![Some Empirical Formulas
𝑯𝒖𝒎𝒊𝒅 𝑯𝒆𝒂𝒕 ( 𝑪 𝒔 ): 𝑺𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝒉𝒆𝒂𝒕 𝒄𝒂𝒑𝒂𝒄𝒊𝒕𝒚 𝒐𝒇 𝒉𝒖𝒎𝒊𝒅 𝒂𝒊𝒓
Cs
Cs
𝑯𝒖𝒎𝒊𝒅𝑽𝒐𝒍𝒖𝒎𝒆(^
𝑉 ): 𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒖𝒏𝒊𝒕 𝒎𝒂𝒔𝒔 𝒐𝒇 𝒅𝒓𝒚 𝒂𝒊𝒓 𝒑𝒍𝒖𝒔 𝑯 𝟐𝑶 𝒗𝒂𝒑𝒐𝒓 𝒑𝒓𝒆𝒔𝒆𝒏𝒕 𝒊𝒏𝒊𝒕 .
=[* ] + [* ]*H
H is used to account for the contribution of water vapor to the overall specific heat capacity of the
humid air mixture. The total heat capacity of humid air is a combination of the heat capacities of both
dry air and the water vapor it contains.](https://image.slidesharecdn.com/17-0ct-copy1-241209141038-b4262342/85/17-0ct-Copy-1-pptx-CPC-lecture-slides-iit-kgp-10-320.jpg)
17-0ct - Copy 1.pptx CPC lecture slides iit kgp
- 1. Chemical Process Calculation Course Code: CH21203 Dr. SUVERNA TRIVEDI (Fulbright Fellow) Assistant Professor Department of Chemical Engineering, IIT KGP Email: strivedi@che.iitkgp.ac.in 1 Humidity & Psychrometric Chart
- 2. What is Humidity?? Humidity means presence of water vapor/water molecules in air. If there is no trace of water molecules it means………..air is dry air (Particular term used bone dry air). Humidity Specific Humidity (H) Relative Humidity (%RH) Absolute Humidity (AH)
- 3. Specific Humidity (H) It is defined as mass of water vapor present per mass of bone-dry air. 𝑯= 𝒎 𝑯 𝟐 𝑶 𝒎𝒅𝒓𝒚𝒂𝒊𝒓 (𝒊) Can we write the above equation in terms of moles: 𝑯= 𝟏𝟖 ∗𝒏𝑯 𝟐𝑶 𝟐𝟖.𝟖𝟗∗𝒏𝒅𝒓𝒚𝒂𝒊𝒓 (𝒊𝒊) 𝒘𝒉𝒆𝒓𝒆 ;𝒏𝒅𝒓𝒚 𝒂𝒊𝒓 =𝒏𝑻𝒐𝒕 𝒂𝒍 −𝒏𝑯 𝟐𝑶
- 4. Specific Humidity (H) Can we write the above equation in terms of partial pressure? 𝑯= 𝟏𝟖 ∗𝒑𝑯 𝟐𝑶 𝟐𝟖.𝟖𝟗∗𝒑𝒅𝒓𝒚𝒂𝒊𝒓 (𝒊𝒊𝒊) Mole fraction=Partial pressure fraction 𝑯= 𝟏𝟖∗𝒑𝑯 𝟐 𝑶 𝟐𝟖.𝟖𝟗∗(𝑷𝒕𝒐𝒕𝒂𝒍−𝒑𝑯 𝟐 𝑶𝒗𝒂𝒑𝒐𝒓) (𝒊𝒗) Hmsp Molal Specific humidity
- 5. Specific Humidity (H) 𝑯= 𝟏𝟖∗𝒑𝑯 𝟐𝑶 𝟐𝟖.𝟖𝟗∗(𝑷𝒕 𝒐𝒕𝒂𝒍−𝒑𝑯 𝟐 𝑶𝒗𝒂𝒑𝒐𝒓) (𝒊𝒗) Hmsp Can we write the relations between H and Hmsp? 𝑯= 𝟏𝟖 𝟐𝟖. 𝟖𝟗 ∗ 𝑯𝒎𝒔𝒑(𝒗𝒊)
- 6. Relative Humidity (RH or φ) RH or φ H doesn’t talk about the temperature. But RH is an implicit function of Temperature. Definition: It is ratio of partial pressure of water vapor in mixture to the saturation vapor pressure of water. %RH or φ % RH is similar to % Saturation % Saturation term will come into picture when we will handle with another liquid instead of wate
