Atmospheric Humidity lab report

1. Title and aim

Determination of Atmospheric Humidity and the Psychrometric Constant. Determine the psychrometric constant A, actual water vapor pressure e, relative humidity RH, and dew-point temperature of ambient air across wet-bulb depressions from 2.0 °C to 10.0 °C at dry-bulb temperature 25.0 °C using a ventilated wet-and-dry bulb psychrometer and a polished-mirror dew-point hygrometer, verifying the Ferrel-Sprung psychrometric equation Δe = e_s(t_w) − e = A · P_atm · (t_d − t_w).

2. Abstract

Five observations were generated from the ideal teaching model over the settings listed below. A straight-line fit gave an estimate of Psychrometric constant A of 6.6000e-04 K⁻¹, differing by 0.001% from the model value. The reported scatter comes from scale rounding and any stated model approximation, not measured laboratory noise.

3. Apparatus and fixed settings

• Precision Ventilated Wet-and-Dry Bulb Psychrometer (Assmann Type): Comprises two matched, radiation-shielded secondary standard thermometers graduated in 0.1 °C divisions, equipped with a motor-driven aspiration fan delivering a uniform airflow (≥ 3.0 m s⁻¹) across the dry bulb and cotton-sleeved wet bulb.
• Regnault Polished-Mirror Dew-Point Hygrometer Apparatus: A thin-walled silvered copper thimble containing volatile diethyl ether, equipped with an aspirator air tube to induce rapid evaporative cooling and an illuminated viewing window to detect the exact onset of moisture condensation.
• Fortin Precision Mercurial Laboratory Barometer: Measures the prevailing ambient atmospheric pressure P_atm in mmHg and kPa to ±0.1 mmHg, required for the barometric factor in the Ferrel-Sprung psychrometric relation.
• Fine Muslin Wick and Distilled Water Reservoir: A high-purity, degreased tubular cotton sleeve fitted snugly over the wet bulb, drawing pure distilled water continuously by capillary action without introducing dissolved salts that would lower water vapor pressure.
• Digital Immersion RTD Temperature Sensor (Reference Dew Sensor): Submerged inside the dew cup ether bath adjacent to the polished silver mirror wall to register the appearance and disappearance dew temperatures to ±0.02 °C.
• Rubber Squeeze Bulb and Needle Valve Aspiration Tube: Provides controlled, gentle airflow through the volatile ether bath, allowing the experimenter to regulate the rate of cooling and warming around the dew point.
• Ambient dry-bulb laboratory temperature maintained at t_d = 25.00 °C (saturation vapor pressure e_s(25 °C) = 3.168 kPa = 23.76 mmHg).
• Standard ambient atmospheric barometric pressure P_atm = 101.325 kPa (760.0 mmHg) verified by Fortin mercurial barometer.
• Ventilated psychrometer airflow maintained at constant forced convection velocity v ≥ 3.0 m s⁻¹ via motorized aspiration fan.
• Regnault-style polished silvered-copper dew-point mirror cup with integral internal optical illumination and magnifier.
• Accepted standard psychrometric constant for ventilated psychrometer: A_ref = 6.600 × 10⁻⁴ K⁻¹ (psychrometric slope γ = 66.875 Pa K⁻¹).

