Verify Boyle’s law for a confined sample of dry air at constant room temperature by measuring absolute gas pressure P as a function of volume V using a mercury J-tube manometer, and determine the isothermal Boyle state constant k = P · V via linear regression of absolute pressure P against reciprocal volume 1/V. 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 strict isothermal conditions at constant room temperature T_0 = 20.00 °C (293.15 K) and standard barometric pressure B = 101.325 kPa (760.0 mmHg). In physical laboratory practice, barometric pressure drifts over hours as atmospheric weather fronts pass (±0.2 to 0.5 mmHg), capillary depression differences at the mercury-glass menisci introduce minor hydrostatic offsets (±0.2 to 0.4 mm) if tube diameters are not perfectly matched, room temperature fluctuations alter the gas temperature by ±0.2 °C, slight non-uniformity in the bore cross-section of the closed glass tube produces volume scale calibration deviations, and the presence of trace water vapor in non-dehydrated air causes slight departures from ideal gas behavior due to variable saturated vapor pressure contributions. The simulation evaluates absolute pressure using P = k / V, where the reference state constant is k = P_0 V_0 = 101,325 Pa × 30.0 × 10⁻⁶ m³ = 3.03975 J (confined volume V in cm³, with 1 cm³ = 10⁻⁶ m³). The differential mercury head is computed from Δh = (P − B) / (ρ_Hg g), with ρ_Hg = 13,546 kg m⁻³, g = 9.80665 m s⁻², and standard atmosphere B = 101.325 kPa. The calculated pressure in kPa is rounded to 0.01 kPa to simulate precision digital manometry. Ordinary least-squares regression of P (Pa) against 1/V (m⁻³) across five volume settings (20.0, 25.0, 30.0, 35.0, 40.0 cm³) yields the reported isothermal state constant k and statistical uncertainty.
Hermetically confines the dry air sample of variable volume V over a liquid mercury column, featuring precision linear graduations etched along a bore of uniform internal diameter to permit direct volumetric readings in cm³ (±0.1 cm³).
Provides an adjustable atmospheric mercury column that can be elevated or lowered along a sturdy vertical rack-and-pinion sliding mount to vary the hydrostatic head pressure Δh applied to the trapped gas column.
Fluidly interconnects the base of the closed specimen tube with the movable open leveling reservoir, containing triple-distilled mercury while resisting hydrostatic expansion, leakage, and wall distortion under pressure.
Measures the prevailing ambient atmospheric pressure B in millimeters of mercury (mmHg) and kilopascals (kPa) with vernier accuracy (±0.1 mmHg) to establish the barometric reference datum for absolute pressure calculations.
A rigid brass or steel millimeter scale mounted symmetrically between the two glass tubes, equipped with sliding hairline vernier indices to measure the exact vertical liquid meniscus heights h_closed and h_open without optical parallax.
Continuously monitors ambient air and mercury column temperatures to ensure that isothermal conditions (ΔT < 0.2 °C) are strictly preserved throughout the compression and expansion measurement sequence.
Verify Boyle’s law for a confined sample of dry air at constant room temperature by measuring absolute gas pressure P as a function of volume V using a mercury J-tube manometer, and determine the isothermal Boyle state constant k = P · V via linear regression of absolute pressure P against reciprocal volume 1/V. Suggested independent settings: 20.0, 25.0, 30.0, 35.0, 40.0 cm³.
Read the prevailing ambient laboratory atmospheric pressure B from the Fortin precision mercury barometer to ±0.1 mmHg, applying standard capillary and brass-scale temperature corrections to establish the exact reference datum B = 101.325 kPa (760.0 mmHg). Record the baseline room temperature T_0 = 20.00 °C.
Precise measurement of atmospheric pressure is required because the J-tube manometer measures gauge pressure relative to ambient atmosphere; absolute pressure equals B + Δh.
Adjust the height of the movable open leveling tube until the mercury meniscus in the open tube aligns precisely in the same horizontal plane as the mercury meniscus in the closed specimen tube (h_open = h_closed), establishing a differential hydrostatic head of Δh = 0. Verify that the enclosed air volume corresponds to the nominal baseline volume V_0 = 30.0 cm³.
Zeroing the differential head confirms that the trapped gas sample initially resides at pure atmospheric pressure B without any residual hydrostatic compression or dilation.
Execute the compression series by systematically raising the open leveling tube above the closed tube along its vertical rack slider, imposing positive hydrostatic mercury heads to compress the air sample to designated volumes of V = 25.0 cm³ and V = 20.0 cm³. Align the sliding vernier index with the apex of each meniscus to eliminate parallax.
Systematic compression reduces gas volume and increases hydrostatic head, providing the high-pressure data points (P > B) needed to test the hyperbolic isotherm.
Following each vertical adjustment of the leveling tube, pause for a dwell period of at least two to three minutes before recording pressure values. Observe the thermometer immersed in the adjacent thermal buffer to verify that the air column returns to baseline temperature T_0 = 20.00 °C.
Compressing the gas performs boundary work that causes transient adiabatic temperature elevation; dwelling allows heat to conduct through the glass walls into ambient air, preserving isothermal conditions.
Execute the expansion series by lowering the open leveling tube beneath the closed specimen tube, applying negative hydrostatic heads to expand the confined air column to volumes of V = 35.0 cm³ and V = 40.0 cm³. Record the open tube height h_open and closed tube height h_closed, computing the differential head Δh = h_open − h_closed.
Lowering the reservoir explores the rarefied, sub-atmospheric pressure regime (P < B), verifying that Boyle’s inverse law holds symmetrically in expansion as well as compression.
Compute the absolute pressure P = B + Δh (in pascals and kilopascals) and the reciprocal volume X = 1/V (in m⁻³ and display L⁻¹) for each of the five observation stations. Perform an ordinary least-squares linear regression of P against 1/V, evaluating the slope m = k, the y-intercept b, the statistical standard error, and the coefficient of determination R².
Linearization converts the equilateral hyperbola P(V) = k/V into an origin-intercepting straight line y = m x, allowing unbiased determination of the Boyle state constant k = n R T and rapid identification of systematic zero-point offsets.
Points are your observations. The fit uses SI x and y values before display scaling.
| # | Volume V (cm³) | Absolute pressure P (kPa) | Reciprocal volume 1/V (L⁻¹) | Absolute pressure P (kPa) | Remove |
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