Triple Point and Humidity

Subject: Physics

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This note provides us an information about Triple Point and Humidity . In triple point the vaporization curve, fusion curve, and sublimation curve intersect and humidity is two type ,Relative Humidity, and Absolute humidity .
Triple Point and Humidity

Triple point

The triple point is a point in phase diagram representing a particular value of pressure and temperature at which the solid, liquid and gaseous state of the substance can co-exist. In triple point the vaporization curve, fusion curve, and sublimation curve intersect. A and A' are the triple point for water and carbon dioxide in phase diagram shown in the figure.

To figure out the triple point, three-dimensional diagram of pressure, volume and temperature are required. A two-dimensional P-T diagram is sufficient to discuss the phases of matter. Such P-T diagram is called phase diagram. Phase diagram is incomplete without following curves:

Vaporization curve

It is a graph between pressure and a boiling point of the substance in the liquid state.

(a) PT diagram for water, (b) PT diagram for carbondioxide
(a) PT diagram for water, (b) PT diagram for carbon dioxide

When the substances change from liquid to a vapour state, it crosses the vaporization line at a point. Staying at the point, the liquid absorbs required latent heat for phase change. At the pressure and temperature above the vaporization curve, the substance exists in the liquid state whereas as below the vaporization curve the substance exists in the gaseous state.

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Fusion curve

It is a graph between pressure and a melting point of the substance in a solid state. The fusion curve represents the variation of the melting point of the substance with pressure. Each point on the curve gives the value of the pressure and temperature at which the liquid and solid phase can co-exist. When the substance changes from solid to liquid state, it has to cross the fusion line at a point. Staying at a point, the substance in solid state absorbs required latent heat for the phase change. At the pressure and temperature on the left side of the fusion curve, the substance exists in the solid state whereas right-side of the fusion line, the substances exists in the liquid state.

Sublimation curve

It is a graph of pressure and temperature at which a solid directly changes into the vapour state. Each point on the curve gives the value of the pressure and temperature at which the vapour and solid phase can co-exist. When the substance changes from solid to vapour state, it has to cross the sublimation line at a point. For the substance above the sublimation curve, it shows solid state whereas below it shows gaseous state.

To prove that all the three curves meet at one point

The three curves AB< CD and EF come to meet at a single point. If they do not meet at a point, they are enclosed in an area AEC as shown in the figure.

pT diagram showing the three curves meeting at a single point.
pT diagram showing the three curves meeting at a single point.

Since area AEC lies above the vaporization line so it corresponds liquid state only, the area AEC lies below the fusion curve CD so it corresponds solid state only and area AEC lies below sublimation curve EF so it corresponds vapour state only.

It means area AEC is the common region for solid, liquid and gaseous state hence the three curves meet at a single.

Humidity

Humidity is an indicator of the amount of water vapour in the air.

Absolute humidity

The mass of water vapour present in 1 cubic meter of air is called absolute humidity of the air. It is commonly expressed in g/m3.

Relative Humidity

The ratio of the mass of water vapour, m present in a certain volume of air at room temperature to the mass of water vapour, M required to saturate the same volume of the air at the same temperature ie relative humidity. i.e.

$$\text {relative humidity} = \frac {m}{M} \times 100 \%$$

As the pressure exerted by vapour id directly proportional to the amount of vapour present in the given volume, the relative humidity may also be defined as

$$RH = \frac {\text{vapour pressure of air}} {\text {SVP at same temperature}} \times 100 \%$$

the vapour pressure of air at the actual temperature is equal to the saturated vapour pressure at the dew point. Thus, it is also

$$RH = \frac {\text{SPV at the dew point}} {\text {SVP at same temperature}} \times 100 \%$$

It is unitless quantity. The amount of vapour pressure near the sea-level is comparatively more and so is relative humidity.

Dew point

Dew point is the temperature at which water vapour present in the air is just sufficient to saturate it. So, the vapour pressure at room temperature is equal to the saturated vapour pressure at dew point.

Things to remember

Triple point is a point in phase diagram representing a particular value of pressure and temperature at which the solid, liquid and gaseous state of the substance can co-exist. 

Vaporization curve is a graph between pressure and boiling point of the substance in the liquid state. 

Fusion curve is a graph between pressure and melting point of the substance in solid state.

Sublimation curve is a graph between pressure and temperature at which a solid directly changes into vapour state. 

Humidity is an indicator of the amount of water vapour in the air.

The mass of water vapour present in 1 cubic meter of air is called absolute humidity of air. 

The ratio of the mass of water vapour, m present in certain volume of air at room temperature to the mass of water vapour, M required to saturate the same volume of the air at the same temperature ie relative humidity.

Dew point is the temperature at which water vapour present in the air is just sufficient to saturate it.

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