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On a hot day, a balloon seems to puff up a bit more, right? And if you take it outside when it's chilly, it might look a little sad and shrunken. That everyday observation is actually touching on a neat bit of science called Charles's Law. It simply describes how gases like to expand when they get warmer and shrink when they get cooler, as long as you're not squishing them (keeping the pressure the same). A Charles's Law calculator is a helpful calculator that takes this idea and puts numbers to it, letting you figure out exactly how much a gas's volume will change if you know its temperature swing, or vice versa, making that relationship easy to explore.
Calculate the relationship between gas volume and temperature with our free Charles' Law calculator. Discover how the Charles's Law formula (V₁/T₁ = V₂/T₂) defines volume and temperature changes for gases under constant pressure.
Understand how gas volume changes proportionally with absolute temperature at constant pressure using the Charles' Law equation
Work with various volume units and temperature scales (K, °C, °F) with built-in conversions
Learn gas laws with step-by-step calculations and detailed examples
Get customized explanations for your specific calculation scenarios
Perfect for chemistry students, teachers, scientists, and anyone working with gas behavior, Charles's Law, or the combined gas law calculator. Get accurate results instantly without complex manual calculations.
Easily calculate the final volume or temperature of a gas using Charles' Law equation (V₁/T₁ = V₂/T₂). Understand the direct relationship between gas volume and absolute temperature at constant pressure with examples, clear explanations, and our interactive Charles's Law calculator. Whether you're a student tackling gas laws or need a quick temperature-volume formula calculation, this tool and guide provide everything you need.
Select what you want to calculate (Final Volume or Final Temperature)
Enter the Initial Volume (V₁) and select its unit
Enter the Initial Temperature (T₁) and select its unit (K, °C, or °F)
Depending on your selection, enter either Final Temperature or Final Volume
Click 'Calculate' to get your result instantly
Use the AI Explain button to get a detailed explanation of your calculation
Charles' Law is a fundamental principle in physics and chemistry that describes how gases tend to behave with changes in temperature. It was formulated by Jacques Charles around 1787, though it was Joseph Louis Gay-Lussac who published it first in 1802, crediting Charles's unpublished work.
Charles' Law states that for a fixed mass of gas held at a constant pressure, the volume occupied by the gas is directly proportional to its absolute temperature. This temperature volume formula is essential for understanding gas behavior.
This means if you increase the absolute temperature of a gas, its volume will increase proportionally, and if you decrease the absolute temperature, its volume will decrease proportionally, provided the pressure and amount of gas don't change.
Where:
This formula highlights that the ratio of volume to absolute temperature remains constant for a fixed amount of gas at constant pressure. This can also be written as:
Where k is a constant specific to the amount of gas and the pressure.
It is essential to use an absolute temperature scale, like Kelvin (K), when applying Charles' Law. Here's why:
Charles' Law describes a direct proportionality that only works when temperature is measured from absolute zero (0 K or -273.15 °C), the theoretical point where particle motion ceases. Volume is directly proportional to Kelvin temperature.
Celsius (°C) and Fahrenheit (°F) scales have arbitrary zero points and can have negative values. Using these in the ratio V/T would lead to incorrect results, division by zero (at 0°C or 0°F), or meaningless negative volumes.
Our calculator handles these conversions automatically when you select °C or °F, but performs the core calculation using Kelvin.
Imagine gas particles (atoms or molecules) inside a container with a movable piston (to keep pressure constant).
When you heat the gas, you give the particles more kinetic energy. They move faster and collide more frequently and forcefully with the container walls and the piston.
To maintain constant pressure (the force per unit area on the walls/piston), the volume must increase. The piston moves outwards, giving the particles more space to move in, reducing the collision frequency on any given area back to the original pressure level.
Conversely, cooling the gas reduces particle kinetic energy. They move slower, collide less often and less forcefully. To maintain constant pressure, the volume must decrease (piston moves inwards) until the reduced collision frequency in the smaller space balances the external pressure again.
Think of it like popcorn kernels in a pot with a loose lid: as you heat them, they pop more energetically (higher kinetic energy) and push the lid up (increase volume) to maintain the pressure inside.
A flexible container holds 3.0 Liters of Nitrogen gas at 27 °C. The container is heated to 127 °C while the pressure is kept constant at 1 atm. What is the final volume of the gas?
Answer: The final volume of the Nitrogen gas is approximately 4.0 Liters.
A gas sample occupies a volume of 250 cubic feet (ft³) at a temperature of 400 K. If the gas is compressed to a volume of 150 ft³ at constant pressure, what is its final temperature in degrees Fahrenheit (°F)?
Answer: The final temperature of the gas is 240 K, which is approximately -27.7 °F.
Charles' Law isn't just a textbook concept; it explains many everyday phenomena:
The most classic example! Burners heat the air inside the balloon envelope. According to Charles' Law, the heated air expands. This makes the air inside less dense than the cooler, denser outside air, generating buoyant force and causing the balloon to rise.
An inflated ball or raft left in the sun gets firmer as air inside expands. Car tire pressure also drops in cold weather as the air inside contracts according to Charles' Law.
When dough bakes, yeast or chemical leaveners produce carbon dioxide gas bubbles. As the oven heats the dough, the gas inside these bubbles expands according to Charles' Law, causing the bread or cake to rise and become fluffy.
