The Lenoir cycle is a model for the operation of a combustion engine patented by Jean Joseph Etienne Lenoir in 1860 (Figs. 7.2 and 7.3). This idealised cycle is defined y three reversible processes:
• 1→ 2 isochoric compression
• 2→ 3 adiabatic expansion
• 3→ 1 isobaric contraction
Assume that the cycle is performed on an ideal gas characterised by the coefficient c found in relation (5.62). The following values of some state variables of the gas are assumed to be known: the pressure p₁, volumes V₁ and V₃, temperature T₁ and the number of moles of gas N. Analyse this cycle by using the following instructions :
a) Draw the (p, V) and (T, S) diagrams of the cycle.
b) Determine the entropy variation ΔS₁₂ of the gas during the isochoric process 1 → 2.
c) Express the temperature T₂ in terms of the heat exchanged Q₁₂ during the isochoric process 1 → 2.
d) Determine the pressure p2 in terms of the pressure p₁, the volume V₁ and the heat exchanged Q₁₂.
e) Determine the pressure p₃ in terms of the pressure p₂ and volumes V₂ and V₃.
f) Determine the work W₂₃ performed during the adiabatic process 2 → 3 and the heat Q₂₃ exchanged during this process.
g) Find the work W₃₁ performed during the isobaric process 3 → 1 and the heat Q₃₁ exchanged during this process.
h) Find the efficiency of the cycle η_L defined in conformity with relation (7.38) as,

Express the efficiency η_L in terms of the temperatures T₁, T₂ and T₃.

Figure 7.2

Figure 7.3

Transcribed Image Text:

ML W23 + W31 Q12