Enthalpy Of Moist Air (total Heat) Dry Bulb Temperature 5p6p3q

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Lecturer: -Dr. Esam Mejbil Abid Subject: Air Conditioning and Refrigeration Year: Fourth B.Sc.

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Babylon University College of Engineering Department of Mechanical Engineering

LECTURE-2 9. Enthalpy of Moist Air (Total Heat): The enthalpy of moist air is numerically equal to the enthalpy of dry air plus the enthalpy of water vapour associated with dry air. 𝒉𝒂 = 𝒄𝒑𝒂 𝒕𝒅 …………………………………..…….……..13 Where:a= specific heat of dry air which is normally taken 1.005kj/kg.K

Enthalpy of water vapour associated with 1 kg of dry air 𝒉𝒗 = 𝑾𝒉𝒔 ………………………………………….……14 Where: hs=enthalpy of water vapour per 1 kg dry air at dew point temperature (tdp).

If the moist air is superheated, then enthalpy of water vapour is: 𝒉𝒘 = 𝑾𝒄𝒑𝒔 𝒕𝒅 − 𝒕𝒅𝒑 …………………………………15

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Where: s=specific heat of superheated water vapour which is normally taken as 1.9 kJ/kg.K. td-tdp=Degree of superheat of water vapour.

The specific enthalpy of water vapor hv at constant pressure can be approximated as: 𝒉𝒗 = 𝒉𝒇𝒈𝒅 + 𝒄𝒑𝒗 𝒕𝒅 …………………………….………..16

Where: hfgd = specific enthalpy of saturated water vapor v= specific heat of vapour = 1. 84 kj/kg.K In a temperature range of 0 to 60 oC, its value can be taken as 1.84 kJ/kg.K. Then the total enthalpy of moist air can be evaluated as:

𝒉 = 𝒉𝒂 + 𝒉𝒗

…………………….…17

After rearrangement the total enthalpy of moist air is: 𝒉 = 𝒄𝒑𝒂 𝒕𝒅 + 𝑾 𝒉𝒇𝒈𝒅 + 𝒄𝒑𝒗 𝒕𝒅 ………………….……….…18 When 𝒉𝒇𝒈𝒅 =2500 at zero temperature, the total enthalpy of moist air is: 𝒉 = 𝟏. 𝟎𝟎𝟓 𝒕𝒅 + 𝑾 𝟐𝟓𝟎𝟎 + 𝟏. 𝟖𝟒𝒕𝒅 ………………………19

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10. Dry Bulb Temperature: It is the temperature of air recorded by a thermometer, when it's not affected by the moister present in the air. The dry bulb temperature is generally denoted by td.

11. Wet Bulb Temperature: It is the temperature of air recorded by a thermometer, when its bulb is surrounded by a wet cloth exposed to the air. The wet bulb temperature is generally denoted by tw. A sling-type psychrometer, as shown in Figure (1), is an instrument that determines the temperature, relative humidity, and thus the state of the moist air by measuring its dry bulb and wet bulb temperatures. It consists of two mercury-in-glass thermometers. The sensing bulb of one of them is dry and is called the dry bulb.

Figure (1): sling-type psychrometer

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 Thermodynamic Wet Bulb Temperature and Wet Bulb Temperature: -

1. Ideal Adiabatic Saturation Process If moist air at an initial temperature T1, humidity ratio W1, enthalpy h1, and pressure p flows over a water surface of infinite length in a well-insulated chamber, as shown in Figure (2), liquid water will evaporate into water vapor and will disperse in the air. The humidity ratio of the moist air will gradually increase until the air can absorb no more moisture.

As there is no heat transfer between this insulated chamber and the surroundings, the latent heat required for the evaporation of water will come from the sensible heat released by the moist air. This process results in a drop in temperature of the moist air. At the end of this evaporation process, the moist air is always saturated. Such a process is called an ideal adiabatic saturation process, where an adiabatic process is defined as a process without heat transfer to or from the process.

Figure (2) Ideal adiabatic saturation process.

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2- Thermodynamic Wet-Bulb Temperature For any state of moist air, there exists a thermodynamic wet-bulb temperature T* that exactly equals the saturated temperature of the moist air at the end of the ideal adiabatic saturation process at constant pressure. Applying a steady flow energy equation, get: 𝒉𝟏 + 𝑾∗𝒔 − 𝑾𝟏 𝒉∗𝒘 = 𝒉∗𝒔 ………………………………….……20 Where: 𝒉𝟏 , 𝒉∗𝒔 =enthalpy of moist air at initial state and enthalpy of saturated air at end of ideal adiabatic saturation process, (kJ /kg) 𝑾𝟏 , 𝑾∗𝒔 =humidity ratio of moist air at initial state and humidity ratio of saturated air at end of ideal adiabatic saturation process, (kg /kg) 𝒉∗𝒘 = enthalpy of water as it is added to chamber at a temperature T*, (kJ /kg) 3- Heat Balance of an Ideal Adiabatic Saturation Process When water is supplied to the insulation chamber at a temperature T* in an ideal adiabatic saturation process, then the decrease in sensible heat due to the drop in temperature of the moist air is just equal to the latent heat required for the evaporation of water added to the moist air. This relationship is given by: 𝒄𝒑𝒅 𝑻𝟏 − 𝑻∗ + 𝒄𝒑𝒔 𝑾𝟏 𝑻𝟏 − 𝑻∗ = 𝑾𝒔∗ − 𝑾𝟏 𝒉∗𝒇𝒈…….…21 Where: T1 = temperature of moist air at initial state of ideal adiabatic saturation process (°C) 𝒉∗𝒇𝒈= latent heat of vaporization at thermodynamic wet-bulb temperature, (J /kg) Since d =a + W1s, after rearranging the in Eq. (21),

INTRODUCTION AIR-CONDITIONING SYSTEM 𝑾∗𝒔 −𝑾𝟏 𝑻𝟏 −𝑻∗

=

𝒄𝒑𝒅 ∗ 𝒉𝒇𝒈

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……………………………………………....22

Also ∗

𝑻 = 𝑻𝟏 −

𝑾∗𝒔 −𝑾𝟏 𝒉∗𝒇𝒈 𝒄𝒑𝒅

…………………………………..…....23

Where: a=1.005 kJ/kg.K s=1.859 kJ/kg.K  Pressure of Water Vapour: 𝒑𝒗 = 𝒑𝒘 − 𝒑𝒃𝑨 𝒕𝒅 − 𝒕𝒘 ………………………………….24 Where pw=saturation pressure at wet bulb temperature from steam table. A=6.66×10-4

for tw≥0

A=5.94×10-4

for tw≤0