Thermodynamic temperatures in saturated air For a saturated air–water vapour mixture (100% relative humidity), what is the relationship among dry-bulb temperature, wet-bulb temperature, and dew-point temperature?

Introduction / Context:In psychrometrics, the relation among dry-bulb (DBT), wet-bulb (WBT), and dew-point (DPT) temperatures depends on humidity level. Recognizing the equality at saturation (100% RH) is essential for interpreting charts and instruments.

Given Data / Assumptions:

• Saturated air–water vapour mixture (RH = 100%).
• Steady-state conditions at a fixed barometric pressure.
• Thermometers and hygrometers are properly functioning.

Concept / Approach:At saturation, the air is holding the maximum possible moisture at that temperature. The adiabatic evaporation that normally lowers a wetted-bulb thermometer cannot proceed because the air is already saturated; thus WBT equals DBT. Dew point equals the temperature at which condensation begins; in saturated air, the current temperature is already at the dew point, so DPT equals DBT as well. Therefore, all three temperatures coincide.

Step-by-Step Solution:

Verification / Alternative check:On the psychrometric chart, saturated states lie along the saturation curve where lines of constant DBT, WBT, and DPT intersect, confirming equality.

Why Other Options Are Wrong:

DBT higher than WBT or DPT: true only for unsaturated air (RH < 100%).WBT exceeding DBT: not physically achievable under standard definitions.

Common Pitfalls:Assuming a small measurement error implies a fundamental difference. In perfect saturation, instrument readings should coincide; slight deviations are due to instrument accuracy or transient effects.

Final Answer:

Dry-bulb, wet-bulb, and dew-point temperatures are equal