The combustion in a gasoline engine may be approximated by a...

The combustion in a gasoline engine may be approximated by a constant-volume heat addition process. The cylinder contains the air-fuel mixture before combustion and the combustion gases after it, and both may be approximated as air, an ideal gas. In a gasoline engine, the cylinder conditions are $1.2 \mathrm{MPa}$ and $450^{\circ} \mathrm{C}$ before the combustion and $1900^{\circ} \mathrm{C}$ after it. Determine the pressure at the end of the combustion process.

The combustion in a gasoline engine may be approximated by a constant-volume heat addition process. The cylinder contains the air-fuel mixture before combustion and the combustion gases after it, and both may be approximated as air, an ideal gas. In a gasoline engine, the cylinder conditions are $1.2 \mathrm{MPa}$ and $450^{\circ} \mathrm{C}$ before the combustion and $1900^{\circ} \mathrm{C}$
after it. Determine the pressure at the end of the combustion process.

Key Concepts

Constant-Volume Process

A constant-volume process is one in which the volume of the system remains unchanged throughout the process. In thermodynamics, such processes simplify analysis because the work done by or on the system is zero, allowing energy changes to be directly linked to heat transfer and changes in pressure and temperature. This is particularly useful when modeling rapid processes where the volume does not change appreciably, as seen in internal combustion engine approximations.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental relation that connects pressure, volume, temperature, and the amount of gas. This law provides a useful approximation for the behavior of gases under many conditions, and it allows for the analysis of state changes in processes with fixed volume. By using the law, relationships between pressure and temperature during processes like combustion can be directly assessed.

Pressure-Temperature Relationship in a Constant-Volume Process

In a constant-volume process involving an ideal gas, the pressure is directly proportional to the absolute temperature (P ? T). This means that if the temperature increases, the pressure will increase as well, provided the volume and the number of moles of gas remain constant. This proportionality is central to analyzing how combustion, modeled as a constant-volume heat addition process, affects the pressure inside an engine cylinder.

Temperature Conversion to Absolute Scale

When applying the ideal gas law and related formulas, temperatures must be expressed on an absolute scale, typically in Kelvin, to ensure accuracy. Converting temperatures from Celsius to Kelvin involves adding 273.15 to the Celsius value. This conversion is crucial for correctly applying the direct proportionality between pressure and temperature in thermodynamic calculations.

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