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Drying &
Humidification Guide

Psychrometry, wet-bulb temperature, drying-rate curves, and drying time for the GATE Chemical Engineering paper.

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Overview

Drying & Humidification deals with the air-water(vapor) system specifically, how moist air holds water vapor, and how that governs the rate at which a wet solid gives up its moisture. Within the Mass Transfer section of the GATE CH syllabus, it's a self-contained subtopic: psychrometry (properties of moist air) sets up the driving force, and drying-rate curves (how a solid loses moisture over time) apply that driving force to a physical drying process.

Psychrometry defines a set of properties, humidity, relative humidity, wet-bulb and dry-bulb temperature, humid volume, and adiabatic saturation temperature, that all describe the same air-water vapor mixture from different angles, connected through vapor pressure via the Antoine equation. Drying itself splits into two rate regimes: a constant-rate period, where surface moisture evaporates as fast as heat can reach it (the drying rate is limited by external heat/mass transfer, not by the solid), and a falling-rate period after a critical moisture content, where internal moisture movement within the solid becomes the bottleneck and the rate declines as moisture content drops.

Every drying numerical on GATE reduces to correctly identifying which period (constant- or falling-rate) applies, then integrating the appropriate rate equation, this site's Antoine Equation Calculator supplies the vapor-pressure piece that both psychrometry and constant-rate drying calculations need as an input.

Real GATE CH PYQ Frequency (2024–2026)

No questions in our 2024–2026 archive were tagged to this specific subtopic on its own, they're grouped under the broader Mass Transfer category. See the full topic weightage table for the real, computed numbers.

GATE Weightage

Drying & Humidification typically contributes 2–3 questions (about 3–5 marks) within the Mass Transfer section of the GATE CH paper, split between psychrometric property calculations and drying-time numericals.

Sub-areaApprox. Marks
Psychrometry (humidity, wet-bulb, dew point)~1–2
Constant-rate & falling-rate drying~1–2

Sub-area split is a directional estimate (our archive doesn't tag marks at this granularity), for the real, computed topic-level total, see "Real GATE CH PYQ Frequency" above.

Key Subtopics

1

Humidity & humid volume

Absolute humidity (mass of water vapor per mass of dry air) and humid volume (volume of moist air per mass of dry air), both derived from the partial pressure of water vapor.

2

Relative humidity & percentage humidity

Relative humidity compares actual vapor partial pressure to the saturation vapor pressure at the same temperature; percentage humidity is the analogous ratio defined on humidity itself.

3

Wet-bulb & dry-bulb temperature

Dry-bulb is the ordinary thermometer reading; wet-bulb is the (lower) temperature reached by a wetted wick in the same air stream, from simultaneous heat and mass transfer at its surface.

4

Adiabatic saturation temperature

The temperature reached by air in prolonged contact with water at constant enthalpy, numerically very close to (though conceptually distinct from) the wet-bulb temperature for the air-water system specifically.

5

Psychrometric chart

A graphical tool plotting humidity against dry-bulb temperature, with wet-bulb, relative humidity, and humid volume lines overlaid, used to read multiple properties from any two known values.

6

Drying-rate curve

A plot of drying rate against moisture content, showing an initial adjustment period, a constant-rate period, and one or more falling-rate periods, separated by the critical moisture content.

7

Constant-rate drying

Surface moisture evaporates at a rate limited only by external heat and mass transfer to/from the drying surface, moisture content decreases linearly with time in this period.

8

Falling-rate drying

After the critical moisture content, internal moisture diffusion within the solid limits the rate, which now decreases as moisture content drops, often modeled as linear in this regime for a first estimate.