- 7. Relative Humidity (RH or φ) 𝒚 𝒑 = 𝒑 𝒗 𝒑 𝒔 ∗ 𝟏𝟎𝟎( 𝒊𝒙) Relative Saturation (% Saturation): Where, pv= partial pressure of vapor; ps=partial pressure of vapor at saturation 𝒚 𝒑 = 𝒏 𝒗 𝒏 𝒔 ∗ 𝟏𝟎𝟎 ( 𝒙 ) Where, nv= moles of vapor/moles of dry air; ns=moles of vapor/mole of dry air at saturation 𝒚 𝒑 = 𝒑 𝒗/( 𝑷𝑻 − 𝒑𝒗) 𝒑 𝒔/(𝑷𝑻 − 𝒑𝒔) ∗ 𝟏𝟎𝟎(𝒙𝒊) From Eqn (x) substitute the value in (xi): 𝒏𝒗 𝒏 𝒔 = 𝒑 𝒗 / ( 𝑷𝑻 − 𝒑𝒗 ) 𝒑 𝒔 /( 𝑷𝑻 −𝒑𝒔 ) ( 𝒙𝒊𝒊 )
- 8. Absolute Humidity (AH) 𝑨 𝑯 = 𝒎 𝒘 𝑽 𝒏𝒆𝒕 ( 𝒊 ) 𝒘𝒉𝒆𝒓𝒆 ;𝒎𝒘=𝒎𝒂𝒔𝒔 𝒐𝒇 𝒘𝒂𝒕𝒆𝒓 𝒗𝒂𝒑𝒐𝒓 ;𝑽𝒏𝒆𝒕=𝒄𝒐𝒎𝒃𝒊𝒏𝒆𝒅𝒗𝒐𝒍 .𝒐𝒇 𝒅𝒓𝒚 𝒂𝒊𝒓 𝒂𝒏𝒅 𝑯 𝟐 𝑶 𝒗𝒂𝒑𝒐𝒓 But AH is having dimensions. 𝑰𝒇 𝒚𝒐𝒖𝒓𝒆𝒎𝒆𝒃𝒆𝒓 𝒏𝒖𝒎𝒆𝒓𝒂𝒕𝒐𝒓 𝒇𝒐𝒓 𝒔𝒑.𝒉𝒖𝒎𝒊𝒅𝒊𝒕𝒚 𝒂𝒏𝒅 𝑨𝑯 𝒂𝒓𝒆 𝒔𝒂𝒎𝒆
- 9. Other Parameters associated with Humid Air 𝑪 𝒑𝒅𝒓𝒚 𝒂𝒊𝒓 =𝑺𝒑 . 𝒉𝒆𝒂𝒕 𝒐𝒇 𝒅𝒓𝒚 𝒂𝒊𝒓 =𝟏 𝒌𝑱 / 𝒌𝒈𝑲 𝑪 𝒑𝑯 𝟐 𝑶𝒗𝒂𝒑𝒐𝒓 =𝑺𝒑 . 𝒉𝒆𝒂𝒕 𝒐𝒇 𝒘𝒂𝒕𝒆𝒓 𝒗𝒂𝒑𝒐𝒓 =𝟏.𝟖𝟖 𝒌𝑱 /𝒌𝒈𝑲 =4502kJ/kg Δ ^ 𝐻 𝒂𝒊𝒓 =𝒔𝒑 . 𝑬𝒏𝒕𝒉𝒂𝒍𝒑𝒚 𝒐𝒇 𝑫𝒓𝒚 𝒂𝒊𝒓 Δ ^ 𝐻 𝑯 𝟐 𝑶𝑽𝒂𝒑𝒐𝒓 =𝒔𝒑 . 𝑬𝒏𝒕𝒉𝒂𝒍𝒑𝒚 𝒐𝒇 𝑯 𝟐 𝑶 𝒗𝒂𝒑𝒐𝒓
- 10. Some Empirical Formulas 𝑯𝒖𝒎𝒊𝒅 𝑯𝒆𝒂𝒕 ( 𝑪 𝒔 ): 𝑺𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝒉𝒆𝒂𝒕 𝒄𝒂𝒑𝒂𝒄𝒊𝒕𝒚 𝒐𝒇 𝒉𝒖𝒎𝒊𝒅 𝒂𝒊𝒓 Cs Cs 𝑯𝒖𝒎𝒊𝒅𝑽𝒐𝒍𝒖𝒎𝒆(^ 𝑉 ): 𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒖𝒏𝒊𝒕 𝒎𝒂𝒔𝒔 𝒐𝒇 𝒅𝒓𝒚 𝒂𝒊𝒓 𝒑𝒍𝒖𝒔 𝑯 𝟐𝑶 𝒗𝒂𝒑𝒐𝒓 𝒑𝒓𝒆𝒔𝒆𝒏𝒕 𝒊𝒏𝒊𝒕 . =[* ] + [* ]*H H is used to account for the contribution of water vapor to the overall specific heat capacity of the humid air mixture. The total heat capacity of humid air is a combination of the heat capacities of both dry air and the water vapor it contains.
- 11. Dry Bulb Temperature The dry bulb temperature is the air temperature measured by a standard thermometer exposed to the air but protected from moisture and direct radiation (like sunlight). It represents the actual temperature of the air and is called "dry bulb" because the thermometer is dry (not influenced by moisture). DBT is what we typically refer to as "air temperature" in weather reports.
