A design study sweeps the compression ratio of an air-standard Otto cycle at a fixed…
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · The laws of thermodynamics · The laws of thermodynamics
Thermal Physics, Ch Internal-combustion cycles and indicator diagrams
Problem
A design study sweeps the compression ratio of an air-standard Otto cycle at a fixed peak temperature. In every case the working substance is air treated as an ideal gas with constant γ=Cp/CV=1.40, the cycle is closed and quasistatic with no friction or heat leaks, the compression begins at T1=310K, and the constant-volume heat input brings the gas to the peak T3=2050K. The compression ratios studied are r=6, 10, 20 and 100. The same fixed mass of air, with the same CV, is used throughout.
((a)) Find the temperature T2 at the end of compression for each r.
((b)) Find the efficiency of each cycle.
((c)) Find the Carnot bound between the extreme temperatures of these cycles. Show from your numbers that eOtto=1−T1/T2, and write the gap eC−eOtto in terms of T1, T2 and T3.
((d)) The heat taken in per cycle is Qh=CV(T3−T2). Find the ratio Qh(r=100)/Qh(r=6), and say in one sentence what the sweep shows about approaching the bound this way.