What is Charles's Law?

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Grade Level:

Class 12

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Definition

What is it?

Charles's Law states that for a fixed amount of gas at constant pressure, its volume is directly proportional to its absolute temperature. This means if you increase the temperature of a gas, its volume will increase, and if you decrease the temperature, its volume will decrease.

Simple Example

Quick Example

Imagine you have a balloon filled with air. If you take this balloon out into the hot Indian summer sun, it will expand and become bigger. This is because the air inside gets hotter, and according to Charles's Law, its volume increases.

Worked Example

Step-by-Step

Let's say you have a gas in a container with an initial volume of 2 Liters (L) at a temperature of 27 degrees Celsius (°C). If you heat the gas to 127 °C, what will be its new volume, assuming pressure remains constant?

Step 1: Convert temperatures to Kelvin. Remember, Kelvin = °C + 273.15.
Initial temperature (T1) = 27 °C + 273.15 = 300.15 K.
Final temperature (T2) = 127 °C + 273.15 = 400.15 K.
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Step 2: Identify knowns and unknowns.
Initial Volume (V1) = 2 L
Initial Temperature (T1) = 300.15 K
Final Volume (V2) = ?
Final Temperature (T2) = 400.15 K
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Step 3: Apply Charles's Law formula: V1/T1 = V2/T2.
2 L / 300.15 K = V2 / 400.15 K
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Step 4: Solve for V2.
V2 = (2 L * 400.15 K) / 300.15 K
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Step 5: Calculate the value.
V2 = 800.3 / 300.15 = 2.666 L

Answer: The new volume of the gas will be approximately 2.67 Liters.

Why It Matters

Understanding Charles's Law is crucial for designing engines, weather balloons, and even for safely storing gases. Engineers in fields like automotive (EVs), aerospace (Space Technology), and even medical device manufacturing use this principle to ensure things work correctly and safely. It's a fundamental concept for anyone aspiring to work in science or engineering.

Common Mistakes

MISTAKE: Using Celsius or Fahrenheit temperatures directly in the formula. | CORRECTION: Always convert temperatures to the absolute Kelvin scale before using them in Charles's Law calculations.

MISTAKE: Forgetting that pressure must remain constant for Charles's Law to apply. | CORRECTION: Remember that Charles's Law specifically deals with gas behavior when only volume and temperature change, while pressure is kept fixed.

MISTAKE: Confusing direct proportionality with inverse proportionality. | CORRECTION: Charles's Law states volume and temperature are directly proportional (V is proportional to T). If one increases, the other increases.

Practice Questions

Try It Yourself

QUESTION: A balloon contains 5 L of air at 300 K. If the temperature is increased to 450 K while keeping pressure constant, what will be the new volume? | ANSWER: 7.5 L

QUESTION: A gas occupies 100 mL at 27 °C. To what temperature in °C must it be heated for its volume to double, assuming constant pressure? | ANSWER: 327 °C

QUESTION: An aerosol can of deodorant (fixed volume) is left in a car on a hot day. The temperature inside the car rises from 25 °C to 50 °C. Explain using Charles's Law why this is dangerous and what might happen. (Hint: Think about what happens if volume can't change). | ANSWER: Charles's Law states that for a fixed amount of gas, volume is directly proportional to absolute temperature at constant pressure. However, in an aerosol can, the volume is fixed. If the temperature increases, the gas inside tries to expand, but it can't. This leads to a massive increase in pressure inside the can, which can cause the can to explode, making it very dangerous.

MCQ

Quick Quiz

Which of the following conditions must be constant for Charles's Law to be applicable?

Temperature and Volume

Pressure and Amount of gas

Volume and Amount of gas

Temperature and Amount of gas

The Correct Answer Is:

Charles's Law describes the relationship between volume and temperature of a gas. For this relationship to hold true, the amount of gas (number of moles) and the pressure must remain constant. Options A, C, and D involve changes in variables that Charles's Law relates or keeps constant.

Real World Connection

In the Real World

Charles's Law helps explain why hot air balloons fly! The air inside the balloon is heated, causing it to expand and become less dense than the cooler air outside. This difference in density creates lift, allowing the balloon to rise, much like a lighter object floats on water. This principle is also used by ISRO scientists when they design cryogenic engines where gases are stored at very low temperatures.

Key Vocabulary

Key Terms

VOLUME: The amount of space a substance occupies. | TEMPERATURE: A measure of the average kinetic energy of the particles in a substance. | PRESSURE: The force exerted per unit area. | ABSOLUTE TEMPERATURE: Temperature measured on the Kelvin scale, where 0 K is absolute zero. | PROPORTIONAL: When two quantities change at the same rate or by the same factor.

What's Next

What to Learn Next

Now that you understand Charles's Law, you're ready to explore Boyle's Law, which describes the relationship between pressure and volume. After that, you can combine these ideas into the Ideal Gas Law, a powerful equation used widely in chemistry and physics.