A research engine is charged with argon

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 research engine is charged with argon, a monatomic ideal gas with γ=5/3\gamma = 5/3 and constant heat capacities. It is analysed as an air-standard Otto cycle: a fixed mass of gas taken quasistatically round 1→21\to2 adiabatic compression through a volume ratio r=V1/V2r = V_1/V_2, 2→32\to3 heat in at constant volume, 3→43\to4 adiabatic expansion back to V1V_1, 4→14\to1 heat out at constant volume; no friction and no heat leaks. Here r=9r = 9. ((a)) Starting from Qh=CV(T3−T2)Q_h = C_V(T_3 - T_2), Qc=CV(T4−T1)Q_c = C_V(T_4 - T_1) and the adiabatic relation TVγ−1=constTV^{\gamma-1} = \text{const}, derive eOtto=1−r1−γe_{\rm Otto} = 1 - r^{1-\gamma}. ((b)) Evaluate the efficiency for this engine. ((c)) The gas is at 300 K300\ \mathrm{K} at the start of compression and the peak temperature is 2000 K2000\ \mathrm{K}. Find the temperature at the end of compression and the temperature at the end of the expansion.

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