Charles’ Law Calculator - Solve (V₁/T₁ = V₂/T₂)

To Calculate:

Initial volume (V₁)

m³ ▾

Initial temperature (T₁)

K ▾

Final volume (V₂)

m³ ▾

The Charles Law calculator calculates the initial and final volume or temperature of an ideal gas using V₁/T₁ = V₂/T₂ during an isobaric process. Enter any three of the four values (V₁, T₁, V₂, T₂), and get the missing one.

What Is Charles' Law?

The Charles law states that the volume of a fixed mass of ideal gas is directly proportional to its absolute temperature (Kelvin), keeping the pressure constant.

So, by definition the Charles law equation is:

⇨ V ∝ T

By adding the constant of proportionality “k”

⇨ V = kT

Charles' Law Formula:

The Charles law formula is expressed as:

V₁/T₁ = V₂/T₂

V₁ = Initial volume
T₁ = Initial temperature (in Kelvin)
V₂ = Final volume
T₂ = Final temperature (in Kelvin)

Note: This Charle’s Law Formula only applies to an isobaric process of a fixed mass of an ideal gas.

How to Calculate Charles' Law?

Charles' Law can be used to find any one of the four variables in the Charles' Law equation:

V₁/T₁ = V₂/T₂

First, identify the unknown variable in the Charles' Law equation and gather the three known values.

⇨ Step 1: Identify Your Knowns and Unknowns

Identify which three values are known and which variable you need to calculate: V₁, T₁, V₂, or T₂.

⇨ Step 2: Convert Temperatures to Kelvin (Critical Step)

Charles' Law requires temperature to be measured in absolute units (Kelvin).

Convert the temperature to Kelvin if it is given in Celsius or Fahrenheit:

Celsius to Kelvin: K = °C + 273.15
Fahrenheit to Kelvin: K = (°F − 32) × 5/9 + 273.15

⇨ Step 3: Rearrange the Formula

Depending on which variable is unknown, rearrange the base formula (V₁/T₁ = V₂/T₂) to solve for it:

To solve for Final Volume (V₂):

V₂ = (V₁ × T₂) / T₁

To solve for Final Temperature (T₂):

T₂ = (V₂ × T₁) / V₁

To solve for Initial Volume (V₁):

V₁ = (V₂ × T₁) / T₂

To solve for Initial Temperature (T₁):

T₁ = (V₁ × T₂) / V₂

Charles Law Examples:

Example 1:

If a sample of gas has an initial volume (V₁) of 4 L at an initial temperature (T₁) of 280 K, and its volume expands to a final volume (V₂) of 8 L at constant pressure. Now, how do I solve for T₂ using Charles' Law?

Given:

V₁ = 4L
T₁ = 280K
V₂ = 8L

Solution:

T₂ = (V₂ × T₁) / V₁

The temperature in Kelvin

T₂ = 82804 = 560K

Answer: The final temperature (T2) is 560K.

Example 2:

A gas occupies an initial volume of 2.5L at an absolute temperature of 300K. If the temperature is increased to 450K at a constant pressure, then how to calculate volume using Charles law?

Identify Given Values:
- V₁ = 2.5L
- T₁ = 300K
- T₂ = 450K
Select the Rearranged Formula:

V₂ = (V₁ × T₂) / T₁

Substitute and Calculate:

V₂ = (2.5 x 450) / 300

V₂ = 1125 / 300 = 3.75L

Answer: The final volume of the gas is 3.75L.

How to Use the Charles Law Calculator?

Follow these steps to use the Charles' Law calculator accurately:

Select the Target Variable: Choose the variable you want to find from the dropdown: V₁, T₁, V₂, or T₂
Input Known Values: Add the known numerical values of the remaining 3 variables of the Charles' Law equation
Click Calculate: Press the “CALCULATE” button to get the final result with a step-by-step calculation

Real-Life Applications of Charles' Law:

Charles' Law has many practical applications in everyday life, including:

Hot Air Balloons:

Hot air balloons are a common example of Charles' Law; when the air inside the Balloon is heated, it rises up in the air. Reason for that the air inside the balloon expands and becomes less dense than the surrounding air. So it rises up in the air, as the volume of a gas changes as its temperature increases, as explained by Charles's Law.

HVAC Systems:

Charles’s Law (VT) plays a fundamental role in the operations, design, and efficiency of HVAC (Heating, Ventilation, and Air Conditioning) systems. HVAC systems constantly cool, heat, and move air at constant pressure. In HVAC systems, the relationship between volume and temperature governs their operations.

Laboratory Experiments:

In the laboratory experiments, Charles's Law is explained by heating or cooling a fixed amount of gas while maintaining constant pressure. Students can record the gas volume at different temperatures and compare the results. They can check that the volume increases as absolute temperature increases.

FAQ’s:

Can this Chemistry Charles Law calculator handle negative temperatures?

Yes, you can enter negative values of temperature in our charles law calculator. It automatically converts the temperature to Kelvin before applying it in the Charles' Law formula.

What are the limitations of Charles' Law?

Charles's law formula has limitations, as it is applicable only if the pressure and amount of the gas remain constant. Charles law only uses absolute temperature in Kelvin and works as an ideal-gas relationship, as real gases may not follow it exactly under extreme conditions.

Is Charles Law applicable to all gases?

No, Charles’ Law applies strictly to ideal gases.

What happens to the density of a gas when it is heated at constant pressure?

The density of the gas decreases when a gas is heated at a constant pressure. This is because heating a gas causes it to expand, increasing its volume. The density of a gas is inversely proportional to the volume. Therefore, as the volume increases, the density decreases due to their (p = m/V) relationship.

Why is temperature measured in Kelvin when using Charles' Law?

Charles' Law defines the relationship between the volume and temperature of a gas when the pressure is kept constant. Kelvin is an absolute temperature scale that starts at absolute zero, so it provides the correct proportional relationship between gas volume and temperature, unlike Celsius or Fahrenheit.

References:

Wikipedia: Relation to Absolute Zero, kinetic theory, law of volumes.
Chemistry LibreTexts: Temperature-Volume Data, Charles's Law, Experimental Gas Law

Charles Law Calculator