Question

Which two properties are sufficient to define the state point of moist air?

• A. Humidity ratio and vapour pressure.
• B. Humidity ratio and wet bulb temperature
• C. Humidity ratio and dry bulb temperature
• D. Dry bulb temperature and wet bulb temperature

Hint:

Remember that at a given total pressure, two independent intensive properties are required to define the state of moist air. Common pairs include (DBT, ω), (DBT, RH), (DBT, WBT), and (DBT, DPT).

Answer 1

The Correct Option is C

Step 1: Understand the state point of moist air.
The state of moist air at a given pressure is defined by its thermodynamic properties. To completely specify this state, we need to know a certain number of independent intensive properties. Step 2: Consider the relevant properties of moist air.
Some common properties used to describe moist air include:
Dry bulb temperature (DBT)
Wet bulb temperature (WBT)
Dew point temperature (DPT)
Relative humidity (RH)
Humidity ratio \((ω)\)
Enthalpy (h)
Specific volume (v)
Vapour pressure of water vapour \((p_v)\)
Total pressure of moist air (p)
Step 3: Apply the Gibbs phase rule to moist air.
Moist air can be considered as a mixture of two components (dry air and water vapour) in a single phase (gas phase). According to the Gibbs phase rule, \( F = C - P + 2 \), where \( F \) is the number of degrees of freedom (number of independent intensive properties needed to define the state), \( C \) is the number of components, and \( P \) is the number of phases.
For moist air, \( C = 2 \) and \( P = 1 \), so \( F = 2 - 1 + 2 = 3 \). However, if the total pressure is specified (which is usually the case for atmospheric air), then the number of independent intensive properties needed to define the state reduces to \( F = 3 - 1 = 2 \).
Step 4: Evaluate the given options.
We need to find a pair of independent intensive properties that can uniquely define the state of moist air at a given pressure. Option 1 (Humidity ratio and vapour pressure): Humidity ratio (\( \omega \)) is directly related to vapour pressure (\( p_v \)) at a given total pressure. They are not entirely independent, but they can define the state.
Option 2 (Humidity ratio and wet bulb temperature): Humidity ratio and wet bulb temperature are independent properties and can define the state of moist air.
Option 3 (Humidity ratio and dry bulb temperature): Humidity ratio and dry bulb temperature are independent properties and are commonly used to define the state of moist air on a psychrometric chart. Knowing these two properties, all other properties can be determined.
Option 4 (Dry bulb temperature and wet bulb temperature): Dry bulb temperature and wet bulb temperature are independent properties and are also commonly used to define the state of moist air.
Step 5: Consider the most fundamental and commonly used pair.
While options 2, 3, and 4 provide pairs of independent properties that can define the state of moist air, the pair of humidity ratio and dry bulb temperature is fundamental and directly plots a unique point on the psychrometric chart, from which all other properties can be easily determined. Step 6: Select the correct answer.
Humidity ratio and dry bulb temperature are sufficient to define the state point of moist air at a given pressure.