• Pixel-art sticker of Charleon, personifying Charles's Law, with the caption “Warmer Gas, Bigger Balloon.”

IndexHeat & EntropySticker

Charleon

Charles's Law Physics

\[\frac{V_1}{T_1} = \frac{V_2}{T_2}\]
Regular price $4.99 USD
Regular price Sale price $4.99 USD
Sale Sold out
Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Charleon, a balloon who grows when the gas inside her warms up.

Charles's law says that for a fixed amount of gas at constant pressure, the volume is proportional to the absolute temperature. Double the temperature in kelvin and the volume doubles. Jacques Charles studied this in the 1780s, and Joseph Louis Gay-Lussac published careful measurements in 1802.

The temperatures must be in kelvin, not degrees Celsius. A 3.0 L balloon at 300 K warmed to 360 K grows to 3.0 × 360 / 300 = 3.6 L. Put a balloon from a 25 °C room (298 K) into a 0 °C freezer (273 K) and its volume shrinks to about 273 / 298 ≈ 0.92 of what it was.

The reason is molecular. Hotter gas molecules move faster and hit the walls harder, so to keep the pressure the same, the gas spreads out until the hits are less frequent.

Hot-air balloons use this. Heating the air inside makes it expand, so some of it leaves through the opening. The air left inside is less dense than the cooler air outside, and the balloon floats.

Equations

\[\frac{V_1}{T_1} = \frac{V_2}{T_2}\]
Symbols
SymbolMeaningUnit
\(V_1\) initial volume \(\mathrm{m³}\)
\(T_1\) initial absolute temperature \(\mathrm{K}\)
\(V_2\) final volume \(\mathrm{m³}\)
\(T_2\) final absolute temperature \(\mathrm{K}\)