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What is the Combined Gas Law?
Grade Level:
Class 10
AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine
Definition
What is it?
The Combined Gas Law helps us understand how the pressure, volume, and temperature of a fixed amount of gas are related when they all change at the same time. It combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into one simple equation. This law is useful for situations where a gas is affected by changes in all three factors.
Simple Example
Quick Example
Imagine you have a deflated football and you fill it with air using a pump. If you then leave the football in the hot sun (temperature increases) and it gets slightly overfilled (volume increases), the pressure inside will also increase. The Combined Gas Law helps predict how much the pressure changes when both temperature and volume are adjusted.
Worked Example
Step-by-Step
Let's say a gas in a cylinder has an initial pressure of 2 atm, a volume of 5 litres, and a temperature of 300 K. If the pressure changes to 4 atm and the temperature increases to 400 K, what will be the new volume of the gas?
Step 1: Write down the formula for the Combined Gas Law: (P1 * V1) / T1 = (P2 * V2) / T2
---Step 2: Identify the given values:
P1 = 2 atm, V1 = 5 L, T1 = 300 K
P2 = 4 atm, T2 = 400 K, V2 = ?
---Step 3: Plug the values into the formula:
(2 atm * 5 L) / 300 K = (4 atm * V2) / 400 K
---Step 4: Simplify both sides:
10 / 300 = (4 * V2) / 400
0.0333 = (4 * V2) / 400
---Step 5: Isolate V2 by multiplying both sides by 400:
0.0333 * 400 = 4 * V2
13.32 = 4 * V2
---Step 6: Divide by 4 to find V2:
V2 = 13.32 / 4
V2 = 3.33 L
Answer: The new volume of the gas will be 3.33 litres.
Why It Matters
Understanding the Combined Gas Law is crucial for engineers designing engines and climate control systems, as well as for scientists in space technology predicting gas behavior in rockets. It's also important in medicine for understanding how gases behave in respirators. This knowledge helps create safer and more efficient technologies.
Common Mistakes
MISTAKE: Using Celsius or Fahrenheit for temperature. | CORRECTION: Always convert temperature to Kelvin (K) before using the formula. Remember, K = degrees Celsius + 273.15.
MISTAKE: Mixing up initial and final values (P1, V1, T1 vs P2, V2, T2). | CORRECTION: Clearly label all initial values with '1' and final values with '2' before starting the calculation to avoid confusion.
MISTAKE: Forgetting to keep units consistent (e.g., using litres for V1 and milliliters for V2). | CORRECTION: Ensure all corresponding units (pressure, volume) are the same on both sides of the equation. If one is in atm, the other must also be in atm.
Practice Questions
Try It Yourself
QUESTION: A gas has a pressure of 1.5 atm, a volume of 10 L, and a temperature of 25 degrees Celsius. If the pressure changes to 3 atm and the volume becomes 6 L, what is the new temperature in Kelvin? | ANSWER: 238.4 K
QUESTION: A balloon filled with air at 20 degrees Celsius and 1 atm pressure has a volume of 500 mL. If the balloon is taken to a place where the temperature is 5 degrees Celsius and the pressure is 0.8 atm, what will be its new volume in mL? | ANSWER: 588.2 mL
QUESTION: A diving tank contains 20 L of air at 10 atm and 27 degrees Celsius. If a diver uses 1/4th of the air, and the remaining air is at 5 atm and 17 degrees Celsius, what is the new volume of the remaining air in the tank? (Hint: First find the initial volume of the remaining air.) | ANSWER: 3.84 L
MCQ
Quick Quiz
Which of the following must always be converted to Kelvin when using the Combined Gas Law?
Pressure
Volume
Temperature
All of the above
The Correct Answer Is:
C
Temperature must always be in Kelvin for gas law calculations because the Kelvin scale is an absolute temperature scale, starting from absolute zero. Using Celsius or Fahrenheit would lead to incorrect results.
Real World Connection
In the Real World
The Combined Gas Law helps engineers at ISRO design and test rocket engines, where gases are stored under extreme pressure and temperature changes. It's also used in everyday life, for example, when a gas cylinder for cooking (LPG) is stored in a hot kitchen, its internal pressure changes, which can be predicted using this law to ensure safety.
Key Vocabulary
Key Terms
PRESSURE: The force exerted by a gas per unit area. | VOLUME: The amount of space occupied by a gas. | TEMPERATURE: A measure of the average kinetic energy of gas particles. | KELVIN: The absolute temperature scale used in gas law calculations. | ATMOSPHERE (atm): A common unit of pressure.
What's Next
What to Learn Next
Great job understanding the Combined Gas Law! Now you're ready to explore the Ideal Gas Law. This next concept builds on what you've learned by introducing the number of moles of gas, making the calculations even more precise and applicable to real-world scenarios.