Large-scale atmospheric phenomena involve air masses heating and cooling. Heated air expands, becomes less dense, and rises, contributing to weather systems and wind.
Charles' Law provides an excellent model, but it relies on certain assumptions:
The law is most accurate for ideal gases, theoretical gases whose particles have no volume and no intermolecular forces. Real gases behave most like ideal gases at low pressures and high temperatures. At high pressures or low temperatures (near liquefaction), real gas behavior deviates significantly.
The law strictly applies only if the pressure of the gas remains unchanged throughout the volume and temperature change. If pressure varies, you need the Combined Gas Law or the Ideal Gas Law.
The mass or number of moles (n) of the gas must remain fixed. The container must be sealed, with no gas leaking out or being added, and no chemical reactions occurring that consume or produce gas.
Charles' Law is one of the fundamental gas laws, which together describe the relationships between pressure (P), volume (V), temperature (T), and amount of gas (n). Understanding Charles's Law formula helps in using the combined gas law calculator.
| Gas Law | Formula | Relationship |
|---|---|---|
| Charles' Law (Temperature-Volume Formula) | V₁/T₁ = V₂/T₂ | Volume is directly proportional to absolute temperature (constant P and n) |
| Boyle's Law | P₁V₁ = P₂V₂ | Volume is inversely proportional to pressure (constant T and n) |
| Gay-Lussac's Law | P₁/T₁ = P₂/T₂ | Pressure is directly proportional to absolute temperature (constant V and n) |
| Avogadro's Law | V₁/n₁ = V₂/n₂ | Volume is directly proportional to amount of gas (constant P and T) |
| Combined Gas Law | (P₁V₁)/T₁ = (P₂V₂)/T₂ | Combines Boyle's, Charles', and Gay-Lussac's laws (constant n) |
| Ideal Gas Law | PV = nRT | Most comprehensive, relates all variables (R is the gas constant) |
Charles' Law can be derived from the Ideal Gas Law: If PV = nRT and both P and n are constant, then V = (nR/P)T. This shows that V is directly proportional to T, or V/T = constant.
Calculate either final volume or final temperature based on your inputs, with support for a wide range of units
Work with various volume units and temperature scales with automatic conversions to and from base units
Learn through detailed calculation examples showing real-world applications of Charles' Law
Get customized step-by-step explanations for your specific calculation scenarios
Clear, intuitive design makes complex gas law calculations accessible to everyone
Include pressure and gas amount values for more comprehensive analysis of your gas system
Q1. What is Charles' Law?
•
Charles' Law states that the volume of a gas is directly proportional to its absolute temperature when pressure and amount of gas remain constant. Mathematically, it's expressed as V₁/T₁ = V₂/T₂, where V is volume and T is temperature in Kelvin.
Q2. Why must temperature be in Kelvin for Charles' Law?
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Charles' Law requires absolute temperature (Kelvin) because the direct proportionality only works with a temperature scale that starts at absolute zero. Using Celsius or Fahrenheit would lead to incorrect results since these scales have arbitrary zero points that don't represent zero molecular motion.
Q3. Can I use Charles' Law for all gases?
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Charles' Law is most accurate for ideal gases at moderate pressures and temperatures well above their liquefaction point. Real gases deviate from this behavior at high pressures or low temperatures, but for most practical applications, the law provides good approximations.
Q4. What happens if pressure changes during the process?
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Charles' Law applies only when pressure remains constant. If pressure changes, you should use the Combined Gas Law ((P₁V₁)/T₁ = (P₂V₂)/T₂) or the Ideal Gas Law (PV = nRT) instead.
Q5. How do I convert between temperature units?
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To convert to Kelvin: K = °C + 273.15 or K = (°F - 32) × 5/9 + 273.15. To convert from Kelvin: °C = K - 273.15 or °F = (K - 273.15) × 9/5 + 32. Our calculator handles these conversions automatically.
Q6. What are some real-world applications of Charles' Law?
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Charles' Law explains many phenomena including how hot air balloons rise, why car tires lose pressure in cold weather, how bread rises during baking, and aspects of weather patterns like air mass movement.
Q7. How does Charles' Law relate to other gas laws?
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Charles' Law is one of several gas laws that together describe gas behavior. It can be derived from the Ideal Gas Law (PV = nRT) when pressure and amount of gas are constant. Other related laws include Boyle's Law (pressure-volume relationship) and Gay-Lussac's Law (pressure-temperature relationship).
Q8. What units should I use for volume in Charles' Law calculations?
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You can use any volume units (liters, cubic meters, cubic feet, etc.) as long as you're consistent between initial and final states. Our calculator supports multiple volume units and handles conversions automatically.
Q9. Why does gas volume increase with temperature?
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When a gas is heated, its molecules gain kinetic energy and move faster, colliding more frequently and forcefully with the container walls. To maintain constant pressure, the volume must increase to reduce the collision frequency per unit area.
Q10. Who discovered Charles' Law?
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Jacques Charles discovered the relationship between gas volume and temperature around 1787, but didn't publish his findings. Joseph Louis Gay-Lussac later conducted more detailed experiments and published the law in 1802, giving credit to Charles for the initial discovery.