A piston/cylinder has 100 kg saturated moist air at 100 kPa, 5^∘ C. If it is heated to 45^∘ C i

step 1 So let's solve this question. So in this question we have pv1 by p total, p total minus pv1 equa

A piston/cylinder has 100 kg saturated moist air at 100...

A piston/cylinder has $100 \mathrm{~kg}$ saturated moist air at $100 \mathrm{kPa}, 5^{\circ} \mathrm{C}$. If it is heated to $45^{\circ} \mathrm{C}$ in an isobaric process, find ${ }_{1} Q_{2}$ and the final relative humidity. If it is compressed from the initial state to $200 \mathrm{kPa}$ in an isothermal process, find the mass of water condensing.

Key Concepts

Moist Air Properties

Moist air is a mixture of dry air and water vapor where the thermodynamic properties of the mixture depend on the composition. Key parameters include the humidity ratio, relative humidity, and the state of saturation. Understanding these properties is crucial when analyzing processes involving phase changes or heating/cooling of the air–vapor mixture.

Saturated Vapor Pressure

Saturated vapor pressure is the pressure exerted by the vapor in equilibrium with its liquid at a given temperature. It is a fundamental concept in thermodynamics that determines whether the air is in a saturated state. The value changes with temperature, and any additional water vapor beyond this limit leads to condensation.

Relative Humidity

Relative humidity is the ratio of the actual partial pressure of water vapor in the air to the saturated vapor pressure at the same temperature, expressed as a percentage. It indicates how close the air is to becoming saturated and is key to predicting condensation when conditions change, such as during heating or compression.

Isobaric Process

An isobaric process is one that occurs at constant pressure. In the context of moist air, heating under constant pressure alters the temperature and the capacity of the air to hold water vapor. This affects the relative humidity and can lead toward a drier or more saturated state depending on the thermal energy added.

Isothermal Process

An isothermal process is one that occurs at a constant temperature. In such a process, while the temperature remains unchanged, changes in pressure or volume can lead to phase changes in the moist air. Compression, for instance, may increase the partial pressure of water vapor beyond the saturation limit at the fixed temperature, resulting in condensation.

Condensation in Moist Air

Condensation occurs when the air cannot maintain all its water vapor in the gas phase because the conditions (typically temperature and pressure) force the vapor pressure to exceed the saturation value. This excess vapor condenses into liquid water. Calculating the mass of condensed water requires analyzing the change in the saturation condition and the water vapor content before and after the process.

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