4. Theory and graph choice

Atmospheric humidity—the concentration of invisible gaseous water vapor dispersed throughout ambient air—is a paramount meteorological parameter that governs terrestrial weather dynamics, atmospheric thermodynamics, cloud formation, precipitation, and biophysical evaporative cooling. In atmospheric physics, humidity is characterized through several complementary metrics: absolute humidity (vapor density, expressed in grams of water vapor per cubic meter of air), specific humidity (mass of vapor per unit mass of moist air), mixing ratio (mass of vapor per unit mass of dry air), partial vapor pressure e (exerted by water molecules in Pascals or millimeters of mercury), and relative humidity (RH, the ratio of actual vapor pressure e to the saturation vapor pressure e_s at prevailing dry-bulb temperature t_d, expressed as a percentage: RH = (e / e_s(t_d)) × 100%). While direct gravimetric determination—drawing a metered volume of air through desiccating tubes containing phosphorus pentoxide or anhydrous calcium chloride and weighing the absorbed water—is conceptually straightforward, it is experimentally tedious and slow. Consequently, physical meteorology universally relies on indirect thermodynamic instruments, principally the wet-and-dry bulb psychrometer (formulated by Ernst Ferdinand August in 1825 and Adolf Sprung in 1888) and the dew-point hygrometer (devised by John Frederic Daniell in 1820 and Henri Victor Regnault in 1845). In a psychrometer, two matched thermometers are exposed to a steady stream of air: the dry bulb indicates true ambient air temperature t_d, while the wet bulb is enveloped in a porous cotton muslin sleeve saturated with pure distilled water. Evaporation of water into the unsaturated airstream absorbs latent heat of vaporization (L_v ≈ 2.45 × 10⁶ J kg⁻¹), chilling the wet bulb until dynamic thermal equilibrium is established—where convective heat transfer from the warmer ambient air to the wet bulb exactly balances the latent heat carried away by the diffusing water vapor. The resulting wet-bulb depression Δt = t_d − t_w is thermodynamically related to ambient vapor pressure e via the classical Ferrel-Sprung psychrometric equation: e = e_s(t_w) − A · P_atm · (t_d − t_w), where e_s(t_w) is the saturation vapor pressure at wet-bulb temperature t_w, P_atm is ambient barometric pressure, and A is the empirical psychrometric constant (A ≈ 6.60 × 10⁻⁴ K⁻¹ for ventilated airflow ≥ 2.5 m s⁻¹). In complementary dew-point hygrometry, ambient air is brought into contact with a brightly polished metallic mirror whose temperature is progressively lowered by evaporative cooling of an internal volatile liquid until the surrounding air layer becomes saturated, whereupon the first microscopic film of dew dulls the mirror finish. At this dew-point temperature t_dew, the actual vapor pressure equals the saturation vapor pressure: e = e_s(t_dew). By pairing psychrometric wet-bulb depressions with dew-point determinations across diverse ambient humidity states, students can directly verify the Ferrel-Sprung relation, plot the vapor pressure depression Δe = e_s(t_w) − e against wet-bulb depression Δt, extract the psychrometric slope γ = A · P_atm, determine the universal psychrometric constant A = γ / P_atm, and accurately calculate atmospheric relative humidity.

The calculation fits y = mx + b in SI units. The graph may display scaled axes for readability; those display factors are removed before calculating the physical result. The gradient has units Pa K⁻¹.

5. Method

1. Read the laboratory Fortin mercurial barometer to 0.1 mmHg, applying temperature corrections to establish the true ambient barometric pressure P_atm (baseline P_atm = 101.325 kPa = 760.0 mmHg). Clean the wet-bulb cotton muslin sleeve thoroughly with pure distilled water, ensuring it fits snugly without wrinkles or air gaps over the thermometer bulb, and fill the wetting reservoir with fresh distilled water.
2. Activate the motor-driven aspiration fan on the psychrometer to generate a steady airflow of at least 3.0 m s⁻¹ through the protective radiation shields. Allow the airflow to stabilize for three minutes, then record the steady dry-bulb temperature t_d (nominal baseline t_d = 25.0 °C). Confirm that the dry bulb reading remains constant to within ±0.05 °C.
3. Observe the descending temperature of the wet-bulb thermometer under forced aspiration, recording readings every thirty seconds. Once the wet-bulb temperature stabilizes at its minimum plateau for two consecutive minutes (indicating dynamic equilibrium between convective sensible heat gain and latent heat loss), record the wet-bulb temperature t_w and compute the wet-bulb depression Δt = t_d − t_w.
4. Gently squeeze the rubber aspirator bulb to bubble ambient air through the volatile ether contained within the silvered dew cup, watching the highly polished mirror surface through the optical magnifier. As evaporative cooling lowers the cup temperature, note the exact thermometer reading t_1 at the first instant a dulling film of condensed dew droplets mists the silver mirror.
5. Immediately cease air aspiration through the ether, allowing the dew cup to warm slowly by heat conduction from the room. Note the exact temperature t_2 at which the moisture film completely vanishes and the mirror regains its brilliant specular reflection. Compute the true dew-point temperature as the arithmetic mean: t_dew = (t_1 + t_2) / 2.
6. Using saturation vapor pressure tables (or the Tetens equation), evaluate the saturation vapor pressure at the wet-bulb temperature e_s(t_w) and the actual vapor pressure e = e_s(t_dew). Compute the vapor pressure depression Δe = e_s(t_w) − e in Pascals. Repeat the observations across multiple ambient humidity states (wet-bulb depressions Δt = 2.0, 4.0, 6.0, 8.0, 10.0 °C). Plot Δe versus Δt, determine the slope γ, and compute the psychrometric constant A = γ / P_atm.

