What is an Isothermal Process?

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Grade Level:

Class 12

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Definition

What is it?

An isothermal process is a type of thermodynamic process where the temperature of the system remains constant throughout. Even if heat is exchanged or work is done, the system's temperature does not change. This happens when the system is in good thermal contact with a large heat reservoir.

Simple Example

Quick Example

Imagine you have a glass of cold lassi on a hot summer day. If you put it in a special cooler that perfectly absorbs any heat trying to warm it up, the lassi will stay at the same cold temperature for a very long time. This is like an isothermal process – the temperature doesn't change even though the surroundings are hot.

Worked Example

Step-by-Step

PROBLEM: A gas undergoes an isothermal expansion at a constant temperature of 300 K. Its initial pressure is 2 atm and initial volume is 10 litres. If the final volume is 20 litres, what is the final pressure of the gas? (Assume it's an ideal gas).
---Step 1: Understand the process. Since it's an isothermal process, the temperature (T) remains constant. For an ideal gas, we use Boyle's Law, which is a special case of the ideal gas law for isothermal processes: P1V1 = P2V2.
---Step 2: Identify the given values. Initial pressure (P1) = 2 atm. Initial volume (V1) = 10 litres. Final volume (V2) = 20 litres. We need to find the final pressure (P2).
---Step 3: Substitute the values into the formula: 2 atm * 10 litres = P2 * 20 litres.
---Step 4: Calculate the product on the left side: 20 atm-litres = P2 * 20 litres.
---Step 5: Isolate P2 by dividing both sides by 20 litres: P2 = 20 atm-litres / 20 litres.
---Step 6: Perform the division. P2 = 1 atm.
---Answer: The final pressure of the gas is 1 atm.

Why It Matters

Understanding isothermal processes is crucial in many fields. In Engineering, it helps design efficient engines and refrigerators. In Biotechnology, it's used in processes like DNA amplification where temperature control is key. Even in Climate Science, it helps model atmospheric changes, showing how fundamental physics impacts our world and opens doors to exciting careers.

Common Mistakes

MISTAKE: Assuming temperature changes during an isothermal process. | CORRECTION: The core definition of an isothermal process is that temperature (T) remains constant. Any change in internal energy (which depends on temperature for ideal gases) is zero.

MISTAKE: Confusing isothermal with adiabatic processes. | CORRECTION: In an isothermal process, heat can be exchanged to maintain constant temperature. In an adiabatic process, no heat is exchanged, causing temperature to change if work is done.

MISTAKE: Applying P1V1 = P2V2 when the gas is not ideal or the process is not isothermal. | CORRECTION: The relation P1V1 = P2V2 (Boyle's Law) is strictly valid for an ideal gas undergoing an isothermal process.

Practice Questions

Try It Yourself

QUESTION: If a gas at 5 atm pressure occupies 10 litres and undergoes an isothermal compression to 5 litres, what is its new pressure? | ANSWER: 10 atm

QUESTION: An ideal gas expands isothermally from 2 litres to 8 litres. If its initial pressure was 400 kPa, what is its final pressure? | ANSWER: 100 kPa

QUESTION: A cylinder with a movable piston contains 0.5 moles of an ideal gas at 27 degrees Celsius. The gas expands isothermally, doing 1247 Joules of work. Calculate the heat absorbed by the gas during this expansion. (Hint: For an isothermal process, change in internal energy is zero). | ANSWER: 1247 Joules (Heat absorbed = Work done)

MCQ

Quick Quiz

Which of the following remains constant during an isothermal process?

Pressure

Volume

Temperature

Heat exchanged

The Correct Answer Is:

In an isothermal process, the temperature of the system is held constant. Pressure, volume, and heat exchanged can all change during the process.

Real World Connection

In the Real World

You see isothermal processes in action in refrigerators and air conditioners. These devices work to keep the internal temperature constant even when the outside environment is much hotter. Similarly, some chemical reactions in labs, especially in biotechnology, are carefully controlled to happen at a constant temperature using water baths or incubators to ensure consistent results.

Key Vocabulary

Key Terms

THERMODYNAMICS: The branch of physics dealing with heat and its relation to other forms of energy and work. | IDEAL GAS: A theoretical gas composed of randomly moving point particles that do not interact with each other. | HEAT RESERVOIR: A large system that can exchange heat with a system without changing its own temperature. | WORK DONE: Energy transferred when a force causes displacement.

What's Next

What to Learn Next

Now that you understand isothermal processes, explore 'Adiabatic Processes' next! It's another fascinating type of process where no heat is exchanged, showing how different conditions lead to different outcomes in physics. Keep learning!