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Qwestrum Engineering360 · Chemical Engineering · Process Calculations

Humidity and Psychrometry

Psychrometry describes moist air using absolute humidity (kg water per kg dry air) and relative humidity (partial pressure over saturation pressure); most problems are read directly off the psychrometric chart at the intersection of dry- and wet-bulb temperatures.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

  • Wet-bulb temperature ≤ dry-bulb; equal at saturation
  • Adiabatic saturation process follows constant H or wet-bulb line on chart
  • Cooling tower and dryer problems use psychrometric chart

Topic details

Introduction

Bhatt & Vora present psychrometry as the basis for drying, humidification and cooling-tower design. The standard method is to fix the state of the air from two measured properties, look up saturation pressure from steam tables, and then track how humidity and enthalpy change as air is heated, cooled or contacted with water. Everything is referenced to a fixed mass of bone-dry air, which stays constant through the equipment.

Key relations & formulas

AbsolutehumidityH=mvmdaAbsolute humidity H = \frac{m_{v}}{m_{da}}
(kg vapour / kg dry air)

Formulas (Indian textbook notation)

  • Relativehumidityϕ=PvPv,sat(T)×100Relative humidity \phi = \frac{P_{v}}{P_{v}},sat(T) \times 100%
HumidvolumeVH=RT(1/Mda+H/Mv)PHumid volume V_{H} = R T \frac{(1/M_{da} + H/M_{v})}{P}
(ideal gas mixture)

Notation and sign conventions

Relation 1 —
AbsolutehumidityH=mvmdaAbsolute humidity H = \frac{m_{v}}{m_{da}}
AbsolutehumidityH=mvmdaAbsolute humidity H = \frac{m_{v}}{m_{da}}
(kg vapour / kg dry air)
Write this relation with symbols exactly as in Stoichiometry — Bhatt & Vora before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
Relativehumidityϕ=PvPv,satRelative humidity \phi = \frac{P_{v}}{P_{v}},sat

Formulas (Indian textbook notation)

  • Relativehumidityϕ=PvPv,sat(T)×100Relative humidity \phi = \frac{P_{v}}{P_{v}},sat(T) \times 100%
Write this relation with symbols exactly as in Stoichiometry — Bhatt & Vora before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
HumidvolumeVH=RTHumid volume V_{H} = R T
HumidvolumeVH=RT(1/Mda+H/Mv)PHumid volume V_{H} = R T \frac{(1/M_{da} + H/M_{v})}{P}
(ideal gas mixture)
Write this relation with symbols exactly as in Stoichiometry — Bhatt & Vora before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

Using dry air as the invariant basis is what makes psychrometric bookkeeping clean, because only the water content changes. Relative humidity tells you how close the air is to saturation, while absolute humidity is what actually transfers in a dryer. The wet-bulb temperature is the steady temperature of a wetted surface where evaporative cooling balances sensible heat gain; for the air–water system it nearly coincides with the adiabatic saturation temperature, which is why a single sloping line on the chart serves both. Humid volume and humid heat let you convert between mass and volumetric air flows.

Assumptions and validity limits

State assumptions explicitly before using any relation for humidity and psychrometry — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Process Calculations viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Process Calculations papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to humidity and psychrometry.
4. Use equation 1:
AbsolutehumidityH=mvmdaAbsolute humidity H = \frac{m_{v}}{m_{da}}
.
5. Use equation 2:
Relativehumidityϕ=PvPv,satRelative humidity \phi = \frac{P_{v}}{P_{v}},sat
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Humidity and Psychrometry appears in every chemical process design. In Indian chemical curricula this topic is tested because it connects theory to material and energy balances.
GATE and semester exams often combine humidity and psychrometry with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use humidity and psychrometry?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

Common errors include using total pressure instead of partial pressure in the relative-humidity ratio, forgetting that absolute humidity is per unit dry air (not per unit moist air), and reading the wrong sloping line on the chart (wet-bulb versus enthalpy). Students also confuse dew point with wet-bulb temperature.

Quick revision checklist

Before attempting humidity and psychrometry problems, confirm you can:
1. Wet-bulb temperature ≤ dry-bulb; equal at saturation
2. Adiabatic saturation process follows constant H or wet-bulb line on chart
3. Cooling tower and dryer problems use psychrometric chart
Revise the solved examples in Stoichiometry — Bhatt & Vora and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Absolute humidity from partial pressure

Problem

Air at 1 atm has a water partial pressure of 2.34 kPa. Find the absolute humidity (M_water = 18, M_air = 29).

Solution

H = (18/29) × P_v/(P − P_v) = 0.621 × 2.34/(101.3 − 2.34) = 0.621 × 0.02365 = 0.0147 kg water/kg dry air.

Conceptual check — Humidity and Psychrometry

Problem

In a Process Calculations semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of humidity and psychrometry." What should a complete answer include?

Exams & GATE

Use steam tables for P_sat; psychrometric chart for air-water systems.

📖 Standard books (India)

  • Stoichiometry — Bhatt & Vora

    Read: Syllabus unit

    Process calculations for chemical engineering

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