Charles's law calculator

What is Charles’ law?

Charles’ law is a part of thermodynamic theory, describing how the volume of a gas changes with changes in temperature at constant pressure. This law is named after the French physicist and inventor Jacques Alexandre César Charles, who conducted a series of experiments with gases in the late 18th century. Charles’ Law states that the volume of an ideal gas is directly proportional to its absolute temperature when pressure remains constant. Simply put, if the temperature of a gas increases, its volume increases, and vice versa.

This law is part of the ideal gas law equation that helps describe the behavior of gases under various conditions. If you are interested in understanding the interaction of volume, temperature, and pressure more comprehensively, you might want to try the ideal gas law calculator, which provides complete calculations for different gas states.

Isochoric process

An isochoric process is a thermodynamic process in which the volume of the system remains constant. In such conditions, any change in heat directly affects the temperature and pressure of the gas. In isochoric processes, changes occur in the pressure at a constant volume, highlighting another aspect of thermodynamic phenomena. The isochoric process is closely related to Gay-Lussac’s law, which states that at a constant volume, the pressure of a gas is proportional to its temperature (P/T = const). This demonstrates how pressure increases with the absolute increase in temperature.

An example of an isochoric process can be observed in a tightly sealed container holding gas when heated. As the gas temperature rises, the pressure also increases.

History of Charles’ law

Charles’ Law was first experimentally discovered by Jacques Charles in 1787. Charles conducted his experiments using hydrogen gas to show how temperature affects the volume of gas. These investigations were a key step in the development of gas knowledge and molecular theory, contributing to the progress of the entire field of science.

This research laid the foundation for the development of thermodynamics and the practical use of gases, for instance, in aerostatics. In the 18th century, one of the most famous experiments was conducted by the Montgolfier brothers, who built the first hot air balloon, lifted by heating the air.

Boyle’s law and its connection to Charles’ law

Boyle’s Law, also known as the law of isothermal processes, asserts that at constant temperature, the volume of a gas is inversely proportional to its pressure $(P_1V_1 = P_2V_2)$. Together with Charles’ Law, they form the fundamental components of the ideal gas law equation. If you want to experiment with these changes, visit the Boyle’s law calculator. It will help you assess how pressure changes with volume changes while temperature remains constant.

Formula

Charles’ law is expressed as follows:

$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$

where:
$V_1$ and $V_2$ are the initial and final volumes of the gas,
$T_1$ and $T_2$ are the initial and final temperatures of the gas in Kelvin.

Units and conversion

• Volume (V): Typically measured in liters (L) or cubic meters (m³). If your data is in different units, such as milliliters, you need to convert them to liters (1 L = 1000 mL) to comply with the required standards in physical equations.

• Temperature (T): Measured in Kelvin for accuracy. Ensure to convert degrees Celsius to Kelvin by adding 273.15 (e.g., 20 °C = 293.15 K).

If conversion is needed, you can use the formula:

$$T (\text{K}) = T (\text{°C}) + 273.15$$

Examples

Example 1

Suppose we have a gas cylinder with a volume of 5 liters at a temperature of 300 K. If the temperature increases to 400 K, how will the volume of the gas change if the pressure remains constant?

Using Charles’ law formula:

$$\frac{5}{300} = \frac{V_2}{400}$$

Now solve for $V_2$:

$$V_2 = \frac{5 \times 400}{300} = \frac{2000}{300} ≈ 6.67 \text{ liters}$$

Example 2

A tank with a gas has a volume of 8 liters at a temperature of 250 K. After heating, the volume increased to 10 liters. What is the new temperature of the gas?

Using the same formula:

$$\frac{8}{250} = \frac{10}{T_2}$$

Solve for $T_2$:

$$T_2 = \frac{10 \times 250}{8} = \frac{2500}{8} = 312.5 \text{ K}$$

Interesting experiments

• Montgolfier hot air balloons: In the late 18th century, the Montgolfier brothers conducted experiments with hot air balloons demonstrating the practical importance of Charles’ law. They heated the air inside the balloon, which increased its volume and decreased its density, allowing it to lift.

• Experiment on the International Space Station: Gas experimental setups on the space station investigate how laws, including Charles’ law, apply under microgravity conditions. This helps study the behavior of gases in space where pressure and temperature can change drastically.

Notes

1. Temperature in calculations: Always use temperature in Kelvin. This excludes the possibility of negative temperatures, which can lead to incorrect results in gas calculations.

2. Applicability of Charles’ law: It is valid for ideal gases, but in real conditions, there are deviations that may affect results. It is best to apply the law under conditions where the gas behaves ideally: low pressures and high temperatures.

Frequently asked questions

How to find the final temperature of a gas if its volume and initial conditions are known?

To find the final temperature of a gas $T_2$ when its volume changes, apply the formula: $T_2 = \frac{V_2 \times T_1}{V_1}$.

In what units should volume and temperature be measured for Charles’ Law application?

Volumes need to be converted to liters or cubic meters. Temperature should be presented in Kelvin to ensure calculation accuracy.

How does Charles’ law relate to other gas laws?

Charles’ law is part of the ideal gas law equation, which also includes Boyle’s and Avogadro’s laws, linking volume, pressure, and temperature of gas.

Does Charles’ law apply to real gases?

Charles’ law is intended for ideal gases, but at high temperatures and low pressures, real gases can conform closely to this law.

Why is it important to use temperature in Kelvin?

Using Kelvin allows for maintaining direct proportionality as it is an absolute temperature scale, preventing the use of negative values.