6. Observations and calculation table

All observations use fixed model settings. Values are rounded only at the instrument reading stage; further calculations use full precision. Repeated physical trials are not claimed.

Download the sample observations (CSV) ↓

7. Worked calculation for one observation

8. Graph, gradient and final calculation

Dots show the sample observations. The line is the ordinary least-squares fit.

9. Uncertainty and comparison

Percentage difference = |estimate − model value| / |model value| × 100 = 0.0007%. Percentage difference is not experimental uncertainty.

For n = 5 observations, Σresidual² = 0.00300; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 0.00500. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 0.03317.

Propagating only the relevant fit coefficient gives a fit-only standard error of 4.9346e-08 K⁻¹. This is a one-standard-error quantity under the regression assumptions. Deterministic rounded model data do not supply a complete physical uncertainty budget.

Ventilation airflow velocity variations across the wet-bulb wick (Sprung psychrometric constant A assumes steady forced draft ≥ 2.5 m s⁻¹; stagnant air elevates A to ~8.0 × 10⁻⁴ K⁻¹), wick cleanliness and dissolved mineral salts altering pure water vapor pressure, thermometer calibration offset and emergent stem cooling, subjective visual detection of the initial microscopic dew deposit on the silvered mirror surface (±0.2 °C), ambient barometric pressure fluctuations (±0.2 mmHg), and thermal conduction along the dew-cup thermometer sheath contribute experimental uncertainty. The OLS regression standard error quantifies random scatter across depression stations, but does not capture shared air-speed calibration errors or water impurities.

10. Result and discussion

The observations follow the stated model relationship. Check whether the intercept and residual pattern suggest a systematic offset or a missing approximation. Agreement with the model does not independently verify its input constants.

11. Precautions and limitations

• Always use pure distilled or deionized water on the wet-bulb muslin sleeve; tap water leaves mineral deposits that depress the saturation vapor pressure.
• Ensure the aspiration fan operates continuously at ≥ 3.0 m/s during psychrometric readings to maintain a standardized convective boundary layer.
• Carefully average the temperatures of appearance and disappearance of the dew film on the polished mirror to cancel thermal conduction gradients through the metal cup.
• Avoid breathing toward the psychrometer or dew cup during observations, as exhaled moisture and carbon dioxide will alter local humidity and temperature.

The teaching model assumes a constant psychrometric factor A = 6.60 × 10⁻⁴ K⁻¹ corresponding to ideal forced ventilation and pure water. In an unventilated room or with a contaminated wick, A can increase to ~8.0 × 10⁻⁴ K⁻¹, and non-ideal gas compressibility factors become slightly noticeable at high ambient temperatures. The Ferrel-Sprung psychrometric equation and the dew-point method illustrate the fundamental thermodynamic balance between sensible convective heat transfer and latent mass transfer. The experimental psychrometric constant A = 6.60 × 10⁻⁴ K⁻¹ bridges microscopic molecular diffusion with macroscopic meteorological observations of humidity and weather.

12. Conclusion

The worked example illustrates how to obtain Psychrometric constant A from measurements, graph variables and a fitted coefficient. The estimate is 6.6000e-04 K⁻¹. A real experiment must additionally evaluate the apparatus-specific uncertainties and corrections described above.