# Otto Cycle Problem

## 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 $$\gamma = 1.4$$, 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

$$\frac {\theta_3}{\theta_1} = \frac {P_3}{P_1}r^{-1}$$

That was just using

$$PV = nRT$$

which seemed like very little work for a 3 mark question. I tried it a few other ways, using $$PV^{\gamma}$$ 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 $$\theta_2$$ 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 $$\theta_3$$ and work out the value of P3 quite easily from that, but the wording of the question suggests it isn't.

Thanks