Physics & Mechanics

Charles's Law Calculator

Calculate changes in volume and temperature of an ideal gas at a constant pressure. Essential for thermodynamics and chemistry calculations.

L
K
K
Final Volume (V₂)
10

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Temperature vs. Volume

Charles's Law (also known as the law of volumes) is an experimental gas law which describes how gases tend to physically expand when heated. It states that if the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be directly proportional.

As the temperature of a gas increases, the gas molecules gain kinetic energy and move much faster. To maintain a constant pressure against the walls of their container, they must spread further apart, physically expanding the volume of the gas.

Real-World Heating

  • Hot Air Balloons: This is the most famous application. A burner violently heats the air inside the balloon's envelope. According to Charles's law, the heated air expands. Since it now occupies a larger volume for the exact same mass, its density decreases. The balloon becomes less dense than the cold air around it, and buoyancy lifts it into the sky.
  • Tires in Winter: If you inflate your car tires to the perfect pressure during a hot summer day, you will often trigger a 'Low Tire Pressure' warning on the first freezing morning of winter. The cold temperature causes the volume of the air inside the tire to shrink.
  • Baking Bread: Yeast produces pockets of carbon dioxide gas inside dough. When placed in a hot oven, Charles's Law dictates that these gas bubbles will expand rapidly due to the heat, causing the bread to rise and become fluffy.

The Formula

V1T1=V2T2\begin{aligned} \frac{V_1}{T_1} = \frac{V_2}{T_2} \end{aligned}

Where:
V1V_1=
Initial Volume
T1T_1=
Initial Absolute Temperature (Kelvin)
V2V_2=
Final Volume
T2T_2=
Final Absolute Temperature (Kelvin)

Example Calculation

A perfectly elastic balloon contains $5 , \text{Liters}$ of air at a room temperature of $300 , \text{K}$ (about $27^\circ\text{C}$). You place it in a hot oven at $600 , \text{K}$.

  1. Divide Initial Volume by Initial Temp ($V_1 / T_1$): $5 / 300 = 0.01666...$
  2. Multiply by New Temp ($T_2$): $0.01666... \cdot 600 = 10 , \text{Liters}$.

Because you exactly doubled the absolute temperature (from 300K to 600K), the volume of the balloon perfectly doubled to $10 , \text{Liters}$.

Frequently Asked Questions

Absolutely not. Charles's Law states that volume is directly proportional to absolute temperature. If you use Celsius, doubling a temperature from $1^\circ\text{C}$ to $2^\circ\text{C}$ would imply the volume doubles, which is mathematically false (in Kelvin, that is only a change from $274 , \text{K}$ to $275 , \text{K}$, a minuscule change in volume).

It is named after Jacques Charles, a French inventor and scientist who formulated the original law in the 1780s. Fascinatingly, Charles was an avid balloonist and launched the world's very first unmanned hydrogen-filled balloon in 1783.

According to the mathematical strictness of Charles's Law, if the temperature drops to exactly $0 , \text{K}$ (absolute zero), the volume of the gas would shrink to exactly zero. In reality, all known gases will physically condense into liquids or freeze into solids long before they reach absolute zero.