What is Gay-Lussac's Law?

S4-SA2-0209

Grade Level:

Class 8

Space Technology, EVs, Climate Change, Biotechnology, HealthTech, Robotics, Chemistry, Physics

Definition

What is it?

Gay-Lussac's Law states that for a fixed amount of gas kept at a constant volume, the pressure of the gas is directly proportional to its absolute temperature. This means if you increase the temperature, the pressure also increases, and vice versa.

Simple Example

Quick Example

Imagine you have a pressure cooker (Patila) at home. When you heat it up, the steam inside gets hotter. As the temperature of the steam increases, the pressure inside the cooker also goes up, making the whistle blow. This is Gay-Lussac's Law in action – hotter gas means more pressure.

Worked Example

Step-by-Step

A gas in a sealed container has a pressure of 2 atm at a temperature of 300 K. What will be the new pressure if the temperature is raised to 450 K, assuming the volume remains constant?

1. **Understand the Law:** Gay-Lussac's Law states P1/T1 = P2/T2.
---2. **Identify Given Values:**
* Initial Pressure (P1) = 2 atm
* Initial Temperature (T1) = 300 K
* Final Temperature (T2) = 450 K
* Final Pressure (P2) = ?
---3. **Rearrange the Formula:** To find P2, we can write P2 = P1 * (T2 / T1).
---4. **Substitute Values:** P2 = 2 atm * (450 K / 300 K).
---5. **Calculate:** P2 = 2 atm * 1.5.
---6. **Final Answer:** P2 = 3 atm.

So, the new pressure will be 3 atm.

Why It Matters

Understanding Gay-Lussac's Law is crucial for designing safe space rockets, efficient car engines, and even understanding weather patterns. Engineers in fields like Space Technology and Automotive design use this law to ensure systems work correctly under extreme temperature and pressure changes.

Common Mistakes

MISTAKE: Using Celsius or Fahrenheit for temperature in calculations. | CORRECTION: Always convert temperature to the absolute Kelvin scale (K) before using it in Gay-Lussac's Law. Add 273.15 to Celsius to get Kelvin.

MISTAKE: Assuming pressure and temperature are inversely proportional. | CORRECTION: Remember they are *directly* proportional. If temperature increases, pressure increases (and vice versa) when volume is constant.

MISTAKE: Forgetting that the law applies only when the amount of gas and volume are constant. | CORRECTION: Clearly identify that the container is sealed (fixed amount of gas) and rigid (fixed volume) before applying Gay-Lussac's Law.

Practice Questions

Try It Yourself

QUESTION: A gas in a cylinder has a pressure of 400 kPa at 250 K. If the temperature increases to 500 K while the volume stays the same, what is the new pressure? | ANSWER: 800 kPa

QUESTION: A spray can (fixed volume) has a pressure of 1.5 atm at 27 degrees Celsius. If the can is left in direct sunlight and its temperature rises to 77 degrees Celsius, what will be the new pressure inside? (Hint: Convert Celsius to Kelvin first!) | ANSWER: 1.75 atm

QUESTION: A sealed container of gas has a pressure of 300 Pa at 10 degrees Celsius. If the pressure needs to be increased to 450 Pa, what temperature (in Celsius) must the gas reach, assuming constant volume? | ANSWER: 156.5 degrees Celsius (approx)

MCQ

Quick Quiz

Which of the following statements correctly describes Gay-Lussac's Law?

Pressure is inversely proportional to temperature at constant volume.

Volume is directly proportional to temperature at constant pressure.

Pressure is directly proportional to temperature at constant volume.

Volume is inversely proportional to pressure at constant temperature.

The Correct Answer Is:

Gay-Lussac's Law specifically states that for a fixed amount of gas at constant volume, pressure and absolute temperature are directly proportional. Option B describes Charles's Law, and Option D describes Boyle's Law.

Real World Connection

In the Real World

This law helps in understanding why tires on a scooter or car gain pressure after a long drive – the friction heats up the air inside, increasing its pressure. It's also why you should never throw an aerosol spray can (like deodorant or paint spray) into a fire, as the increasing temperature will drastically increase internal pressure, causing it to explode.

Key Vocabulary

Key Terms

Pressure: Force applied perpendicular to a surface per unit area | Temperature: A measure of the average kinetic energy of the particles in a substance | Absolute Temperature: Temperature measured from absolute zero, typically in Kelvin (K) | Constant Volume: The container's size does not change | Direct Proportionality: When one quantity increases, the other increases by the same factor.

What's Next

What to Learn Next

Next, explore Charles's Law and Boyle's Law to understand how volume and pressure change with temperature when other factors are constant. These laws together form the foundation of the Ideal Gas Law, which helps predict gas behavior in many situations.