- 12. Wet Bulb Temperature The wet bulb temperature is the lowest temperature that can be reached by evaporating water into the air. It is measured using a thermometer with a wet cloth (wick) wrapped around the bulb, which cools as water evaporates from it. As water evaporates from the cloth, it removes heat from the thermometer, cooling it. The rate of cooling depends on the moisture content (humidity) of the air. In humid conditions, evaporation is slower, so the wet bulb temperature is close to the dry bulb temperature. In dry conditions, evaporation is faster, and the wet bulb temperature will be significantly lower than the dry bulb temperature. Units: Also measured in °C or °F. Example: If the air is very dry, the wet bulb temperature might be much lower than the dry bulb temperature.
- 13. Practical Applications Weather Forecasting: Wet bulb temperature is important for understanding heat stress. High WBT can indicate dangerous levels of humidity, where the body struggles to cool down through sweating. Evaporative Cooling: The wet bulb temperature is crucial in understanding how evaporative cooling works, as the closer the WBT is to the DBT, the less effective evaporative cooling will be.
- 14. Dew Point The dew point is the temperature at which air becomes saturated with moisture, meaning that the air contains as much water vapor as it can hold. When air cools to this temperature, the water vapor begins to condense into liquid water, forming dew, fog, or frost. At the dew point, the relative humidity reaches 100%. If the temperature drops below this point, excess moisture in the air will condense, and dew will form on surfaces. A higher dew point means more moisture in the air, leading to a muggy, uncomfortable feeling, whereas a lower dew point indicates drier air.
- 15. Example Problem: The dry bulb temperature and dew point of ambient air were found to be 302K (29o C) and 291K (18o C) respectively. Barometer reads 100kPa. Calculate: a. Specific molal humidity b. Specific humidity c. %RH d. Humid heat Data: Partial pressure of water vapor at 291K =2.0624kPa; Vapor pressure at 302K=4.004kPa At dew point partial pressure of water in air is equal to vapor pressure of water