Solve Otto Cycle Problem: Max Pressure Lambo Murcielago w/r=11.0

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In summary, the cylinder head of a Lamborghini Murcielago with a compression ratio of 11.0 must be able to withstand a minimum temperature of 300K and an initial pressure of 1 atm using the assumptions that the fuel/air mixture must reach 680K for combustion to occur.
  • #1
NavalChicken
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Homework Statement


(a.) This was just a log-log plot of the otto cycle
(b.) Derive an expression for the ratio of maximum to minimum temperature experienced by the cylinder head during the part of the cycle that contains only isochoric and and adiabatic transitions in terms of the compression ratio and the ratio of the maximum to
minimum pressure.

(c.) What is the maximum pressure that the cylinder head of a Lamborghini Murcielago with compression ratio r = 11.0, must be able to withstand using these assumptions and [tex] \gamma = 1.4 [/tex], if the fuel/air mixture must reach 680K for combustion to occur. Assume the minimum temperature is 300 k and the initial pressure is 1 atmosphere.

The Attempt at a Solution



For part (b.) I get

[tex] \frac {\theta_3}{\theta_1} = \frac {P_3}{P_1}r^{-1} [/tex]

That was just using

[tex] PV = nRT [/tex]

which seemed like very little work for a 3 mark question. I tried it a few other ways, using [tex] PV^{\gamma} [/tex] and such and came out with the same answer each way I tried it. So, that suggests that its the right answer, but I'm not entirely convinced.

My major problem is in part C. Where 680 K is given, I presumed this was [tex] \theta_2 [/tex] since it is the temperature required for combustion to occur. From there I went round and round in circles trying to get an expression with variables given in the question, but couldn't seem to quite get there. I always have at least one other unknown in the question! This part is only a 2 mark question, so it doesn't seem like it should require that much work. Part of me is wanting to say 680 K is [tex] \theta_3 [/tex] and work out the value of P3 quite easily from that, but the wording of the question suggests it isn't.

Any advice?
Thanks
 
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  • #2
My advice would be to email Adrian Skelton complaining about the standard of the lecturer!
 
  • #3
Haha, excellent. I basically just handed in a load of rubbish!
 

What is the Otto Cycle Problem?

The Otto Cycle Problem is a theoretical thermodynamic process that describes the idealized performance of a spark-ignition internal combustion engine. It involves four steps: intake, compression, power, and exhaust.

What is the Max Pressure for a Lambo Murcielago with a Compression Ratio of 11.0?

The maximum pressure for a Lambo Murcielago with a compression ratio of 11.0 would depend on various factors such as the fuel used, engine design, and operating conditions. It is typically between 100-150 bar.

How does the Compression Ratio affect the Max Pressure?

The compression ratio has a direct impact on the maximum pressure achieved during the power stroke. A higher compression ratio results in a higher maximum pressure, leading to better engine performance and efficiency.

What are the limitations of solving the Otto Cycle Problem for a specific car model?

Solving the Otto Cycle Problem for a specific car model is a theoretical exercise that does not account for various real-world factors such as engine wear, fuel quality, and driving conditions. It also assumes ideal engine performance, which may not be achievable in reality.

How can solving the Otto Cycle Problem help improve engine performance?

Solving the Otto Cycle Problem can help identify the optimal operating conditions for an engine and provide insights into how different design and operational changes can impact performance. It can also aid in the development of more efficient and powerful engines.

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