Hygrometry | Triple point | Conceptual notes | Short answer questions and numerical problem solutions | Grade 11 NEB (Physics) | Physics in Depth

Hygrometry

• Hygrometry is the branch of physics that deals with the amount of water vapour present in the atmosphere.



• When the space contains the maximum possible amount of water vapour it can hold at the given temperature, the vapour is called saturated vapour.



• When the space contains less than the maximum possible amount of water vapour it can hold at the given temperature, the vapour is called unsaturated vapour.



• The pressure exerted by a saturated vapour is called saturated vapour pressure . It is denoted by the symbol SVP. The saturation vapour pressure of a substance is constant at a given temperature. It increases when the temperature is increased.



• Boling :
  If we heat the liquid, the average kinetic energy of the entire liquid increases and at a certain stage the energy becomes sufficient to break the molecular attraction. The molecules anywhere in the liquid can form vapour bubbles. These bubbles float to the surface of the liquid and finally come out of the liquid. This phenomenon is called boiling and the temperature at which boiling occurs is called boiling point. In evaporation, only the molecules near the surface which have kinetic energy greater than the average escape from the liquid, whereas, in boiling, the molecules all over the liquid gain enough energy to become vapour.
  The boiling point of a liquid depends on the external pressure over its surface. Boiling occurs at a temperature where the SVP equals the atmospheric pressure.



• Triple point :
  It is a point in a phase diagram representing a particular value of pressure and temperature at which the solid, liquid and gaseous state of the substance can co - exist. The phase diagram (P-T diagram) representing the triple point of water is shown in diagram below:
  



• Humidity :
  The amount of water vapour present in a unit volume of air is called the absolute humidity of air. It is generally mentioned in terms of \(g/m^3\).
  The ratio of water vapour present in a given volume to the amount of water vapour required to saturate the volume at the same temperature is called the relative humidity . The relative velocity is expressed as, \[RH=\frac{\text{amount of water vapour present in a given volume of air at a given temperature}}{\text{amount of water vapour required to saturate the same volume of air at the same temperature}}\]



• Critical temperature is the distinguishing feature between the gas and vapour. A vapour above the critical temperature is gas and a gas below the critical temperature for the substance is a vapour.



• In winter nights, the atmospheric temperature goes down. The surfaces of window - panes, flowers, grass, etc. become colder due to radiation. The air near them becomes saturated and condensation begins. The droplets condensed on such surfaces are known as dew .
  If the temperature falls further, the whole atmosphere in that region may become saturated. Small droplets then condense on the dust particles present in the air. These droplets keep floating in the air and form a thick mist which restricts the visibility. This thick mist is called fog .

Short Answer Questions Solution

1. Define triple point of water with figure. Show that there exists a single value of triple point.
   Solution :
   Triple point of water is a point in a 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 the phase diagram below, \(T_{tr}\) represents the triple point of water.
   
   To prove that there exists a single value of triple point:
   
   
   
   Consider that the three curves (fusion curve (CD), steam curve (AB) and sublimation curve (EF) ) do not meet at a single point. Since an area AEC lies below the vaporization curve AB, it corresponds liquid state only, the area AEC lies below the fusion curve CD so it corresponds solid state only and the area AEC lies below the sublimation curve EF so it corresponds to 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 point.



2. Define dew point.
   Solution :
   Dew point is the temperature below which water droplets begin to condense and dew can form. The air must be cooled to this point to become saturated with water vapor. When cooled down further, the airborne water vapor will condense to form liquid water.



3. In winter, fog is formed in a clear night but not in a cloudy night. Why?
   Solution :
   During clear night, the earth's surface and atmosphere looses heat by radiation and thus cool below the dew point. Due to this reason, the fogs are formed. However, during cloudy night, the cloud acts as a blanket layer so that most of the heat radiated by the earth cannot escape from the cloud. Due to this reason, the temperature cannot fall sufficiently to reach the dew point and thus fog cannot form.



4. Why dews are more prominently formed at the blades of grass on cooler night?
   Solution :
   Prominent formation of dews on the blades of grass on cooler night relies on two main properties of grass :
   
   • Grass are good radiators of heat.
   • Grass blades gives out water vapours and the space near the blades is in water vapour.
   So, this water vapours condense on the grass blades and turn to dew drops.



5. Write any two differences between Saturated vapor and unsaturated vapor.
   Solution :
   The two differences between saturated and unsaturated vapor are:
   Saturated vapor :
   
   • If a space contains maximum amount of vapor that it can hold at that temperature, the vapor in the space is saturated vapor.
   • It doesnot obey gas laws.
   Unsaturated vapor :
   
   • If a space contains less than maximum amount of vapor that it can hold at that temperature, the vapor in the space is unsaturated vapor.
   • It obeys gas laws.



6. Define relative humidity and absolute humidity.
   Solution :
   Relative humidity
   The relative humidity of air at room temperature is defined as the ratio of the saturated vapor pressure at the dew point to the saturated vapor pressure at room temperature, i.e., \[\text{Relative humidity}=\frac{\text{saturated vapor pressure at dew point}}{\text{saturated vapor pressure at room temperature}} \times 100 \%\] Absolute humidity
   The mass of water vapour present in one cubic meter of air is called absolute humidity of air. It is commonly expressed in \(g/m^3\).



