Chemistry · Ch 10 — States of Matter
Charles's Law
Charles's Law
J. Charles and Gay-Lussac independently found, from experiment, that for a fixed mass of gas held at constant pressure, its volume rises by exactly of its volume at °C for every one-degree rise in temperature: . Rewriting the Celsius temperature as an absolute temperature (K) °C (the scale named after Lord Kelvin, who calculated absolute zero to be °C in 1854) turns this into the much simpler statement , i.e. (constant), or . This is Charles's law: at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature. Graphically, a plot of against Celsius temperature at fixed pressure (called an isobar) is a straight line that, when extrapolated backwards, always crosses zero volume at exactly °C, regardless of the gas or the fixed pressure chosen -- this hypothetical zero-volume point defines absolute zero (0 K) on the kelvin scale; in reality every gas liquefies before reaching that temperature, so absolute zero itself is never actually attainable. In everyday terms, Charles's law means gases expand on heating and contract on cooling at constant pressure -- which is exactly why hot a …
What this figure shows. Two cylinder-with-piston diagrams at a fixed 1 atm pressure, connected by a 'Heat' arrow. The first (cooler) cylinder shows 2 litres of gas at 300 K; after heating, the second cylinder shows the piston having risen so the gas now occupies 4 litres at 600 K -- a direct illustration that doubling the absolute temperature at constant pressure doubles the volume, consistent with Charles's law. …
What this figure shows. A graph with volume V on the y-axis and Celsius temperature on the x-axis, showing two straight lines with positive slope, one for pressure P1 and a second, differently-sloped line for a different pressure P2 -- each line is called an isobar. Both lines, when extended backwards (dashed) toward zero volume, meet the temperature axis at exactly the same point, -273.15 degrees Celsius (marked as 0 K on a second, kelvin, temperature axis running alongside 273.15 K at the Celsius zero mark) -- visually demonstrating that every gas's zero-volume extrapolation converges on the same absolute-zero temperature regardless of t …
Worked out. A certain mass of gas occupies 1x10^-4 dm3 at 300 K; find its volume at 450 K, same pressure. By Charles's law, V1/T1 = V2/T2, so V2 = V1 x T2/T1 = (1x10^-4 dm3 x 450 K)/300 K = 1.5x10^-4 dm3. Raising the absolute temperature by a factor of 1.5 (300 K to 450 K) increases the volume by the same factor, exactly as Charles's law predicts at constant pressure. …