The humidity of air at a dry-bulb temperature of $65^{\circ}C$ is $0.025 \; kg \; water/kg \; dry \; air$. The latent heat of vaporization of water at $0 ^{\circ}C$ is $2500 \; kJ/kg$. The psychrometric ratio of air is $0.95 \; kJ \; (kg \; dry \; air)^{-1} \; K^{-1}$. Considering $0 ^{\circ}C$ as reference temperature, the enthalpy of air (in kJ/kg) at its adiabatic saturation temperature of $35 ^{\circ}C$ is ________ (rounded off to two decimal places).
Key Information Extraction
The problem provides the following data for calculating air enthalpy at a specific adiabatic saturation temperature:
- Latent heat of vaporization of water at $0^{\circ}C$ ($h_{fg,0}$): $2500 \; kJ/kg$.
- Specific heat of dry air ($C_a$), given as the psychrometric ratio: $0.95 \; kJ \; (kg \; dry \; air)^{-1} \; K^{-1}$.
- Adiabatic saturation temperature ($T_{ad}$): $35^{\circ}C$. This is the target temperature for enthalpy calculation.
- Reference temperature ($T_0$): $0^{\circ}C$.
Note: The initial conditions ($T_{db}=65^{\circ}C$, $W=0.025 \; kg/kg$) describe the current air state but are not used for calculating the enthalpy *at* the specified adiabatic saturation temperature.
Enthalpy Calculation Principle
The enthalpy of moist air at its adiabatic saturation temperature ($T_{ad}$) is equivalent to the enthalpy of saturated air at that temperature. A widely used simplified formula for enthalpy ($h$) is:
$h = C_a T + W h_{fg,0}$
Where $T$ is the dry-bulb temperature and $W$ is the humidity ratio. For this calculation, $T = T_{ad}$ and $W = W_{sat}(T_{ad})$.
Adiabatic Saturation Temperature Enthalpy Calculation
Step 1: Determine the saturation humidity ratio ($W_{sat}$) at $T_{ad} = 35^{\circ}C$.
This requires the saturation vapor pressure ($P_{ws}$) at $35^{\circ}C$. Assuming standard atmospheric pressure ($P_{atm} \approx 101.325 \; kPa$):
- Saturation vapor pressure at $35^{\circ}C$, $P_{ws}(35^{\circ}C) \approx 5.628 \; kPa$.
The saturation humidity ratio is calculated using:
$W_{sat}(T) = 0.622 \frac{P_{ws}(T)}{P_{atm} - P_{ws}(T)}$
Substituting values for $35^{\circ}C$:
$W_{sat}(35^{\circ}C) = 0.622 \times \frac{5.628 \; kPa}{101.325 \; kPa - 5.628 \; kPa} \approx 0.03657 \; kg \; water/kg \; dry \; air$.
Step 2: Calculate the enthalpy ($h_{ad}$) at $T_{ad} = 35^{\circ}C$.
Apply the enthalpy formula using $T_{ad}$ and $W_{sat}(T_{ad})$:
$h_{ad} = C_a T_{ad} + W_{sat}(T_{ad}) h_{fg,0}$
Substitute the known and calculated values:
$h_{ad} = (0.95 \; kJ/(kg \cdot K) \times 35 \; K) + (0.03657 \; kg/kg \times 2500 \; kJ/kg)$
$h_{ad} = 33.25 \; kJ/kg + 91.425 \; kJ/kg$
$h_{ad} = 124.675 \; kJ/kg$
Rounding to two decimal places as requested, the enthalpy is $124.68 \; kJ/kg$. This value lies within the provided range of 124 to 125.
Important Questions from Humidification
- Vapor pressure of water at various temperature is given in the table.
Temperature (in K) 284 289 294 299 310 Vapor pressure of water (in kPa) 1.28 1.80 2.50 3.40 6.40
An air and water vapor mixture at $100 \text{ kPa}$ with a relative humidity of $20\%$ has a dry-bulb temperature of $310 \text{ K}$. Assume latent heat of vaporization for water is $44 \text{ kJ mol}^{-1}$ and specific heat capacity of the air and water vapor mixture is $0.035 \text{ kJ mol}^{-1}\text{K}^{-1}$. Which one of the following is the closest to its wet-bulb temperature (in K)? Consider moist air with absolute humidity of 0.02 (kg moisture)/(kg dry air) at 1 bar pressure. The vapour pressure of water is given by the equation
$\ln P^{sat} = 12 - \frac{4000}{T-40}$
where $P^{sat}$ is in bar and $T$ is in K. The molecular weight of water and dry air are 18 kg/kmol and 29 kg/kmol, respectively. The dew temperature of the moist air is ____________ °C (rounded off to the nearest integer).- For what value of Lewis number, the wet-bulb temperature and adiabatic saturation temperature are nearly equal?
Partially saturated air at 1 bar and $50 ^{\circ}C$ is contacted with water in an adiabatic saturator. The air is cooled and humidified to saturation, and exits at $25^{\circ}C$ with an absolute humidity of 0.02 kg water per kg dry air. Use latent heat of vaporization of water as 2450 kJ. $kg^{-1}$, and average specific heat capacity for dry air and water, respectively as 1.01 kJ.$kg^{-1}K^{-1}$ and 4.18 kJ. $kg^{-1}K^{-1}$. If the absolute humidity of air entering the adiabatic saturator is $H \times 10^{-3}$ kg water per kg dry air, the value of $H$ is ________ (rounded off to two decimal places).
The dry-bulb temperature of air in a room is $30 \ \degree C$. The Antoine equation for water is given as
$ln \ P^{sat} = 12.00 - \frac{4000}{T-40}$
where $T$ is the temperature in $K$ and $P^{sat}$ is the saturation vapor pressure in $bar$. The latent heat of vaporization of water is $2000 \ kJ \ kg^{-1}$, the humid heat is $1.0 \ kJ \ kg^{-1} \ K^{-1}$, and the molecular weights of air and water are $28 \ kg \ kmol^{-1}$ and $18 \ kg \ kmol^{-1}$, respectively. If the absolute humidity of air is $Y' \ kg$ moisture per $kg$ dry air, then for a wet-bulb depression of $9 \ \degree C$, $1000 \times Y' = $ _________ (rounded off to one decimal place).
