Consider two engines operating on Otto and Diesel air-standard cycles with the same compression ratio.

Which of the following is/are TRUE about the thermal efficiency ($\eta$) and the peak pressure ($p_{peak}$)?

Question

A single degree of freedom system is undergoing free oscillation. The natural frequency and damping ratio of the system are $1$ rad/s and $0.01$ respectively. The reduction in peak amplitude over three cycles is __________% (rounded off to one decimal place).

Answer 1

Both engines start from the same state and compress the charge through the same compression ratio, so the difference between them comes only from how heat is added after compression.

$\eta_{Otto} < \eta_{Diesel}$: Wrong. At equal compression ratio the Diesel cycle always carries a correction factor below 1 in its efficiency formula, which pulls its efficiency under the Otto value.
$\eta_{Otto} > \eta_{Diesel}$: Correct. Constant volume heat addition in the Otto cycle uses the compression ratio more effectively than the constant pressure addition in the Diesel cycle, so Otto wins on efficiency here.
$(p_{peak})_{Otto} > (p_{peak})_{Diesel}$: Correct. Since heat is added at constant volume in the Otto cycle, pressure rises steeply right after compression, producing a higher peak than the Diesel cycle where pressure stays flat during heat addition.
$(p_{peak})_{Otto} = (p_{peak})_{Diesel}$: Wrong, the peak pressures are not equal for the reason given above.

So the correct choices are B and C.

Answer 2

Both engines start from the same state and compress the charge through the same compression ratio, so the difference between them comes only from how heat is added after compression.

$\eta_{Otto} < \eta_{Diesel}$: Wrong. At equal compression ratio the Diesel cycle always carries a correction factor below 1 in its efficiency formula, which pulls its efficiency under the Otto value.
$\eta_{Otto} > \eta_{Diesel}$: Correct. Constant volume heat addition in the Otto cycle uses the compression ratio more effectively than the constant pressure addition in the Diesel cycle, so Otto wins on efficiency here.
$(p_{peak})_{Otto} > (p_{peak})_{Diesel}$: Correct. Since heat is added at constant volume in the Otto cycle, pressure rises steeply right after compression, producing a higher peak than the Diesel cycle where pressure stays flat during heat addition.
$(p_{peak})_{Otto} = (p_{peak})_{Diesel}$: Wrong, the peak pressures are not equal for the reason given above.

So the correct choices are B and C.

Consider two engines operating on Otto and Diesel air-standard cycles with the same compression ratio.

Which of the following is/are TRUE about the thermal efficiency (\(\eta\)) and the peak pressure (\(p_{peak}\))?

Show Hint

The Correct Option is B, C

Solution and Explanation

Top Questions on Air Standard Cycles

Questions Asked in GATE NM exam

Consider two engines operating on Otto and Diesel air-standard cycles with the same compression ratio.Which of the following is/are TRUE about the thermal efficiency (\(\eta\)) and the peak pressure (\(p_{peak}\))?