Essential Formulas

Full formula reference →

H=1829⋅pwP−pwH = \dfrac{18}{29}\cdot\dfrac{p_w}{P-p_w}

Absolute humidity from water vapor partial pressure pw and total pressure P

%RH=pwpw∗×100\%RH = \dfrac{p_w}{p_w^{*}} \times 100

Relative humidity, ratio of actual to saturation vapor pressure at the same temperature

%H=HHs×100\%H = \dfrac{H}{H_s} \times 100

Percentage humidity, ratio of actual to saturation humidity at the same temperature

vH=(129+H18)RT/Pv_H = \left(\dfrac{1}{29} + \dfrac{H}{18}\right)RT/P

Humid volume, volume of moist air per unit mass of dry air

Tdb−Twb≈kyλh(Hs−H)/ky  (air-water system: Twb≈Tas)T_{db} - T_{wb} \approx \dfrac{k_y \lambda}{h}(H_s - H)\Big/k_y \;\text{(air-water system: } T_{wb} \approx T_{as}\text{)}

Wet-bulb depression relates to humidity driving force via the psychrometric ratio h/(ky·cs), ≈ 1 for air-water

Rc=Ls(W1−Wc)A tcR_c = \dfrac{L_s(W_1-W_c)}{A\,t_c}

Constant-rate drying, rate Rc from initial moisture W1 to critical moisture Wc over time tc

tc=Ls(W1−Wc)ARct_c = \dfrac{L_s(W_1-W_c)}{AR_c}

Time to complete the constant-rate period

tf=LsWcARcln⁡ ⁣(WcW2)t_f = \dfrac{L_s W_c}{AR_c}\ln\!\left(\dfrac{W_c}{W_2}\right)

Time for the (linear) falling-rate period, from Wc down to final moisture W2

Visual Reference

Free moisture content, W (kg/kg dry solid)Drying rate, R← drying proceeds this waycritical point, Wc = 0.15constant-rate periodfalling-rate period
Same numbers as the worked example above (W1 = 0.35, Wc = 0.15, Rc = 2) — rate holds flat while surface moisture keeps pace with the heat supply, then declines linearly once internal moisture movement becomes the bottleneck.
The interior lifting plates of an industrial rotary dryer
Inside a rotary dryer — the lifting flights cascade wet solid through the hot gas stream, exactly the surface-renewal mechanism the constant-rate period above depends on. RICHI Manufacture, CC BY 4.0, via Wikimedia Commons.

Derivations & Physical Insight

Why the Falling-Rate Drying Time Uses a Logarithmic Form

In the linear falling-rate model, drying rate R is assumed directly proportional to the free moisture content W (measured above equilibrium moisture), with the same proportionality constant that made R = Rc exactly at the critical moisture Wc: R = (Rc/Wc)·W. Since R = −(Ls/A)(dW/dt) by definition (moisture loss rate per unit drying area), setting these equal gives a first-order linear ODE in W:

Separating variables and integrating from Wc (at t = 0 of the falling-rate period) to W2 (final moisture) produces a natural logarithm, not a linear time dependence, physically, this is exactly the same mathematical structure as any process whose rate is proportional to its own remaining "amount" (like first-order reaction decay or RC-circuit discharge), which is why falling-rate drying time scales as ln(Wc/W2) rather than linearly with moisture removed.

−LsAdWdt=RcWcW  ⇒  tf=LsWcARcln⁡ ⁣(WcW2)-\dfrac{L_s}{A}\dfrac{dW}{dt} = \dfrac{R_c}{W_c}W \;\Rightarrow\; t_f = \dfrac{L_s W_c}{AR_c}\ln\!\left(\dfrac{W_c}{W_2}\right)

Why Wet-Bulb Temperature Is Lower Than Dry-Bulb (Unless Air Is Saturated)

A wetted wick in an unsaturated air stream loses water by evaporation, which requires latent heat, and that heat can only come from the air and the wick itself cooling down, since there's no other heat source at the wick surface in the simplest adiabatic picture. As the wick cools below the air's dry-bulb temperature, a temperature difference (Tdb − Twb) develops, driving sensible heat transfer from the warmer air into the wick, which exactly balances the latent heat carried away by evaporating moisture at steady state.

The wick keeps cooling (and evaporation keeps proceeding) until this balance is reached, at that equilibrium wet-bulb temperature, incoming sensible heat exactly equals outgoing latent heat of vaporization, so the wick temperature stabilizes below the surrounding dry-bulb temperature by an amount that depends on how far the air is from saturation. If the air were already saturated (100% relative humidity), no net evaporation could occur, sensible heat transfer would have nothing to balance, and wet-bulb and dry-bulb temperatures would coincide.

