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Qwestrum Engineering360 · Mechanical Engineering · Refrigeration & HVAC

Psychrometrics

Moist-air state uses specific humidity ω = 0.622·P_v/(P − P_v), relative humidity RH = P_v/P_vs, and enthalpy h = c_pa·T + ω(h_fg + c_pv·T). These are read from the psychrometric chart, per RK Rajput.
Exam tip: lock the sign convention (Q into system, W by system in P.K. Nag) before substituting; use absolute temperature for ideal-gas and efficiency ratios.

Key formulas & points

Skim these first — then read the full notes below.

  • Psychrometric chart: dry bulb, wet bulb, dew point
  • SensibleheatfactorSHF=Qs(Qs+Ql)Sensible heat factor SHF = \frac{Q_{s}}{(Q_{s} + Q_{l})}
  • Adiabatic saturation process follows constant WB line

Topic details

Introduction

Psychrometrics is the study of air-water-vapour mixtures and is essential for air-conditioning design. RK Rajput defines the psychrometric properties — dry-bulb, wet-bulb, dew-point temperatures, humidity ratio, and enthalpy — and their representation on the psychrometric chart.

Scope in B.Tech and GATE syllabus

The chart lets students locate an air state from any two independent properties and read the rest without calculation. Dry-bulb temperature is the x-axis; humidity ratio the y-axis; constant wet-bulb, enthalpy, and RH lines cross it.

Why this topic matters in practice

Adiabatic saturation and the wet-bulb process follow constant wet-bulb (≈ constant enthalpy) lines. Being able to fix a state and read ω, h, and RH off the chart quickly is the exam skill, since most AC-process problems build on it.

Key relations & formulas

ω=0.622⋅Pv(P−Pv)\omega = 0.622\cdot \frac{P_{v}}{(P - P_{v})}
(specific humidity, kg/kg dry air)
h=cpa⋅T+ω(hfg+cpv⋅T)h = c_{pa}\cdot T + \omega(h_{fg} + c_{pv}\cdot T)
(enthalpy of moist air)
RH=PvPvs×100RH = \frac{P_{v}}{P_{vs}} \times 100%
(relative humidity)

Formulas (Indian textbook notation)

  • WBT≈Twhensaturated;WBT<DBTwhenunsaturatedWBT \approx T when saturated; WBT < DBT when unsaturated

Notation and sign conventions

Relation 1 —
ω=0.622⋅Pv/\omega = 0.622\cdot P_{v}/
ω=0.622⋅Pv(P−Pv)\omega = 0.622\cdot \frac{P_{v}}{(P - P_{v})}
(specific humidity, kg/kg dry air)
Write this relation with symbols exactly as in Refrigeration & Air Conditioning — RK Rajput before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
h=cpa⋅T+ωh = c_{pa}\cdot T + \omega
h=cpa⋅T+ω(hfg+cpv⋅T)h = c_{pa}\cdot T + \omega(h_{fg} + c_{pv}\cdot T)
(enthalpy of moist air)
Write this relation with symbols exactly as in Refrigeration & Air Conditioning — RK Rajput before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
RH=PvPvs×100RH = \frac{P_{v}}{P_{vs}} \times 100%
RH=PvPvs×100RH = \frac{P_{v}}{P_{vs}} \times 100%
(relative humidity)
Write this relation with symbols exactly as in Refrigeration & Air Conditioning — RK Rajput before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 4 —
WBT≈Twhensaturated;WBT<DBTwhenunsaturatedWBT \approx T when saturated; WBT < DBT when unsaturated

Formulas (Indian textbook notation)

  • WBT≈Twhensaturated;WBT<DBTwhenunsaturatedWBT \approx T when saturated; WBT < DBT when unsaturated
Write this relation with symbols exactly as in Refrigeration & Air Conditioning — RK Rajput before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Fundamentals and definitions

Specific (absolute) humidity ω = 0.622·P_v/(P − P_v) is the mass of vapour per kg of dry air, derived from the ideal-gas ratio and the molecular-mass ratio 18/29 ≈ 0.622.

Governing relations in practice

Relative humidity RH = P_v/P_vs compares the actual vapour pressure to the saturation value at the same temperature; it drives comfort and condensation. Degree of saturation is the ratio of actual to saturated humidity ratio.

Design and analysis considerations

Enthalpy of moist air (per kg dry air) is h = c_pa·T + ω(h_fg + c_pv·T), combining the sensible heat of dry air and the latent-plus-sensible heat of the vapour. This is the quantity that changes in AC processes.

Advanced theory and extensions

Dew-point temperature is where vapour begins to condense on cooling at constant ω; wet-bulb temperature is the adiabatic-saturation temperature, always between dew-point and dry-bulb for unsaturated air. The psychrometric chart encodes all these relations graphically for rapid problem solving.

