Variation with Vapour Pressure with Volume

Subject: Physics

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Overview

Water vapour condenses from the saturated air and saturation varies with temperature. So cooling down a sample air often results in condensation of water molecules. The formation of clouds and rain is governed by these effects. Actually, the boiling point of a liquid depends on the external pressure over its surface. The liquid boils at a temperature when its saturated vapour pressure is equal to the external pressure.
Variation with Vapour Pressure with Volume

Introduction

Hygrometry is a branch of physics which deals with dampness of air (i.e. amount of water vapour). Water vapour condenses from the saturated air and saturation varies with temperature. So cooling down a sample air often results in condensation of water molecules. The formation of clouds and rain is governed by these effects.

Saturated and Unsaturated Vapour

(a) Unsaturated vapour (b) Saturated vapour
(a) Unsaturated vapour (b) Saturated vapour

Let us consider two barometer tubes X and Y each of length about 1 m filled with mercury, when the tubes are inverted into the trough containing mercury, the mercury level in the tube falls down so that a vacuum is created there. The vacuum is called toricellian vacuum. The height of mercury in the tube from mercury level in the trough measures the atmospheric pressure. Let us introduce few drops of water in water in Y by means of a pipette, water rises in it as water is lighter than mercury and vaporises there. So, mercury level falls in tube Y. Here difference in the mercury levels of Y and X measures vapours pressure. Vapour so produced in tube Y is called unsaturated vapour and pressure given by it is called unsaturated vapour pressure.

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If more water drops are introduced in B, the mercury level will fall more which shows that vapour increases with increase in water vapour. Now water drops do not evaporate and mercury level remains steady. As no more evaporation takes place and vapours are in contact with its liquid, the vapour is called saturated vapour pressure. This is measured by the difference of mercury levels in tube X and Y in fig.

Variation with Vapour Pressure with Volume

variation of Vapour pressure with volume
variation of Vapour pressure with volume

Let us take a barometer trough X and Y, filled with mercury inverted in a trough. Here X has Torricelli an vacuum and Y has unsaturated water vapour. When volume of unsaturated vapour is decreased by lowering the tube Y in the mercury, the pressure increases with the decrease in the volume and reaches to point B from A. The difference in the levels of mercury in the tube X and Y shows unsaturated vapour pressure. On further decreasing of the volume, a point B is reached at which the vapour is saturated and exerts maximum pressure. There is no change in pressure on further decreasing of volume and a vapour condenses into water vapour. As shown in the figure.

Variation with Vapour Pressure with Temperature

(a) Experiment arrangement for variation in vapour pressure with temperature (b) Variation of vapour pressure with temperature
(a) Experiment arrangement for variation in vapour pressure with temperature (b) Variation of vapour pressure with temperature

Let us take two barometer tube X and Y, filled with mercury inverted in a trough. Here X has toricellian vacuum and Y has unsaturated vapour. Both tubes are enclosed by wider gas tube containing water which can be heated with a heating coil and temperature can be noted with thermometer.

Water is heated to about 80 oC. The vapour in Y at higher temperature becomes an unsaturated and vapour pressure increases. When temperature decreases vapour pressure also decreases in Y.

Behaviour of saturated vapour pressure

  1. The saturated vapour pressure depends on the nature of the substance.
  2. The saturated vapour pressure of a liquid depends on its temperature. The saturated vapour pressure increases with increase in temperature and decreases with decrease in temperature.
  3. The saturated vapour pressure is always greater than unsaturated vapour pressure.
  4. It does not depend on the volume occupied by the vapours.
  5. It is independent of the pressure of vapours of other liquid present. The vapours should not have any chemical reaction.
  6. The total pressure exerted by the vapours of all substances is equal to the sum of the pressure exerted by the vapour of the individual substance i.e. P = P1+ P2+ P3 …..
  7. The saturated vapour does not obey the gas laws whereas unsaturated vapour obeys the gas laws.
(a) P-V diagram, (b) P-t diagram
(a) P-V diagram, (b) P-t diagram

In figure a) curve AB shows that pressure increases with decrease in volume. From A to B graph follows Boyle's law. At point B, the vapour is unsaturated and exerts maximum pressure. Beyond B with decrease in volume, pressure remains constant. From B to Cgraph represents the change from the saturated vapour to the liquid state.

In figureb) curve AB shows that pressure increases with increase in temperature. From A to B vapour is saturated. Beyond B with increase in Temperature the vapour pressure becomes unsaturated and pressure increase with increase in temperature. In BC, the pressure of unsaturated vapour is directly proportional to its absolute temperature.

Effect of Pressure on Boiling Point

The boiling point of a liquid increases with increase in pressure and vice-versa. So, water boils at higher temperature at sea level and lower temperature at high altitudes. The atmospheric pressure decreases with increase in height from earth's surface.

Actually, the boiling point of a liquid depends on the external pressure over its surface. Liquid boils at a temperature when its saturated vapour pressure is equal to the external pressure.

Things to remember
  1. The total pressure exerted by the vapours of all substances is equal to the sum of the pressure exerted by the vapour of the individual substance i.e. P = P1+ P2+ P3 …..
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