Project ForgeA thermodynamic cycle with an ideal gas as working fluid is shown (P-V diagram): process 1→2 is at constant pressure 100 kPa (V1 to 1 m³), process 2→3 is at constant volume 1 m³ (100 kPa to 400 kPa), and process 3→1 follows PVᵞ=constant back to state 1. The above cycle is represented on the T-S plane by
- ADiagram (A)
- BDiagram (B)
- CDiagram (C)
- Diagram (D)
Explanation
Using PVᵞ=const between states 3 (V=1,P=400) and 1 (V=V1,P=100) with γ=1.4: V1=4^(1/1.4)≈2.69 m³. Relative temperatures (T∝PV): T1∝269, T2∝100, T3∝400, so T3>T1>T2. Since 3→1 is isentropic, states 1 and 3 share the SAME entropy (connected by a vertical line on the T-S plane); entropy decreases along 1→2 (isobaric cooling/compression) and increases along 2→3 (isochoric heating) back up to S1=S3, with point 2 at the LOWEST entropy of the three. Only the diagram placing 2 at lowest-S/lowest-T, with 3 directly above 1 via a vertical (constant-S) segment, matches this — diagram (D).
Source: GATE ME 2007 (2007)
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