Charles' Law Calculator

This calculator allows you to calculate the change in volume of a given gas volume under constant pressure and with changes in temperature using Charles' Law. Enter three out of four values, either two volumes and two temperatures or leave one value blank. The calculator will then solve for the unknown value, convert units, and display both the volume ratio and the temperature ratio side by side.

In addition, a straight line is drawn that represents the relationship between volume and temperature. This line represents the shape of Charles' Law and points to absolute zero.

What is Charles' Law?

Charles' Law states that the volume of an ideal gas is directly proportional to its absolute temperature given a constant pressure and mass. When heated, the gas expands; when cooled, it contracts. These changes are relative to the temperature at absolute zero.

This observation is commonly attributed to the French scientist Jacques Charles who investigated the thermal expansion of gases in the 1780s. Joseph Louis Gay-Lussac published this relationship in 1802, citing earlier work by Charles. For that reason both names are sometimes associated with this law.

Charles's law formula:

Since the value resulting from dividing volume by temperature is constant, the ratios are equal to each other. This is used in the calculator.

V1 and T1 represent the volume and absolute temperature of the first state respectively, while V2 and T2 are those of the second state. The constant k depends on the amount of gas and its pressure, both of which remain constant here.

By rearranging this one equation you get a direct formula for calculating any quantity so that this calculator can calculate any field left blank.

Why we need to use kelvin for temperature.

This is the step where many people make the most common mistake. Charles' Law only works if temperature is measured on an absolute temperature scale. On this scale zero actually represents a thermal energy of zero. In Celsius, however, zero just means water freezes and not the bottom of the scale. So calculations using Celsius temperatures will give incorrect results that can even lead to divisions by zero or negative values.

To convert, add 273.15 to the Celsius temperature to get the Kelvin temperature. So 27 degrees Celsius is 300.15 Kelvins and 0 degrees Celsius is 273.15 Kelvins. The calculator will automatically do this conversion for you no matter which unit you choose, but if you are doing calculations by hand, convert the temperature to Kelvin before calculating the ratio.

Instructions for using this calculator:

Select the unit for each parameter and enter the three known values. Unknown fields remain blank so that the result is clearly shown. The volume ratio and temperature ratio are displayed in a separate area.

Because all four quantities are contained within the same equation, this tool can be used to solve for any of the variables given that three values are known. If you enter two volumes and a temperature, you can calculate the other temperature. Conversely, if you enter two temperatures and one volume, you can determine the other volume. The units may be mixed; for example, one volume could be entered in liters while another is cubic feet; the calculation tool will automatically convert to a common unit.

Example: Heating a gas

The volume of a certain gas is 8ml and the temperature is 2 degrees celsius, then it was heated to 4 degrees celsius under same pressure, what's the new volume?

First convert the two temperatures to kelvin: 2 degrees C is 275.15 K and 4 degrees C is 277.15 K. Then apply the formula for V2.

The change in volume is small because the two changes are relatively small compared to an initial temperature of about 275 kelvins. This is where the main advantage of the absolute temperature scale comes into play: small changes in degrees Celsius correspond to small percentage changes even in kelvins.

Example of temperature calculation:

A gas with a volume of three and a half cubic meters needs to be cooled or heated until the volume is 3.1 cubic meters. The initial temperature is 15 degrees Celsius. What temperature is required to achieve this volume?

To calculate this we convert 15 degrees Celsius to 288.15 Kelvins and determine the temperature corresponding to a volume of 3.5 cubic meters.

The result is about 52 degrees Celsius. The larger the volume, the higher the required absolute temperature. This corresponds to the predicted proportional relationship.

How to read a volume-temperature graph:

If the volume is plotted on the vertical axis and the absolute temperature on the horizontal axis, Charles's law can be represented by a straight line passing through the origin. Doubling the kelvin temperature doubles the volume.

The same data can also be represented in Celsius, which will again produce a straight line, but this time the line does not intercept at the origin; instead it intercepts the temperature axis at -273.15 degrees. Extending the Kelvin line to zero volume is a classic method by which physicists first estimated the value of absolute zero.

Applications of Charles' Law:

A hot air balloon rises because the air inside it is heated and expands. The same mass of air takes up more volume and becomes less dense than the surrounding cooler air. If you put a balloon in a cold car, it shrinks; if you heat it, it expands again.

Engineers use the same principle to determine how much gas is stored based on temperature changes, or to study how much air an engine takes in when it's hot. The expansion of weather balloons in cold and thin air also follows this principle.

How are gas laws related?

Charles' Law is one of three simple gas laws, each holding a certain quantity constant. Boyle's law describes the relationship between pressure and volume at a constant temperature, while Gay-Lussac's law deals with the relationship between pressure and temperature at a constant volume.

Combining these three laws together gives the combined gas law. Adding the quantity of gas as a variable produces the ideal gas law: PV = nRT.

Common mistakes to avoid:

The most common mistake is using degrees Celsius or Fahrenheit instead of Kelvin. This will result in all the answers being wrong. Other common mistakes are mixing up volume and temperature, forgetting that pressure and amount of gas must be constant to apply a law, and mixing units of volume between two states without converting.

Real gases also deviate from this law, particularly at very high pressures or very low temperatures, because the conditions for the ideal gas law are no longer met.