A steam radiator in a room at 25^∘ C has saturated water vapor at 110 kPa flowing through it whe

step 1 Control volume radiator. After the valve is closed, no more flow. Constant volume and mass. 1. 1

A steam radiator in a room at 25^∘ C has saturated water...

A steam radiator in a room at $25^{\circ} \mathrm{C}$ has saturated water vapor at $110 \mathrm{kPa}$ flowing through it when the inlet and exit valves are closed. What are the pressure and the quality of the water when it has cooled to $25^{\circ} \mathrm{C} ?$ How much work is done?

Key Concepts

Saturation Properties

Saturated fluids are in equilibrium between the liquid and vapor phases at a given temperature and pressure. In thermodynamics, knowing the saturation properties allows you to determine the specific volumes and energies of the liquid and vapor phases. This information is crucial when analyzing changes in state during processes like cooling or heating of a saturated mixture.

Quality (Dryness Fraction)

Quality is defined as the mass fraction of vapor in a saturated mixture. It quantifies the proportion of a two-phase mixture that is in the vapor state versus the liquid state. The quality decreases when vapor condenses upon cooling, which is a central concept for determining the composition of the mixture after the process.

Constant Volume Process (Rigid Closed System)

When a system is closed and rigid—that is, its valves are closed so that no mass or volume change occurs—the process is conducted at constant volume (isochoric process). In such processes, any heat loss or gain results in changes in temperature and phase composition rather than volume, and importantly, no boundary work is performed since work is given by the integral ?PdV, which is zero when ?V = 0.

Phase Change and Condensation

Cooling a saturated vapor in a closed system leads to condensation, where some vapor turns into liquid as the temperature drops. Understanding phase change is key to predicting the new equilibrium state, including the final pressure and the reduced quality of the mixture after cooling.

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