7. Why do we feel uncomfortable during very high relative humidity of air?
   Solution :
   Perspiration is very important mechanism in human body to control the body temperature. In high humidity, the evaporation perspiration takes place very slowly and the body's temperature control mechanism is inhibited. Due to this reason, we feel uncomfortable during very high relative humidity of air.



8. A weather report said relative humidity of 80\(\%\). Explain its meaning.
   Solution :
   It means that the air at this temperature is holding 80\(\%\) of the water vapor it can hold.

Numerical Problems Solution

1. At certain day the air temperature in a room is 17.7\(^\circ\) C and the dew point 5.3\(^\circ\) C. Find the relative humidity (SVP at 5\(^\circ\), 6\(^\circ\), 17\(^\circ\) and 18\(^\circ\) C are 0.654 cm, 0.705 cm, 1.442 cm, and 1.546 cm respectively).
   Solution :
   
   room temperature = 17.7\(^\circ\) C
   dew point = 5.3\(^\circ\) C
   SVP at 5\(^\circ\) C = 0.654 cm
   SVP at 6\(^\circ\) C = 0.705 cm
   SVP at 17\(^\circ\) C = 1.442 cm
   SVP at 18\(^\circ\) C = 1.546 cm
   
   Now, the relative humidity is, \[\text{R.H.}=\frac{\text{S.V.P. at dew point}}{\text{S.V.P. at the temperature of air}} \times 100\%\] So, we need to find S.V.P. at dew point (i.e., 5.3\(^\circ\) C) and S.V.P. at the temperature of the air (i.e., 17.7\(^\circ\) C).
   
   In the range from 17\(^\circ\) C and 18\(^\circ\) C, for a difference of 1\(^\circ\) C, the difference in S.V.P. = 1.546 - 1.442 = 0.104 cm
   
   For a difference of 0.7 \(^\circ\) C, the difference in S.V.P. = 0.7 \(\times\) 0.104 = 0.0728 cm
   
   So, S.V.P. at 17.7\(^\circ\) C = 1.442 + 0.0728 = 1.5148 cm
   In the range from 5\(^\circ\) C and 6\(^\circ\) C, for a difference of 1\(^\circ\) C, the difference in S.V.P. = 0.705 - 0.654 = 0.051 cm
   
   For a difference of 0.3 \(^\circ\) C, the difference in S.V.P. = 0.3 \(\times\) 0.051 = 0.0153 cm
   So, S.V.P. at 5.3\(^\circ\) C = 0.654 + 0.0153 = 0.6693 cm
   Thus, the relative humidity is,
   \[\begin{align*} \text{R.H.}&=\frac{\text{S.V.P. at dew point}}{\text{S.V.P. at the temperature of air}} \times 100\%\\ &=\frac{0.6693}{1.5148} \times 100\%\\ &=44.18 \hspace{0.1cm} \% \end{align*}\]



2. On a certain day the temperature of a room is 30\(^\circ\) C and the relative humidity is 40\(\%\). Calculate the relative humidity if the temperature of the room drops to (i) 20\(^\circ\) C (ii) 10\(^\circ\) C. [SVP at 30\(^\circ\) C, 20\(^\circ\) C and 10\(^\circ\) are 31.71 mm, 17.51 mm and 9.20 mm of Hg respectively].
   Solution :
   
   room temperature = 30\(^\circ\) C
   relative humidity at 30\(^\circ\) C = 40\(\%\)
   SVP at 30\(^\circ\) C = 31.71 mm
   SVP at 20\(^\circ\) C = 17.51 mm
   SVP at 10\(^\circ\) C = 9.20 mm
   (i) relative humidity at 20\(^\circ\) C = ?
   (ii) relative humidity at 10\(^\circ\) C = ?
   
   Relative humidity is calculated as, \[\text{R.H.}=\frac{\text{S.V.P. at dew point}}{\text{S.V.P. at the temperature of air}} \times 100\%\] At room temperature,
   \[\begin{align*} \text{R.H.}&=\frac{\text{S.V.P. at dew point}}{31.71} \times 100\%\\ 40&=\frac{\text{S.V.P. at dew point}}{31.71} \times 100\\ \text{S.V.P. at dew point}&=12.68 \hspace{0.1cm}\text{mm} \end{align*}\]
   (i) When the temperature drops to 20\(^\circ\) C,
   \[\begin{align*} \text{R.H.}&=\frac{\text{S.V.P. at dew point}}{\text{S.V.P. at}\hspace{0.1cm}^\circ \text{C}} \times 100\%\\ &=\frac{12.68}{17.51}\times 100\%\\ &=72.4 \% \end{align*}\]
   (ii) When the temperature drops to 10\(^\circ\) C , saturated vapour pressure at this temperature of air is less than the saturated vapour pressure at dew point. Some water vapour will condense so that the actual vapour pressure becomes only 9.20 mm and relative humidity becomes 100 \(\%\).