A cylinder fitted with a piston contains propane gas at 100 kPa and 300 K with a volume of 0.2 m

step 1 Here the process equation and T determines states to use ideal guess law to say P2 is equal to P

A cylinder fitted with a piston contains propane gas at 100...

A cylinder fitted with a piston contains propane gas at $100 \mathrm{kPa}$ and $300 \mathrm{K}$ with a volume of 0.2 $\mathrm{m}^{3} .$ The gas is now slowly compressed according to the relation $P V^{\mathrm{l} .1}=$ constant to a final temperature of $340 \mathrm{K}$. Justify the use of the ideal-gas model. Find the final pressure and the work done during the process.

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Key Concepts

Ideal Gas Model

The ideal gas model assumes that gas molecules have negligible volume and that there are no intermolecular forces acting between them. This model is applicable when the gas is at a relatively low pressure and high temperature compared to its critical values, conditions under which real gases behave similarly to ideal gases. This simplification allows for the use of the ideal gas law (PV = nRT) to relate pressure, volume, and temperature.

Polytropic Process

A polytropic process is one in which the pressure and volume of a system follow the relation PV^n = constant, where n is the polytropic index. This general process model encompasses a variety of process types, including isothermal (n = 1) and adiabatic (n = specific heat ratio) processes. It provides a flexible framework for analyzing systems where heat transfer might occur.

Work in Thermodynamic Processes

In thermodynamics, the work done by or on a system during a quasi-static process is determined by integrating the pressure with respect to volume. For processes following specific paths, such as polytropic processes, the integration can be performed using the defined relationship between pressure and volume, leading to specialized formulas that simplify the calculation of work done during compression or expansion.

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