Mechanical Engineering - Thermodynamics - Discussion

For the same compression ratio, Otto cycle efficiency is more than diesel. But for maximum temperature and pressure efficiency of diesel cycle is more than otto cycle.

The entropy at 3 should be greater than entropy at 3'. It is clear that the heat rejection for Otto cycle is more than that of diesel cycle. Hence, for these conditions, the Diesel cycle is more efficient than the Otto cycle. The efficiency of Dual cycle lies between the two cycles.

For the same maximum pressure and heat input, the Otto cycle (1-2-3-4-1) and Diesel cycle (1-2'-3'-4'-1) are shown on the T-s diagram in the figure. It is evident from the figure that the heat rejection for Otto cycle (area 1-5-6-4 on T-s diagram) is more than the heat rejected in Diesel cycle (1-5-6'-4'). Hence the Diesel cycle is more efficient than the Otto cycle for the condition of same maximum pressure and heat input. One can make a note that with these conditions, the Diesel cycle has a higher compression ratio than that of the Otto cycle. One should also note that the cycle which is having higher efficiency allows maximum expansion. The Dual cycle efficiency will be between these two.

Therefore, ranking the three cycles on the basis on efficiencies,

Diesel Cycle > Dual Cycle > Otto Cycle

Case 2: Same Maximum Pressure and Work Output

The efficiency, η can be written as

Refer to T-s diagram. For same work output, the area 1-2-3-4 (work output of Otto cycle) and area 1-2'-3'-4' (work output of Diesel cycle) are same. To achieve this, the entropy at 3 should be greater than entropy at 3' .It is clear that the heat rejection for the Otto cycle is more than that of the diesel cycle. Hence, for these conditions, the Diesel cycle is more efficient than the Otto cycle. The efficiency of Dual cycle lies between the two cycles.

Therefore, ranking the three cycles on the basis of efficiencies,

Diesel Cycle > Dual Cycle > Otto Cycle

Note: We cannot compare Rankine cycle with Gas Power cycles (Otto, Diesel Dual), since it is a steam cycle and the working medium for a steam cycle is water. Water in the steam cycle has a much lower temperature and pressure than air standard cycles and thus cannot be compared with them.

Also, the Brayton cycle is meant for much larger heat engines and cannot be compared to the much smaller Otto, Diesel and Dual Cycle Engines.

Please explain the right answer.

Simply plotting a common P-V and T-s diagram for Otto and Diesel cycle for same Peak temperature and pressure, you can see that Diesel engine is more efficient. So, B is the right answer.