Charles Law

Overview

Engineering reference data for Charles Law in gases and compressed air.

Key Formulas

Ideal Gas Law

$PV = nRT$

Pressure × Volume = moles × gas constant × temperature.

Boyle's Law

$P_1 V_1 = P_2 V_2$

At constant temperature.

Charles's Law

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

At constant pressure.

Variables

Example Application

Consider a gas occupying a volume of $V_1 = 2$ liters at a temperature of $T_1 = 0^\circ\text{C}$ (equivalent to $273\text{ K}$). To find the volume $V_2$ at $T_2 = 100^\circ\text{C}$ (or $373\text{ K}$), apply Charles' law:

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

Solving for $V_2$:

$$V_2 = \frac{T_2 \cdot V_1}{T_1} = \frac{373 \text{ K} \cdot 2 \text{ liters}}{273 \text{ K}} \approx 2.73 \text{ liters}$$

This calculation illustrates how volume is directly proportional to absolute temperature at constant pressure.

Assumptions and Conditions

Charles' Law describes the behavior of an ideal gas under specific constraints:

• The gas is assumed to be an ideal (perfect) gas, meaning it follows gas laws closely with negligible intermolecular forces.
• The mass (amount of gas) remains constant throughout the process.
• The pressure is held constant.
• Temperature must be in absolute units, such as Kelvin (K) or Rankine (°R), to ensure a direct linear relationship.

Under these conditions, volume $V$ is directly proportional to absolute temperature $T$, leading to the mathematical expression:

$\frac{V}{T} = \text{constant}$

For comparing two states of the same gas at constant pressure and mass, the law is applied as:

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

This proportionality is foundational for calculations in thermodynamics and engineering processes involving gas expansion or compression at constant pressure.

Key Concepts

Charles' Law is a fundamental principle describing the thermal expansion of ideal gases. It demonstrates that a gas's volume is directly proportional to its absolute temperature when pressure and mass are held constant. This linear relationship is crucial in fields like thermodynamics, chemical engineering, and meteorology.

This law highlights the necessity of using an absolute temperature scale (Kelvin or Rankine). Using Celsius or Fahrenheit would break the direct proportionality because their zero points are not at absolute zero, leading to incorrect calculations.

The law can be rearranged to solve for any single variable if the other three are known, making it a versatile tool for predicting gas behavior under controlled pressure conditions.

Practical Considerations

In engineering applications, Charles' Law is applied in systems like hot air balloons, internal combustion engines, and gas storage. It is also foundational for understanding other gas laws, such as Gay-Lussac's Law (which relates pressure and temperature) and the Combined Gas Law.

References

• Original Source