Question

State Gay-Lussac's law.

Short answer

Gay-Lussac's Law states that pressure is directly proportional to temperature for a fixed gas at constant volume.

Step-by-step solution

Define the Relationship

Gay-Lussac's Law defines the relationship between the pressure and temperature of a fixed mass of gas at constant volume. This implies that as long as the volume of the gas does not change, the pressure \( P \) of the gas is directly proportional to its temperature \( T \).

Write the Mathematical Expression

The mathematical expression for Gay-Lussac's Law is as follows: \[ P \propto T \] where \( P \) is the pressure of the gas and \( T \) is the absolute temperature (measured in Kelvin).

Introduce the Proportionality Constant

Since pressure is directly proportional to temperature, we can introduce a constant \( k \):\[ P = k \cdot T \]where \( k \) is the proportionality constant that depends on the amount and nature of the gas.

Describe the Law in Words

Gay-Lussac's Law states that for a given mass and constant volume of gas, the pressure of the gas is directly proportional to its absolute temperature. This means that if the temperature of the gas increases, its pressure increases, provided the volume does not change.

Key concepts

Pressure and Temperature Relationship

In Gay-Lussac's Law, the relationship between pressure and temperature is a fundamental concept. Imagine a sealed container of gas. If the volume remains unchanged, the pressure inside this container is directly related to the temperature. This is because the particles of the gas move more vigorously as they are heated, thereby colliding more frequently with the walls of the container, which results in increased pressure.

One key thing to remember is that this applies only under constant volume circumstances. Therefore, any variation in temperature directly impacts pressure.

• When temperature rises, the gas particles gain energy and speed up, increasing pressure.
• Conversely, when temperature drops, the particles slow down, leading to a decrease in pressure.

This direct relationship is captured mathematically as \( P \propto T \), illustrating that pressure and temperature move together in the same direction.

Proportionality Constant

To understand the role of the proportionality constant in Gay-Lussac's Law, we must look at its mathematical form: \( P = k \cdot T \). Here, the constant \( k \) is crucial as it connects pressure and temperature, making their proportional relationship precise and predictable.

This constant is specific to the amount of gas and its characteristics. Different gases will have different proportionality constants because they have unique properties such as particle mass and intermolecular forces.

• For a particular gas and fixed quantity, \( k \) is consistently maintained, allowing scientists and engineers to make reliable predictions about how a gas will behave under various temperatures.
• The value of \( k \) is determined experimentally and incorporates specific conditions like the type of gas and the system's volume.

Understanding \( k \) is vital for practical applications, from industrial processes to everyday weather predictions.

Fixed Mass of Gas

When discussing Gay-Lussac's Law, the significance of a fixed mass of gas cannot be overstated. "Fixed mass" signifies that the quantity of gas does not change during the experiment or observation.

This condition is crucial because any change in the number of gas molecules would alter the pressure independently of temperature changes, thus invalidating the law from applying accurately.

• It ensures that any variation in pressure is solely due to temperature changes, not due to the addition or subtraction of gas molecules.
• Maintaining a fixed mass helps to focus the relationship between pressure and temperature allowing for precise calculations.

Therefore, in studying or applying Gay-Lussac's Law, it's important to ensure the mass of gas is constant for the law to hold true and yield valid results.