Assumptions and validity limits

State assumptions explicitly before using any relation for psychrometrics — 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 Refrigeration & HVAC 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 Refrigeration & HVAC 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 psychrometrics.
4. Use equation 1:
ω=0.622⋅Pv/\omega = 0.622\cdot P_{v}/
.
5. Use equation 2:
h=cpa⋅T+ωh = c_{pa}\cdot T + \omega
.
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

Psychrometrics appears in buildings, cold storage, and comfort AC. In Indian mechanical curricula this topic is tested because it connects theory to cooling, heating, and air treatment.
GATE and semester exams often combine psychrometrics with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use psychrometrics?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

• Using total pressure instead of (P − P_v) in the humidity-ratio formula
• Confusing dew-point, wet-bulb, and dry-bulb temperatures
• Forgetting the latent-heat term ω·h_fg in moist-air enthalpy
• Reading the wrong constant-property line on the psychrometric chart

Quick revision checklist

Before attempting psychrometrics problems, confirm you can:
1. Psychrometric chart: dry bulb, wet bulb, dew point
2.
SensibleheatfactorSHF=Qs(Qs+Ql)Sensible heat factor SHF = \frac{Q_{s}}{(Q_{s} + Q_{l})}

3. Adiabatic saturation process follows constant WB line
Revise the solved examples in Refrigeration & Air Conditioning — RK Rajput 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.

Specific humidity of air

Problem

Air at total pressure P = 101.3 kPa has a vapour partial pressure P_v = 2.0 kPa. Find the specific humidity.

Solution

ω = 0.622·P_v/(P − P_v) = 0.622 × 2.0/(101.3 − 2.0) = 1.244/99.3 = 0.01253 kg/kg dry air.

Conceptual check — Psychrometrics

Problem

In a Refrigeration & HVAC semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of psychrometrics." What should a complete answer include?

Practice questions

Most-asked interview and GATE questions for this topic — expand any item for a model answer.

  1. 1
    What is Psychrometrics, and why does it appear in B.Tech / GATE syllabi?

    Model answer

    Moist-air state uses specific humidity ω = 0.622·P_v/(P − P_v), relative humidity RH = P_v/P_vs, and enthalpy h = c_pa·T + ω(h_fg + c_pv·T). These are read from the psychrometric chart, per RK Rajput.
  2. 2
    State the relation ω = 0.622·P_v/ and name each symbol.

    Model answer

    The governing relation is ω=0.622⋅Pv/\omega = 0.622\cdot P_{v}/. Write every symbol with SI units before substituting numbers.
  3. 3
    State the relation h = c_pa·T + ω and name each symbol.

    Model answer

    The governing relation is h=cpa⋅T+ωh = c_{pa}\cdot T + \omega. Write every symbol with SI units before substituting numbers.
  4. 4
    State the relation RH = P_v/P_vs × 100% and name each symbol.

    Model answer

    The governing relation is RH=PvPvs×100RH = \frac{P_{v}}{P_{vs}} \times 100%. Write every symbol with SI units before substituting numbers.
  5. 5
    State the relation WBT ≈ T when saturated; WBT < DBT when unsaturated and name each symbol.

    Model answer

    The governing relation is WBT≈Twhensaturated;WBT<DBTwhenunsaturatedWBT \approx T when saturated; WBT < DBT when unsaturated. Write every symbol with SI units before substituting numbers.
  6. 6
    Explain: Psychrometric chart: dry bulb, wet bulb, dew point

    Model answer

    Psychrometric chart: dry bulb, wet bulb, dew point — state the assumption range and one exam trap linked to this point.
  7. 7
    Explain: Sensible heat factor SHF = Q_s/(Q_s + Q_l)

    Model answer

    SensibleheatfactorSHF=Qs(Qs+Ql)Sensible heat factor SHF = \frac{Q_{s}}{(Q_{s} + Q_{l})} — state the assumption range and one exam trap linked to this point.
  8. 8
    Explain: Adiabatic saturation process follows constant WB line

    Model answer

    Adiabatic saturation process follows constant WB line — state the assumption range and one exam trap linked to this point.
  9. 9
    How would you correct this error in a viva: Using total pressure instead of (P − P_v) in the humidity-ratio formula?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
  10. 10
    How would you correct this error in a viva: Confusing dew-point, wet-bulb, and dry-bulb temperatures?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
  11. 11
    How would you correct this error in a viva: Forgetting the latent-heat term ω·h_fg in moist-air enthalpy?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
  12. 12
    How would you correct this error in a viva: Reading the wrong constant-property line on the psychrometric chart?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.

Exams & GATE

  • 1
    RK Rajput RAC — know how to read ω and h from chart without calculator.
  • 2
    Avoid: Using total pressure instead of (P − P_v) in the humidity-ratio formula
  • 3
    Avoid: Confusing dew-point, wet-bulb, and dry-bulb temperatures
  • 4
    Avoid: Forgetting the latent-heat term ω·h_fg in moist-air enthalpy

📖 Standard books (India)

  • Refrigeration & Air Conditioning — RK Rajput

    Read: Syllabus unit

    VCRS, psychrometry, and cooling load

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