Without turbo, ambient air density was 1.18 kg/m³. Density ratio = 1.56/1.18 = 1.32 → 32% more air molecules.
Kael calculated: Using (η_t = (T₁ - T₂_actual)/(T₁ - T₂_ideal)), he found that 68% of the exhaust’s enthalpy (h = u + Pv) converted into shaft work. The rest became entropy—random molecular motion—which heated the turbine housing.
For air, γ = 1.4, so (0.4/1.4) = 0.286. turbo physics grade 12 pdf
Power_compressor = ṁ_air × cp_air × (T_out – T_in) / η_mech
“More air means more fuel can be burned,” Kael said. “That’s the power gain.” But 135°C air caused engine knock. Dr. Vane handed him an intercooler—an air-to-air radiator. After the intercooler, temperature dropped to 45°C while pressure only dropped to 1.7 atm. Without turbo, ambient air density was 1
He applied the (from the First Law of Thermodynamics, ΔU = Q – W, with Q=0 for rapid compression):
Density ratio vs. ambient: 1.89/1.18 = 1.60 → 60% more air. “That’s the power gain
New density at 1.7 atm, 45°C (318 K): ρ = (1.7×101325)/(287×318) ≈ 172252/91266 ≈ 1.89 kg/m³