What is Work Done in Isochoric Process? | Simple Explanation for Class 12

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What is the Work Done in an Isochoric Process?

Grade Level:

Class 12

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Definition

What is it?

In an isochoric process, the volume of a system remains constant. This means the system does not expand or contract, and therefore, no work is done by or on the system. The work done in an isochoric process is always zero.

Simple Example

Quick Example

Imagine you have a pressure cooker on the stove with the lid tightly sealed. As the water inside heats up, its temperature and pressure increase, but the volume of the steam inside the cooker remains the same because the cooker's walls are rigid. Since the volume doesn't change, no 'work' is done by the steam pushing against the cooker walls.

Worked Example

Step-by-Step

Let's calculate the work done for a gas undergoing an isochoric process.

Step 1: Understand the formula for work done in thermodynamics. Work Done (W) = Pressure (P) × Change in Volume (ΔV).
---Step 2: Identify the condition for an isochoric process. In an isochoric process, the volume remains constant.
---Step 3: This means the change in volume (ΔV) is zero. If the initial volume is V1 and the final volume is V2, then V1 = V2, so ΔV = V2 - V1 = 0.
---Step 4: Substitute ΔV = 0 into the work done formula. W = P × 0.
---Step 5: Any number multiplied by zero is zero.
---Step 6: Therefore, W = 0.

Answer: The work done in an isochoric process is 0 Joules.

Why It Matters

Understanding isochoric processes is crucial in designing efficient engines and refrigerators, impacting fields like EV technology and climate science. Engineers use this principle when creating sealed systems where no volume change is desired, such as in certain chemical reactors or pressure vessels. It helps them predict energy changes and ensure safety.

Common Mistakes

MISTAKE: Assuming work is done if pressure or temperature changes. | CORRECTION: Work done specifically relates to a change in volume. If volume is constant, no work is done, even if pressure or temperature changes.

MISTAKE: Confusing isochoric with isobaric or isothermal processes. | CORRECTION: Isochoric means constant volume (ΔV=0). Isobaric means constant pressure (ΔP=0), and isothermal means constant temperature (ΔT=0). Each has different implications for work done.

MISTAKE: Applying the formula W = nRT ln(V2/V1) for an isochoric process. | CORRECTION: The formula W = nRT ln(V2/V1) is for an isothermal process. For an isochoric process, the work done is simply zero because ΔV = 0.

Practice Questions

Try It Yourself

QUESTION: A gas in a rigid container is heated, causing its pressure to double. If the initial volume was 5 litres, what is the work done by the gas? | ANSWER: 0 Joules

QUESTION: If a system undergoes an isochoric process where its internal energy increases by 100 J, how much heat was supplied to the system? (Hint: Use the First Law of Thermodynamics: ΔU = Q - W) | ANSWER: 100 Joules

QUESTION: A sealed, perfectly insulated tank containing air is exposed to sunlight, increasing its temperature from 27°C to 77°C. If the tank has a fixed volume of 2 cubic meters, calculate the work done by the air. Explain your reasoning. | ANSWER: 0 Joules. Reasoning: The tank is sealed and has a fixed volume, indicating an isochoric process. In an isochoric process, the change in volume (ΔV) is zero, and therefore, the work done (W = PΔV) is also zero, regardless of temperature or pressure changes.

MCQ

Quick Quiz

What is the work done by a system during an isochoric process?

Positive

Negative

Zero

Depends on pressure

The Correct Answer Is:

In an isochoric process, the volume remains constant. Since work done is directly proportional to the change in volume (W = PΔV), if ΔV is zero, then the work done is also zero.

Real World Connection

In the Real World

Pressure cookers in Indian kitchens are excellent examples of systems that operate close to an isochoric process. When you cook dal or rice, the volume inside the cooker stays constant, even as steam pressure builds up. This principle is also used in the design of gas cylinders for LPG or oxygen, where the gas is stored at high pressure in a fixed volume.

Key Vocabulary

Key Terms

Isochoric Process: A thermodynamic process where the volume of the system remains constant | Work Done: Energy transferred by a force acting over a distance; in thermodynamics, it's related to volume change | Volume: The amount of space an object or substance occupies | Pressure: Force applied perpendicular to the surface of an object per unit area

What's Next

What to Learn Next

Next, explore 'What is the Work Done in an Isobaric Process?'. This will help you understand how work is calculated when pressure is constant but volume changes, building on your knowledge of thermodynamics.