlet and delivery pressures?

Introduction / Context:
The work required for gas compression depends on the thermodynamic path between the initial and final states. For a given inlet state and discharge pressure, different idealized paths (isothermal, polytropic, isentropic) yield different areas under the p–v curve, i.e., different work inputs.

Given Data / Assumptions:

• No clearance volume and ideal valves.
• Same inlet pressure and temperature; same discharge pressure.
• Ideal, quasi-static processes for comparison.

Concept / Approach:
On a p–v diagram, the isothermal curve lies below the polytropic (n between 1 and gamma), which lies below the isentropic curve (n = gamma). Therefore, for the same end pressures, the isentropic path has the largest area under the curve (highest work), and the isothermal path has the least.

Step-by-Step Solution:
Isothermal: pv = constant → minimum work for ideal gas compression.Polytropic: pv^n = constant, 1 < n < gamma → intermediate work.Isentropic: n = gamma → maximum work among the listed realistic paths.Thus the maximum indicated work is for isentropic compression.

Verification / Alternative check:
Analytical expressions show W_isothermal = mRT1ln(p2/p1), W_isentropic = (mRT1/(gamma - 1))(r^((gamma - 1)/gamma) - 1), and W_polytropic lies between them for 1 < n < gamma.

Why Other Options Are Wrong:
(a) gives minimum work; (c) intermediate; (d) incorrect—work depends on the path; (e) isobaric compression does not connect the specified end pressures for a compressor.

Common Pitfalls:
Assuming “adiabatic” means “no losses therefore least work.” For compression, adiabatic actually requires more work than isothermal because temperature rises.

Final Answer:
Isentropic (reversible adiabatic) compression