# Estimating temperature inside a cylinder of an internal combustion engine

Estimate the temperature inside a cylinder of an internal combustion engine just after the spark has ignited the fuel. You are provided with the following list of assumptions. Assume the cylinder has a volume of 10 liters. Assume that the oxidant is air containing 20% oxygen. Assume that the fuel is octane (C9H18, molar mass = 114 g/mol) with an energy content of 47.7 kJ/g. Assume that the combustion is complete and uses all of the oxygen in the cylinder based on an intake temperature of 298 K and an intake pressure of 1 atmosphere. Assume that the constant-volume heat capacities of carbon dioxide, water, and nitrogen are respectively 45, 35, and 25 J/mol/K.

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#### Solution Preview

This problem is multi-part. Let's start by trying to dissect it in to little parts.

1. We know that the energy comes out of the combustion of the fuel. We also know that the fuel reacts with oxygen to give off the energy. Since this is an isolated system we also know that any energy given off by the fuel will be absorbed by H2O, CO2 and N2 which are the 3 gases mentioned in our problem. We might be asking ourselves why so far... I'll explain in a second. Note that usually the heat is also taken out by the walls of your system (the engine in this case), but since we are not given any constant for the engine intake of energy we will assume it negligible.

2. We also know that the fuel is ...

#### Solution Summary

This solution is 524 words and discusses the energy in the system, moles of the gases, and energy equations, as well as the final calculation for finding temperature.