Physics · Thermodynamics · Gas Laws
Charles's Law Calculator
Calculate the relationship between volume and temperature of an ideal gas at constant pressure using Charles's Law.
Calculator
Formula
V₁ is the initial volume of the gas, T₁ is the initial absolute temperature in Kelvin, V₂ is the final volume, and T₂ is the final absolute temperature in Kelvin. Pressure remains constant throughout. All temperatures must be in Kelvin (K = °C + 273.15).
Source: Jacques Charles, 1787; formalized in Dalton's and Gay-Lussac's works. Standard treatment in NIST Thermophysical Properties and IUPAC physical chemistry references.
How it works
Charles's Law, formulated by French physicist Jacques Charles in 1787 and later published by Joseph Louis Gay-Lussac in 1802, states that the volume of a fixed amount of gas is directly proportional to its absolute temperature when pressure remains constant. This means if you double the absolute temperature of a gas, its volume will also double, provided pressure does not change. The law applies to ideal gases and is an excellent approximation for real gases under moderate conditions of temperature and pressure.
The mathematical expression is V₁/T₁ = V₂/T₂, where V₁ and T₁ are the initial volume and absolute temperature, and V₂ and T₂ are the final volume and absolute temperature. A critical requirement is that temperature must always be expressed in Kelvin (K), never Celsius or Fahrenheit, because the law is based on absolute temperature. To convert Celsius to Kelvin, add 273.15. Rearranging the formula to solve for final volume gives V₂ = V₁ × (T₂/T₁), which is the form used in this calculator.
Practical applications of Charles's Law are widespread. Hot air balloons rise because heating the air inside increases its volume and decreases its density relative to the surrounding cooler air. Car tires appear to inflate slightly on hot days because trapped air expands with rising temperature. In industrial settings, engineers use Charles's Law to design gas pipelines and storage vessels that must accommodate thermal expansion. Meteorologists apply the principle to understand how air masses change altitude as they warm or cool. In the laboratory, it underpins the design of thermometers and the calibration of gas measurement equipment.
Worked example
Problem: A sample of nitrogen gas occupies a volume of 2.50 L at 25°C. If the gas is heated at constant pressure to 100°C, what will the new volume be?
Step 1 — Convert temperatures to Kelvin:
T₁ = 25 + 273.15 = 298.15 K
T₂ = 100 + 273.15 = 373.15 K
Step 2 — Apply Charles's Law:
V₂ = V₁ × (T₂ / T₁)
V₂ = 2.50 L × (373.15 K / 298.15 K)
V₂ = 2.50 L × 1.2516
Step 3 — Result:
V₂ = 3.129 L
The gas expands from 2.50 L to approximately 3.13 L when heated from 25°C to 100°C at constant pressure. This makes intuitive sense — the temperature increased by roughly 25% on the absolute scale, so the volume also increased by roughly 25%.
Limitations & notes
Charles's Law assumes ideal gas behaviour, meaning gas molecules have negligible volume and no intermolecular attractions. Real gases deviate from this ideal at very high pressures, very low temperatures, or near the gas's liquefaction point. The law strictly applies only when the amount of gas (moles) and the pressure remain perfectly constant — any pressure change requires the combined or ideal gas law instead. Temperatures must always be in Kelvin; using Celsius will produce physically meaningless or grossly incorrect results. At temperatures approaching absolute zero (0 K), real gases condense into liquids or solids and the law no longer applies. For mixtures of gases or reactive systems, the law should be used cautiously, and more complete equations of state such as the van der Waals equation may be more appropriate.
Frequently asked questions
Why must temperature be in Kelvin for Charles's Law?
Charles's Law requires absolute temperature because it is based on the direct proportionality between volume and the kinetic energy of gas molecules, which is zero only at absolute zero (0 K). Using Celsius or Fahrenheit introduces an arbitrary offset that breaks the proportional relationship and produces incorrect results.
What happens to gas volume when temperature decreases according to Charles's Law?
When temperature decreases at constant pressure, the volume of the gas decreases proportionally. For example, if the absolute temperature is halved, the volume is also halved. This is why gas-filled containers can appear to deflate or collapse in very cold environments.
What is the difference between Charles's Law and Boyle's Law?
Charles's Law relates volume and temperature at constant pressure (V ∝ T), while Boyle's Law relates volume and pressure at constant temperature (V ∝ 1/P). Both are special cases of the ideal gas law, which combines them along with the amount of gas: PV = nRT.
Can Charles's Law be used for real gases?
Charles's Law is an excellent approximation for real gases at moderate temperatures and low to moderate pressures. It becomes less accurate near the gas's boiling point, at very high pressures, or for gases with strong intermolecular forces. In those cases, equations of state like the van der Waals equation provide more accurate predictions.
What is an isobaric process and how does it relate to Charles's Law?
An isobaric process is any thermodynamic process that occurs at constant pressure. Charles's Law specifically describes the behaviour of an ideal gas during an isobaric process — it quantifies exactly how volume changes with temperature when pressure is fixed. Isobaric heating and cooling are common in open-air systems and many industrial processes.
Last updated: 2025-01-15 · Formula verified against primary sources.