Subtopic: Power transmission systems – gear trains, differential, final drives and power take-off
Question Statement:
In a diesel engine with variable compression ratio, the initial compression ratio is 16:1. The ratio of specific heats is 1.4. For the same cut-off ratio of 4.0, if the compression ratio is increased by 25%, the air standard thermal efficiency of the engine will be
Options:
(A) increased by 1.0%
(B) increased by 2.8%
(C) increased by 3.5%
(D) increased by 4.0%
Official Answer Key:
D
Step-by-Step Solution & Explanation
Diesel-cycle air-standard efficiency: η = 1 − (1/r^(γ-1))·[(ρ^γ − 1)/(γ(ρ−1))], with cut-off ratio ρ=4.0, γ=1.4. For r₁=16: η₁ = 1 − (1/16^0.4)·[(4^1.4−1)/(1.4×3)] = 1 − 0.3305×0.6811×... = 0.5315 (53.15%). For r₂ = 16×1.25 = 20: η₂ = 1 − (1/20^0.4)·[same bracket] = 0.5715 (57.15%). η₂ − η₁ = 0.5715 − 0.5315 = 0.0400 → a 4.0 percentage-point increase, matching option (D). (Read as a relative increase, (η₂−η₁)/η₁ ≈ 7.5%, which is not among the options — the paper intends the absolute percentage-point change.)
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