Which of the following is true for dual cycle? [x = Compression ratio, y = Expansion ratio, z = Cut-off ratio]

Concept:

Dual cycle:

Processes in Dual Cycle:

Process 1-2: Isentropic compression  

Process 2-3: Constant volume heat addition

Process 3-4: Constant pressure heat addition

Process 4-5: Isentropic heat rejection

Process 5-1: Constant volume heat rejection

Calculation:

Given:

x = compression ratio, y = Expansion ratio, z = cut-off ratio.

we know that,

\(x = \frac{{{v_1}}}{{{v_2}}}\), \(z = \frac{{{v_4}}}{{{v_3}}}\) and \(y = \frac{{{v_5}}}{{{v_4}}}\)

⇒ \(y = \frac{{{v_1}}}{{{v_4}}}\)                    ( ∵ v₁ = v₅)

\( y= \frac{{{v_1}}}{{{v_2}}} \times \frac{{{v_2}}}{{{v_4}}}\)

\(y = \frac{{{v_1}}}{{{v_2}}} \times \frac{{{v_3}}}{{{v_4}}}\)                (∵ v₂ = v₃)

\(y = \frac{{\left( {\frac{{{v_1}}}{{{v_2}}}} \right)}}{{\left( {\frac{{{v_4}}}{{{v_3}}}} \right)}}\)

\( y = \frac{x}{{z\;}}\)

∴ x = yz