Worked Practice Problems

Original practice problems in the GATE CH style, not copied from any question bank. Work them before reading the solution.

1-mark · NAT

Absolute Humidity from Relative Humidity

Problem: Air at 30°C has a relative humidity of 60%. The saturation vapor pressure of water at 30°C is 31.8 mmHg, and total pressure is 760 mmHg. Find the absolute humidity.

Given: T = 30°C, RH = 60%, p*w = 31.8 mmHg, P = 760 mmHg.

pw=RH×pw∗=0.60×31.8=19.08 mmHgp_w = RH \times p_w^{*} = 0.60 \times 31.8 = 19.08\ \text{mmHg}
H=1829⋅pwP−pw=1829⋅19.08760−19.08H = \dfrac{18}{29}\cdot\dfrac{p_w}{P-p_w} = \dfrac{18}{29}\cdot\dfrac{19.08}{760-19.08}

Answer: H ≈ 0.01606 kg water/kg dry air

2-mark · NAT

Constant-Rate Drying Time for a Wet Solid

Problem: A wet solid (dry mass Ls = 50 kg, drying area A = 5 m²) is dried from initial free moisture W1 = 0.35 kg water/kg dry solid to the critical moisture Wc = 0.15 kg water/kg dry solid at a constant drying rate Rc = 2.0 kg/(m²·h). Find the time for the constant-rate period.

Given: Ls = 50 kg, A = 5 m², W1 = 0.35, Wc = 0.15, Rc = 2.0 kg/(m²·h).

tc=Ls(W1−Wc)ARc=50×(0.35−0.15)5×2.0t_c = \dfrac{L_s(W_1-W_c)}{AR_c} = \dfrac{50 \times (0.35-0.15)}{5 \times 2.0}
=50×0.2010= \dfrac{50 \times 0.20}{10}

Answer: tc = 1.0 hour

Topic-wise PYQ Frequency

High

Drying-rate curves (constant & falling rate)

GATE 2024 Q43 and GATE 2025 Q65 both tested drying-time numericals, one of the most consistently examined mass-transfer topics.

Medium

Psychrometry & humidity calculations

GATE 2025 Q47 (humidity/psychrometry) and GATE 2026 Q38 (psychrometry) confirm regular testing.

Recommended Study Order

  1. 1

    1. Humidity, relative humidity & humid volume

    The foundational psychrometric properties, practice converting between them using the Antoine equation for water's vapor pressure.

  2. 2

    2. Wet-bulb & adiabatic saturation temperature

    Builds directly on humidity concepts and is a frequent short numerical or conceptual question.

  3. 3

    3. Drying-rate curve & constant-rate drying

    The highest-yield numerical style, practice identifying the constant-rate period and computing drying time from it.

  4. 4

    4. Falling-rate drying

    A direct extension once constant-rate drying is comfortable, using the same linear-model logarithmic time equation.

Common Pitfalls

✗ Confusing wet-bulb temperature with dew point temperature.

✓ Dew point is where the current vapor pressure equals the saturation pressure (condensation begins, no evaporative cooling involved); wet-bulb is a dynamic evaporative-cooling equilibrium, the two are numerically different except at saturation.

✗ Applying the constant-rate drying equation past the critical moisture content.

✓ Once moisture drops below Wc, the rate no longer stays constant, switch to the falling-rate equation, which uses a different (logarithmic, for the linear model) time relationship.

✗ Mixing up free moisture content (measured above equilibrium moisture) with total moisture content in drying calculations.

✓ Drying-rate curves and time equations use free moisture (W = total moisture − equilibrium moisture), subtract the equilibrium moisture content first if the problem gives total moisture.

✗ Using absolute humidity and percentage humidity interchangeably.

✓ Absolute humidity H is a mass ratio (kg water/kg dry air); percentage humidity %H = H/Hs×100 compares it to the saturation humidity at the same temperature, they are not the same quantity.

Put It Into Practice

Work the humidity and constant-rate drying problems above, then apply the same rate-curve identification method to the Drying & Humidification questions in the full GATE previous-year test set.

Open the Antoine Equation Calculator →Take a Practice Test →

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