A vertical cylinder (Fig. P4.106) has a 61.18 kg piston locked with a pin, trapping 10 L of R-22

step 1 In state 1, in state 1, TX from table we have V1 is equal to 0 .008 plus 0 .9 into 0 .3391. We g

A vertical cylinder (Fig. P4.106) has a 61.18 kg piston...

A vertical cylinder (Fig. P4.106) has a $61.18 \mathrm{kg}$ piston locked with a pin, trapping $10 \mathrm{L}$ of $\mathrm{R}-22$ at $10^{\circ} \mathrm{C}$ with $90 \%$ quality inside. Atmospheric pressure is $100 \mathrm{kPa}$, and the cylinder cross-sectional area is $0.006 \mathrm{m}^{2}$. The pin is removed, alloving the piston to move and come to rest with a final temperature of $10^{\circ} \mathrm{C}$ for the $\mathrm{R}-22 .$ Find the final pressure, final volume, and work done by the R-22.

Key Concepts

Two?Phase Mixture Quality

This concept refers to the definition and use of “quality” in a saturated liquid–vapor system. Quality, defined as the mass fraction of vapor in the mixture, is essential for determining the overall properties (such as specific volume, enthalpy, etc.) of a two?phase system when the individual saturated properties of the liquid and vapor phases are known.

Pressure Force Equilibrium in Piston Systems

In a piston–cylinder assembly, the pressure inside the cylinder must balance the forces acting on the piston, including the piston’s weight and any external pressure such as atmospheric pressure. This equilibrium condition is used to determine the pressure of the gas or vapor inside the cylinder once mechanical equilibrium is reached.

Work in Piston?Cylinder Devices

Work in systems with movable boundaries, like a piston–cylinder device, is associated with the boundary work done as the volume of the system changes. The work performed by the working fluid is typically calculated by integrating the pressure over the change in volume, and its sign convention depends on whether the system is expanding or compressing.

Isothermal Process

An isothermal process is one that occurs at a constant temperature. When a system undergoes a change at a constant temperature, the thermodynamic properties are interrelated in a way that simplifies the analysis. In piston–cylinder problems, a constant temperature process allows the assumption that the saturation conditions remain at the given temperature, which can be used in conjunction with the equilibrium conditions to determine other state properties.

Thermodynamic Property Relationships for Refrigerants

Refrigerants such as R?22 have well?documented thermodynamic properties that vary with temperature and pressure. These property relationships, often provided in tables or charts, are key for analyzing phase-change problems, assessing the state of a two?phase mixture, and performing energy and work calculations in refrigeration cycles and piston–cylinder systems.

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