Determine the thermal coefficient of volume expansion of dry air at constant atmospheric pressure (β) by measuring the expansion volume V of a bulb-confined air sample across temperatures from 0.0 °C to 80.0 °C using a constant-pressure air dilatometer with a mercury leveling reservoir, and extrapolate to determine the absolute zero of temperature. Explore a virtual apparatus, collect readings and analyse a graph.
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Readings are generated by an ideal model. The diagram is schematic and is not to scale.
The teaching simulation models an ideal gas under isobaric conditions at constant atmospheric pressure B = 101.325 kPa (760.0 mmHg) and initial bulb volume V_0 = 100.00 cm³ at 0.00 °C. In physical laboratory experiments, temperature non-uniformity across the heated water bath introduces minor temperature measurement offsets (±0.2 °C), thermal response latency in the thermometer sensor causes reading delays during heating, capillary stem volume exclusion (a small fraction of the gas column in the capillary stem remains outside the bath at room temperature, ~0.8%), meniscus leveling parallax error across the graduated tube (±0.05 cm³), atmospheric barometric drift over the heating run (±0.2 mmHg), and slight thermal expansion of the borosilicate glass bulb envelope (borosilicate volume expansion α_v ≈ 9.9 × 10⁻⁶ K⁻¹) contribute experimental uncertainty. The simulation evaluates confined gas volume using V_t = V_0 (1 + β_ref · t), where V_0 = 100.00 cm³ is the ice-point volume, β_ref = 1 / 273.15 K⁻¹ is the ideal gas volume expansion coefficient, and t is the bath temperature in °C. The volume in cm³ is rounded to 0.01 cm³ to simulate precision burette dilatometry. Ordinary least-squares regression of volume V (m³) against temperature t (°C) across five temperature stations (0.0, 20.0, 40.0, 60.0, 80.0 °C) yields the reported thermal volume expansion coefficient β = m / b and extrapolated absolute zero T_0 = −b / m.
Hermetically encloses the nominal 100.00 cm³ dry air sample within a spherical thin-walled glass chamber designed for high thermal conductance and uniform immersion within the variable-temperature liquid heating bath.
Provides a stable, uniform temperature enclosure around the specimen bulb, equipped with a mechanical motor-driven paddle stirrer to eliminate thermal stratification and an electric heater to control temperatures from 0.0 °C to 80.0 °C.
A uniform-bore precision glass tube with metric millimeter graduations etched along its stem, receiving the gas expanding out of the bulb to measure volumetric dilatation ΔV to ±0.05 cm³.
An open glass mercury reservoir mounted upon a smooth vertical rack-and-pinion sliding carriage, elevated or lowered by the operator to match the mercury level in tube T₂ so that gas pressure remains strictly isobaric at barometric pressure P = B.
Monitors the uniform water bath temperature directly adjacent to the glass bulb with a resolution of ±0.05 °C, ensuring thermal equilibrium between the bath fluid and enclosed air.
Connects the bottom of the graduated measuring tube to the movable leveling reservoir, securely containing triple-distilled liquid mercury without kinking or volume compliance under hydrostatic head changes.
Determine the thermal coefficient of volume expansion of dry air at constant atmospheric pressure (β) by measuring the expansion volume V of a bulb-confined air sample across temperatures from 0.0 °C to 80.0 °C using a constant-pressure air dilatometer with a mercury leveling reservoir, and extrapolate to determine the absolute zero of temperature. Suggested independent settings: 0.0, 20.0, 40.0, 60.0, 80.0 °C.
Fill the thermal bath with finely shaved pure distilled ice and water, ensuring the glass bulb T₁ is completely submerged up to the index mark on the capillary stem. Vigorously agitate the slurry for several minutes until the thermometer reads 0.00 °C. Adjust the movable leveling reservoir until the mercury meniscus in the open tube aligns precisely with the meniscus in the graduated tube T₂ (isobaric condition, Δh = 0). Record the initial ice-point volume V_0 = 100.00 cm³.
Establishing an accurate ice-point volume V_0 at 0.00 °C under true atmospheric pressure provides the reference baseline from which all subsequent fractional thermal expansion coefficients β = ΔV / (V_0 · t) are evaluated.
Replace the ice slurry with distilled water and energize the bath heater, setting the thermal controller to warm the bath to the first elevated target temperature of 20.0 °C. Maintain continuous mechanical stirring to prevent vertical convection currents or thermal boundary layers around the glass bulb.
Active stirring eliminates spatial temperature gradients throughout the water volume, ensuring that the enclosed air column attains the identical temperature indicated by the immersed thermometer.
Upon reaching each target temperature station (20.0 °C, 40.0 °C, 60.0 °C, 80.0 °C), reduce heater power and maintain a dwell time of at least three to four minutes. Confirm that the thermometer reading remains steady within ±0.05 °C and the expanding mercury meniscus in tube T₂ has ceased downward movement.
Because gases possess low volumetric heat capacity and glass has finite thermal conductivity, sufficient dwell time is mandatory to achieve complete thermal equilibrium between the water bath, glass envelope, and enclosed air mass.
Gently manipulate the rack-and-pinion thumb drive on the movable reservoir slider to lower the open mercury tube until its liquid meniscus matches the exact horizontal elevation of the meniscus in graduated tube T₂. Sight across the horizontal level index with an optical magnifier to verify zero differential height (Δh = h_open − h_closed = 0).
As gas expands upon heating, it pushes the mercury downward in tube T₂; lowering the leveling reservoir restores atmospheric pressure parity (P = B), guaranteeing strictly isobaric thermodynamic expansion.
Read the total gas volume V_t on the graduated scale of tube T₂ at the crest of the convex mercury meniscus, recording the volume to the nearest 0.05 cm³. Subtract the initial ice-point volume V_0 to compute the net thermal expansion volume ΔV = V_t − V_0.
Reading at the apex of the convex mercury meniscus with a horizontal sight line eliminates optical parallax and ensures consistent volumetric measurement across all thermal stations.
Compile the data table of volume V (in cm³ and SI units of m³) versus temperature t (in °C). Perform an ordinary least-squares linear regression fitting V = m · t + b, compute the isobaric volume expansion coefficient β = m / b, evaluate its statistical standard error, and project the regression line to V = 0 to determine the experimental absolute zero T_0 = −b / m.
Linear regression provides an unbiased mathematical fit across the entire temperature trajectory, isolating the physical slope m = V_0 β from random meniscus reading scatter and yielding an empirical determination of absolute zero.
Points are your observations. The fit uses SI x and y values before display scaling.
| # | Bath temperature t (°C) | Confined volume V (cm³) | Temperature t (°C) | Volume V (cm³) | Remove |
|---|
No readings yet. Take a virtual measurement and record it.