GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

Question : 58 of 65

Marks: +1, -0

Keeping all other parameters identical, the Compression Ratio (CR) of an air standard diesel cycle is increased from 15 to

21 .

Take ratio of specific heats

=1.3

and cut-off ratio of the cycle

r_{c}=2

The difference between the new and the old efficiency values, in percentage,

(η_{\;\text "new "\;}|_{C R-21})-(η_{01 d}|_{C R-15})=

_____________________ % (round off to one decimal place).

Solution:

η_{1}=1-\;{1}/{(r_{1})^{γ-1} γ}[\;{ρ^{y}-1}/{ρ-1}]

=1-\;{1}/{(15)^{1.3-1} × 1.3}[\;{2^{1.3}-1}/{2-1}]

=1-0.341[1.4611]=50.08 \%

η_{2}=1-\;{1}/{(r_{2})^{γ-1} γ}[\;{ρ^{γ}-1}/{ρ-1}]

=1-\;{1}/{(21)^{1.3-1} × 1.3}[\;{2^{1.3}-1}/{2-1}]

=1-0.3085(1.4622)

=54.89 \%

Difference in efficiencies

=η_{2}-η_{1}=54.89-50.08

=4.81 \%

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