How Does a Six-Stroke Otto-Cycle Engine Perform?

[prudence3]

Homework Statement

A six-stroke engine (Otto-cycle) with 78.4 mm bore, 83.3 mm stroke, 10.7 compression ratio.
Suppose the initial state in the stroke is 1.0 atm (at room temperature).

1. Calculate the work done during an engine cycle.
2. Calculate how muck energy is released to air.
3. Estimate the efficiency. (5500rpm)

Homework Equations

1. I found a http://www.grc.nasa.gov/WWW/K-12/airplane/ottoa.html" .
2. Haven't found yet.
3. Haven't found yet.

The Attempt at a Solution

1. I use the equation mentioned in the above website.
But I don't know the ratio of specific heats.
There are gasoline and air in a stroke, which value should I use?
2. I think the energy generated by the engine is distributed to (1) the kinetic energy of the car. (2) the friction energy in the engine. (3) the remaining energy which I need to find.
How to find these?
3. I think the efficiency is the (the kinetic energy of the car)/(work done during an engine cycle). If I can solve question 1&2, I think the efficiency can be derived.

Thanks for your help!

 

[KataKoniK]

Thank you for your post. I would like to provide some guidance on how you can approach this problem.

1. To calculate the work done during an engine cycle, you can use the formula for the Otto cycle as mentioned in the website you provided. The ratio of specific heats, also known as the adiabatic index, can vary depending on the composition of the fuel and air mixture. For gasoline and air, the adiabatic index is typically around 1.4. You can use this value in your calculation.

2. To calculate the energy released to the air, you can use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In this case, the heat added to the system is the energy released by the fuel combustion, and the work done by the system is the work done during the engine cycle.

3. To estimate the efficiency, you can use the formula for efficiency, which is the ratio of the output energy (in this case, the kinetic energy of the car) to the input energy (in this case, the energy released during the engine cycle). You can use the values calculated in question 1 and 2 to find the efficiency.

I hope this helps. Good luck with your calculations!

 

[Mene]

I would like to clarify a few things before providing a response to the content. Firstly, the efficiency of an engine is a measure of how well it converts the energy from fuel into useful work. It is typically expressed as a percentage and can be calculated using the formula: Efficiency = (useful energy output / energy input) x 100%. Secondly, the work done by an engine is the amount of energy it produces during a cycle, and it is directly related to the efficiency of the engine.

Now, to address the questions:

1. To calculate the work done during an engine cycle, we need to know the pressure and volume at each stage of the cycle. The website you mentioned provides an equation for this, but it requires the ratio of specific heats, which can vary depending on the composition of the fuel and air mixture. The most accurate way to determine this ratio would be to analyze the fuel and air mixture using a gas chromatograph. However, for the purpose of this calculation, an average value of 1.4 can be used for gasoline and air. With this, you can calculate the work done using the formula provided on the website.

2. The energy released to the air can be calculated by subtracting the energy input (from the fuel) from the energy output (from the work done during the cycle). This energy is typically released in the form of heat and can be used to calculate the thermal efficiency of the engine.

3. The efficiency of the engine can be estimated by using the formula mentioned earlier. However, it is important to note that this is a theoretical value and the actual efficiency of the engine may be lower due to factors such as friction, heat loss, and incomplete combustion.

In conclusion, to accurately calculate the work and efficiency of the engine, we would need more information about the fuel and air mixture, as well as the specific design of the engine. However, with the provided information, an estimate can be made using the methods mentioned above.