Abstract

This laboratory experiment investigates the relationship between temperature, pressure, and volume in a closed thermodynamic system, validating the ideal gas law ($PV=nRT$). By systematically increasing the temperature of a sealed vessel from 293K to 353K and recording corresponding pressure changes, we established a direct proportional relationship consistent with Gay-Lussac's Law. Data analysis revealed a high correlation coefficient ($R^2 = 0.998$), confirming standard kinetic theory predictions under ideal conditions.

Keywords: thermodynamics, ideal gas law, Gay-Lussac, pressure, temperature, kinetic theory

The Impact of Thermodynamic Variables on Closed-System Gases

The foundation of classical thermodynamics relies heavily on the behavior of gases under varying environmental conditions. Since the early derivations by Boyle, Charles, and Gay-Lussac, the predictability of gas expansion and pressure exertion has allowed for significant advancements in mechanical engineering and theoretical physics. This study aims to empirically verify the direct proportionality between absolute temperature and pressure in a fixed-volume system.

Methodology

A sealed constant-volume gas thermometer apparatus was utilized. The main chamber, containing 0.5 moles of dry air, was submerged in a water bath outfitted with a digital immersion heater. Pressure was monitored using a highly sensitive piezoelectric absolute pressure sensor (accuracy $\pm 0.05$ kPa). Temperature readings were captured using a calibrated K-type thermocouple.

Empirical Data

The system was allowed to reach thermal equilibrium at 5-degree intervals. The recorded data demonstrates a clear linear trend as visualized in the table below.

Temperature (K)	Pressure (kPa)	Theoretical P (kPa)	% Error
293.15	101.32	101.32	0.00%
313.15	108.15	108.23	0.07%
333.15	115.02	115.15	0.11%
353.15	121.88	122.06	0.15%

The minimal percentage error, peaking at only $0.15\%$, strongly supports the theoretical framework of the ideal gas law at standard temperatures and pressures. Deviations are likely attributable to minute heat loss to the ambient environment and the non-ideal nature of atmospheric air.

References