Questions: Psychrometrics and Humid Air Properties

Question 1

Cold outdoor air at −10°C with 80% relative humidity is brought indoors and heated to 20°C without adding any moisture. How does the relative humidity of the indoor air compare to the outdoor air?

• A. It remains near 80% — the humidity ratio is constant, so relative humidity is constant
• B. It increases — warmer air feels more humid because the water vapor is more energetic
• C. It drops dramatically — P_sat rises steeply with temperature, so the same vapor content becomes a much smaller fraction of saturation capacity
• D. It drops to 0% — heating destroys water vapor

Answer: (C)

Relative humidity φ = P_v / P_sat(T). When air is heated at constant humidity ratio (no moisture added or removed), P_v stays constant but P_sat rises steeply with temperature — roughly doubling every 10°C near typical indoor temperatures. At −10°C, P_sat is about 0.26 kPa; at 20°C it is about 2.34 kPa — nearly 9× higher. So 80% RH outdoors becomes roughly 80% × (0.26/2.34) ≈ 9% RH indoors. This is why heated winter air feels bone dry even though no moisture was removed. Option A is the classic misconception: constant ω does not mean constant φ.

Question 2

An HVAC system cools a supply air stream from 28°C and 65% relative humidity down to 12°C. Which path on the psychrometric chart correctly describes this process?

• A. A horizontal line moving left — temperature decreases while humidity ratio stays constant
• B. A diagonal path moving down and left, eventually reaching the saturation curve, then descending along it as moisture condenses out
• C. A vertical line moving downward — humidity ratio decreases at constant temperature
• D. A path curving rightward — the air gains moisture from the cooling coil condensate

Answer: (B)

Initially, cooling the air without reaching the dew point traces a horizontal path leftward (constant ω, decreasing T). Once the air reaches the dew point, it hits the saturation curve (100% RH). Further cooling requires condensation: moisture is removed, and the state point descends along the saturation curve — both temperature and humidity ratio decrease together. This combined path (horizontal then along the saturation boundary) is characteristic of a cooling coil that dehumidifies. A horizontal path alone (option A) would only apply if cooling stopped before reaching the dew point.

Question 3

Relative humidity is a reliable indicator of the actual mass of water vapor present in an air sample.

• T. True
• F. False

Answer: False

Relative humidity indicates how close the air is to saturation at its current temperature, not the absolute moisture content. The same mass of water vapor per kilogram of dry air (same humidity ratio ω) produces very different relative humidity values at different temperatures. Desert air at 40°C with 20% RH contains far more moisture per kilogram of air than Arctic air at −20°C with 80% RH. For engineering calculations involving moisture addition, removal, or condensation, the humidity ratio ω is the relevant conserved quantity — not relative humidity.

Question 4

On a psychrometric chart, sensible heating (adding heat without changing moisture content) is represented as a horizontal line moving to the right, because the humidity ratio stays constant while dry-bulb temperature increases.

• T. True
• F. False

Answer: True

The humidity ratio ω (kg water per kg dry air) is constant during sensible heating because no moisture is added or removed — only temperature changes. Since the psychrometric chart's vertical axis is humidity ratio, a constant-ω process traces a horizontal line. Moving right means increasing dry-bulb temperature. This geometric representation is the psychrometric chart's primary utility: thermodynamic processes become predictable geometric paths, allowing engineers to read off all state properties at a glance and calculate enthalpy changes directly.

Question 5

Explain why the humidity ratio (ω) rather than relative humidity (φ) is the conserved quantity during sensible heating, and why this distinction matters for HVAC design.

Model answer: Humidity ratio ω is the mass of water vapor per kilogram of dry air — a ratio that depends only on how much water is physically present in the air, independent of temperature. Adding heat does not add or remove water molecules, so ω is unchanged. Relative humidity φ = P_v / P_sat(T) depends on temperature through P_sat, so it changes whenever temperature changes even if water content is constant. For HVAC design, ω is what matters for calculating moisture loads, latent heat, condensation risk, and mixing calculations — because φ changes with every heating or cooling step, you cannot use it to track moisture through a system.

The practical consequence is significant: an engineer who designs a heating system based on keeping relative humidity 'the same' will deliver bone-dry indoor air in winter. Sizing a humidifier or calculating the load on a cooling coil requires working in humidity ratio, not relative humidity. The psychrometric chart makes this visible: sensible heating is a flat horizontal line (ω constant) while RH isolines curve — crossing multiple RH values as temperature increases along constant ω.