Charles' Law Calculator - V and T Gas Law
Calculate volume and temperature changes using Charles' Law for ideal gases at constant pressure.
Formula
V₁/T₁ = V₂/T₂
Volume is directly proportional to Temperature (in Kelvin).
Worked Examples
Example 1: Doubling the Absolute Temperature
Problem:A syringe with a free piston holds 10.0 L of gas at 300 K. It is warmed slowly to 600 K at constant atmospheric pressure. What is the new volume?
Solution:Charles's law: V1 / T1 = V2 / T2 Rearrange: V2 = V1 x T2 / T1 V2 = 10.0 L x 600 K / 300 K V2 = 10.0 x 2.00 = 20.0 L The kelvin temperature doubled, so the volume doubled.
Result:V2 = 20.0 L
Example 2: Balloon Moved Into a Refrigerator
Problem:A 2.50 L balloon sits in a 22 C room and is put into a refrigerator at 4 C. Pressure stays at 1 atm. What volume does it settle at?
Solution:Convert to kelvin first: T1 = 22 + 273.15 = 295.15 K T2 = 4 + 273.15 = 277.15 K V2 = V1 x T2 / T1 = 2.50 L x 277.15 / 295.15 V2 = 2.50 x 0.9390 = 2.35 L Shrinkage = 1 - 0.9390 = 6.1 percent. Using Celsius instead would give 2.50 x 4 / 22 = 0.45 L, which is nonsense.
Result:V2 = 2.35 L, about 6 percent smaller
Example 3: Hot Air Balloon Lift
Problem:A 2,800 cubic metre balloon envelope is filled with 15 C air and the burner heats it to 100 C. The throat is open, so pressure stays constant. How much air spills out and what gross lift results?
Solution:T1 = 288.15 K, T2 = 373.15 K If the air could expand freely: V2 = 2,800 x 373.15 / 288.15 = 3,626 cubic metres The envelope is fixed at 2,800, so 3,626 - 2,800 = 826 cubic metres spills out, about 23 percent of the air. Density scales the same way: 1.225 x 288.15 / 373.15 = 0.946 kg per cubic metre Gross lift = (1.225 - 0.946) x 2,800 = 0.279 x 2,800 = 781 kg
Result:About 826 cubic metres of air expelled; roughly 781 kg of gross lift
Frequently Asked Questions
What does Charles's law say about gas volume and temperature?
Charles's law states that for a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature, so V1/T1 = V2/T2. Double the kelvin temperature and the volume doubles. It is the constant-pressure branch of the ideal gas law: with P and n fixed, PV = nRT reduces to V = (nR/P) x T, a straight line through the origin.
Why must temperature be in kelvin for Charles's law?
Because the proportionality is anchored at absolute zero, not at the freezing point of water. Celsius ratios are meaningless here: going from 10 C to 20 C does not double the volume, but going from 283.15 K to 566.30 K does. Convert with K = C + 273.15 before you calculate. Entering Celsius directly is the most common error in Charles's law problems and can invert the direction of the answer.
How do I rearrange V1/T1 = V2/T2 to find the final volume?
Multiply both sides by T2: V2 = V1 x T2 / T1, which is what Charles' Law Calculator - V and T Gas Law computes. To find the final temperature instead, use T2 = T1 x V2 / V1. Because only the ratio T2/T1 matters, the volume unit cancels, so litres, millilitres or cubic metres all work as long as both volumes use the same one.
What does Charles's law predict at absolute zero?
Extrapolating the straight volume-temperature line to zero volume lands at 0 K, or -273.15 C. That extrapolation is historically how absolute zero was first located. It is a mathematical limit rather than a physical outcome: every real gas condenses to a liquid and then freezes long before that point, so the linear law breaks down well above 0 K.
What has to stay constant for Charles's law to hold?
Pressure and the amount of gas. The sample must be free to expand against a fixed external pressure, which is why demonstrations use a movable boundary such as a syringe with a free piston, a balloon, or a mercury plug above a gas column in a capillary. In a rigid sealed container the volume cannot change, so heating raises pressure instead and Gay-Lussac's law applies.
Why does a plot of volume against temperature give a straight line?
Because V = (nR/P) x T is linear in T with slope nR/P and zero intercept. Plotted against kelvin, the line passes through the origin; plotted against Celsius, the same data give a straight line that crosses the temperature axis at -273.15 C. The slope grows as pressure falls, so each constant-pressure line, called an isobar, has its own gradient.
How does Charles's law explain how a hot air balloon flies?
Heating the air inside the envelope makes it expand at essentially constant pressure. Because the throat is open, the surplus air spills out, so the same volume now holds less mass and the density inside drops below that of the surrounding air. The density difference produces buoyancy. Heating ambient air from about 293 K to 373 K cuts its density by roughly 21 percent.
Why does a balloon shrink in the fridge or outdoors in winter?
Cooling reduces the average kinetic energy of the gas molecules, so they strike the balloon wall less often and less hard. The elastic skin contracts until the inside pressure again balances atmospheric pressure, and the volume falls in proportion to absolute temperature. Moving a balloon from a 295 K room to a 277 K refrigerator shrinks it by about 6 percent, which is visible but not dramatic.
When do real gases stop following Charles's law?
Near condensation and at high pressure. The ideal model ignores molecular volume and intermolecular attraction, both of which matter when molecules are pushed close together or slowed by cooling. Close to the boiling point the measured volume falls faster than the law predicts, and at the boiling point the gas condenses entirely. Near ambient pressure and well above the boiling point the law is accurate to a fraction of a percent.
How does Charles's law relate to the combined gas law?
Charles's law is the constant-pressure special case of the combined gas law P1V1/T1 = P2V2/T2. That combined form also contains Boyle's law, which holds temperature constant, and Gay-Lussac's law, which holds volume constant. If pressure changes during your process, use the combined form; if the amount of gas also changes, go back to the full ideal gas law PV = nRT.