Charles’ Law Calculator
Calculate Gas Volume & Temperature in Isobaric Processes
Charles’ Law states that for a fixed mass of an ideal gas at constant pressure, the volume is directly proportional to the absolute temperature. This tool helps you explore that relationship.
Interactive Calculator
V₁ / T₁ = V₂ / T₂
Initial Parameters
Final Parameters
What is Charles’ Law?
Charles’ Law (also known as the law of volumes) describes the relationship between the volume of a gas and its temperature when the pressure and the mass of the gas are held constant. It states that the volume is directly proportional to the absolute temperature (measured in Kelvin).
In simpler terms, if you heat a gas, it expands. If you cool it down, it contracts. This relationship is linear, meaning if you double the absolute temperature, you double the volume.
This law applies best to ideal gases during an isobaric process (a process that occurs at constant pressure). The law was first formulated by French scientist Jacques Charles in 1787.
The Charles’ Law Formula
The mathematical representation of Charles’ Law is:
V₁ / T₁ = V₂ / T₂
Where:
- V₁ is the initial volume of the gas.
- T₁ is the initial absolute temperature of the gas (in Kelvin).
- V₂ is the final volume of the gas.
- T₂ is the final absolute temperature of the gas (in Kelvin).
This formula can be rearranged to solve for any of the variables:
V₂ = V₁ × (T₂ / T₁)
T₂ = T₁ × (V₂ / V₁)
Step-by-Step Examples
Example 1: Cooling a Ball
A ball has a volume of 2 liters at a beach temperature of 35°C. It’s then taken into an air-conditioned room at 15°C. What is its new volume?
1. Convert temperatures to Kelvin (K):
T₁ = 35°C + 273.15 = 308.15 K
T₂ = 15°C + 273.15 = 288.15 K
2. Apply the formula to find V₂:
V₂ = V₁ × (T₂ / T₁) = 2 L × (288.15 K / 308.15 K)
V₂ ≈ 1.87 Liters
The volume decreases because the temperature dropped.
Example 2: Heating a Container
A flexible container filled with 0.5 m³ of gas at 20°C is heated until its volume expands to 0.8 m³. What is the final temperature?
1. Convert initial temperature to Kelvin (K):
T₁ = 20°C + 273.15 = 293.15 K
2. Apply the formula to find T₂:
T₂ = T₁ × (V₂ / V₁) = 293.15 K × (0.8 m³ / 0.5 m³)
T₂ ≈ 469.04 K
In Celsius, this is 469.04 – 273.15 = 195.89°C.
Real-Life Applications
- Hot Air Balloons: The air inside the balloon is heated, causing it to expand (increase in volume). This makes the air inside less dense than the cooler air outside, generating lift.
- A Turkey Pop-Up Timer: Some timers are made with a small amount of gas trapped in a cylinder. When the turkey reaches the correct temperature, the gas expands enough to “pop” the timer out.
- Tire Pressure: On a hot day, the air inside a car tire heats up, expands, and increases the tire’s pressure. This is why tire pressure should be checked when the tires are cold.
- Liquid Nitrogen Experiments: Placing an inflated balloon in liquid nitrogen causes the air inside to cool rapidly and contract, shrinking the balloon dramatically. When removed, it warms up and expands back to its original size.
Limitations & Important Notes
- Ideal Gas Assumption: Charles’ Law is most accurate for ideal gases. Real gases deviate from this behavior, especially at very high pressures or very low temperatures.
- Constant Pressure is Key: The law is only valid if the pressure of the gas does not change during the process.
- Absolute Temperature: All calculations must use an absolute temperature scale, with Kelvin (K) being the standard. Using Celsius or Fahrenheit directly in the formula will produce incorrect results.
Frequently Asked Questions
What is the relationship between volume and temperature in Charles’ Law?
The relationship is directly proportional. This means if you increase the absolute temperature, the volume increases by the same factor, as long as pressure and mass are constant. For example, doubling the Kelvin temperature will double the volume.
Why must temperature be in Kelvin?
The Kelvin scale is an absolute temperature scale, meaning 0 K is absolute zero—the point where particles have minimal motion. Charles’ Law relies on this absolute zero as its baseline. Using Celsius or Fahrenheit, which have arbitrary zero points, would break the proportional relationship (e.g., going from 10°C to 20°C is not a doubling of thermal energy).
How is Charles’ Law different from Boyle’s Law?
Charles’ Law describes the volume-temperature relationship at constant pressure. Boyle’s Law describes the pressure-volume relationship at constant temperature (an inverse relationship: P₁V₁ = P₂V₂). Both are special cases of the Combined Gas Law.