Question:
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 (\(p_{peak}\))?
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 (\(p_{peak}\))?
Which of the following is/are TRUE about the thermal efficiency (\(\eta\)) and the peak pressure (\(p_{peak}\))?
Show Hint
Compare how pressure and efficiency behave for constant volume heat addition versus constant pressure heat addition at the same compression ratio.
Updated On: Jul 28, 2026
- \(\eta_{Otto} < \eta_{Diesel}\)
- \(\eta_{Otto} > \eta_{Diesel}\)
- \((p_{peak})_{Otto} > (p_{peak})_{Diesel}\)
- \((p_{peak})_{Otto} = (p_{peak})_{Diesel}\)
Show Solution
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The Correct Option is B, C
Solution and Explanation
Step 1: Compare the heat addition process in each cycle.
Both cycles start compression from the same state and use the same compression ratio \(r\), so after isentropic compression they reach the same pressure and temperature at state 2.
In the Otto cycle heat is added at constant volume, while in the Diesel cycle heat is added at constant pressure.
Step 2: Compare the thermal efficiency.
The Otto cycle efficiency is \(\eta_{Otto} = 1 - r^{1-\gamma}\), while the Diesel cycle efficiency is \(\eta_{Diesel} = 1 - r^{1-\gamma}\left[\dfrac{\rho^{\gamma}-1}{\gamma(\rho-1)}\right]\), where \(\rho\) is the cutoff ratio.
The bracket term in the Diesel expression is always greater than 1 for \(\rho > 1\), so it pulls the Diesel efficiency below the Otto value for the same compression ratio.
This gives \(\eta_{Otto} > \eta_{Diesel}\), so option B is correct and option A is wrong.
Step 3: Compare the peak pressure.
Both cycles reach the same pressure \(p_2\) after compression.
In the Otto cycle, heat is added while volume stays fixed, so pressure jumps sharply to a high peak \(p_3\).
In the Diesel cycle, heat is added at constant pressure, so the pressure stays at \(p_2\) during heat addition, giving a lower peak than the Otto cycle.
Final Answer:
The Otto cycle gives both higher efficiency and higher peak pressure than the Diesel cycle at the same compression ratio.
\[ \boxed{\text{B, C}} \]
Both cycles start compression from the same state and use the same compression ratio \(r\), so after isentropic compression they reach the same pressure and temperature at state 2.
In the Otto cycle heat is added at constant volume, while in the Diesel cycle heat is added at constant pressure.
Step 2: Compare the thermal efficiency.
The Otto cycle efficiency is \(\eta_{Otto} = 1 - r^{1-\gamma}\), while the Diesel cycle efficiency is \(\eta_{Diesel} = 1 - r^{1-\gamma}\left[\dfrac{\rho^{\gamma}-1}{\gamma(\rho-1)}\right]\), where \(\rho\) is the cutoff ratio.
The bracket term in the Diesel expression is always greater than 1 for \(\rho > 1\), so it pulls the Diesel efficiency below the Otto value for the same compression ratio.
This gives \(\eta_{Otto} > \eta_{Diesel}\), so option B is correct and option A is wrong.
Step 3: Compare the peak pressure.
Both cycles reach the same pressure \(p_2\) after compression.
In the Otto cycle, heat is added while volume stays fixed, so pressure jumps sharply to a high peak \(p_3\).
In the Diesel cycle, heat is added at constant pressure, so the pressure stays at \(p_2\) during heat addition, giving a lower peak than the Otto cycle.
Final Answer:
The Otto cycle gives both higher efficiency and higher peak pressure than the Diesel cycle at the same compression ratio.
\[ \boxed{\text{B, C}} \]
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