Discussion
In a spark ignition engine working on ideal Otto cycle, the compression ratio is 5.5. The work output per cycle (i.e, area of the P-V diagram) is equal to 23.625×105×Vc J, where Vc is the clearance volume in m3. The indicated mean effective pressure is :
Answer: C
The indicated mean effective pressure is 5.250 bar.
Mean effective pressure is the work per cycle divided by the swept volume. With compression ratio r, the total volume is \(rV_c\), so the swept volume is \((r - 1)V_c\):
\[ \begin{aligned} V_s &= (5.5 - 1)V_c = 4.5V_c \\ p_m &= \frac{23.625 \times 10^5\, V_c}{4.5\, V_c} \\ &= 5.25 \times 10^5\ \text{Pa} = 5.25\ \text{bar} \end{aligned} \]
Dividing by the total volume, \(5.5V_c\), gives the 4.295 bar option, and multiplying by 4.5 instead of dividing gives 106.3 bar. The clearance volume cancels, which is why the answer can be found without knowing it.
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