Project ForgeThermodynamics
First Law of Thermodynamics
GATE 2020
Hard
For an air-standard Diesel cycle with cut-off ratio rc=2 and ratio of specific heats γ=1.3, the compression ratio (CR) is increased from 15 to 21, keeping all other parameters identical. The difference between the new and the old efficiency values, (η_new|CR=21) − (η_old|CR=15), in percentage, is __________ (round off to one decimal place).
4.8 %(± 0.2 accepted)
Explanation
η = 1 − (1/r^(γ−1))×[(rc^γ−1)/(γ(rc−1))]. At r=15: r^0.3≈2.2534, term=1.4625/1.3≈1.1250, η_old≈1−(1/2.2534)(1.1250)≈50.07%. At r=21: r^0.3≈2.4926, η_new≈1−(1/2.4926)(1.1250)≈54.86%. Difference ≈54.86−50.07≈4.79%, rounds to 4.8%.
Source: GATE ME 2020 Session 2 (ME-2) (2020)
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