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What is the Combined Gas Law (P, V, T relationship)?
Grade Level:
Class 8
Space Technology, EVs, Climate Change, Biotechnology, HealthTech, Robotics, Chemistry, Physics
Definition
What is it?
The Combined Gas Law describes how the pressure (P), volume (V), and temperature (T) of a fixed amount of gas are related to each other. It combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into one simple equation. This law helps us understand how gases change when their conditions change.
Simple Example
Quick Example
Imagine you have a balloon filled with air. If you squeeze the balloon (increase pressure) while keeping the temperature the same, its volume will decrease. If you take the same balloon to a very hot place, its volume will increase because the temperature goes up. The Combined Gas Law helps us predict these changes all at once.
Worked Example
Step-by-Step
A gas in a cylinder has a volume of 10 L at 300 K temperature and 2 atm pressure. If the pressure changes to 3 atm and the temperature increases to 450 K, what will be the new volume of the gas?
Step 1: Write down the given initial conditions (P1, V1, T1) and final conditions (P2, V2, T2).
P1 = 2 atm, V1 = 10 L, T1 = 300 K
P2 = 3 atm, V2 = ?, T2 = 450 K
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Step 2: Recall the Combined Gas Law formula: (P1 * V1) / T1 = (P2 * V2) / T2.
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Step 3: Rearrange the formula to solve for V2.
V2 = (P1 * V1 * T2) / (P2 * T1)
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Step 4: Substitute the values into the rearranged formula.
V2 = (2 atm * 10 L * 450 K) / (3 atm * 300 K)
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Step 5: Calculate the product of the numerator.
Numerator = 2 * 10 * 450 = 9000 L*atm*K
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Step 6: Calculate the product of the denominator.
Denominator = 3 * 300 = 900 atm*K
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Step 7: Divide the numerator by the denominator to find V2.
V2 = 9000 / 900 = 10 L
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Answer: The new volume of the gas will be 10 L.
Why It Matters
Understanding the Combined Gas Law is crucial for engineers designing rockets and spacecraft, where gases operate under extreme pressure and temperature changes. It's also vital in HealthTech for medical devices like ventilators and oxygen cylinders. Scientists use this law to study climate change and atmospheric conditions, helping us predict weather patterns.
Common Mistakes
MISTAKE: Using temperature in Celsius | CORRECTION: Always convert temperature to Kelvin (K) before using it in the Combined Gas Law. K = Celsius + 273.15.
MISTAKE: Mixing up units for pressure or volume | CORRECTION: Ensure that the units for initial pressure (P1) and final pressure (P2) are the same, and similarly for initial volume (V1) and final volume (V2). If not, convert them to match.
MISTAKE: Forgetting to rearrange the formula correctly | CORRECTION: When solving for an unknown variable, carefully isolate it by multiplying or dividing both sides of the equation. Double-check your algebraic steps.
Practice Questions
Try It Yourself
QUESTION: A gas occupies 5 L at 3 atm and 27 degrees C. What will be its volume at 1 atm and 127 degrees C? | ANSWER: 25 L
QUESTION: A cylinder contains 20 L of gas at 400 K and 500 kPa. If the volume is reduced to 10 L and the temperature becomes 300 K, what is the new pressure in kPa? | ANSWER: 750 kPa
QUESTION: A balloon has 3 L of air at 1.5 atm and 300 K. If the balloon is moved to a place where the temperature is 200 K and the pressure decreases to 0.5 atm, what will be the new volume of the balloon? | ANSWER: 6 L
MCQ
Quick Quiz
Which of the following conditions must be met when using the Combined Gas Law?
Temperature must be in Celsius
Pressure must be in Pascals only
The amount of gas must remain constant
Volume must be measured in cubic meters
The Correct Answer Is:
C
The Combined Gas Law applies to a fixed or constant amount of gas. Temperature must be in Kelvin, and pressure/volume units just need to be consistent, not specific.
Real World Connection
In the Real World
In India, the Combined Gas Law helps engineers design effective air conditioning systems for homes and cars, especially in our hot summers. It's also used by meteorologists to understand how air pressure and temperature changes affect weather, like predicting monsoon patterns or cyclone intensity, which helps farmers and disaster management teams.
Key Vocabulary
Key Terms
PRESSURE: The force exerted by gas particles on the walls of their container | VOLUME: The amount of space occupied by a gas | TEMPERATURE: A measure of the average kinetic energy of gas particles, always in Kelvin for gas laws | KELVIN: The absolute temperature scale where 0 K is absolute zero
What's Next
What to Learn Next
Next, you can explore the Ideal Gas Law, which builds upon the Combined Gas Law by adding the 'amount of gas' (moles) into the equation. This will give you an even more complete picture of how gases behave in different situations, opening doors to advanced chemistry concepts.
