Short Answer

An isochoric process is a thermodynamic process in which the volume of the system remains constant throughout the change. Even though volume does not change, pressure and temperature may increase or decrease depending on heat transfer.

A simple example of an isochoric process is heating a gas inside a rigid, sealed container. Because the container cannot expand, heat increases the temperature and pressure without changing the volume.

Detailed Explanation :

Isochoric Process

An isochoric process is a thermodynamic process in which the volume (V) of the system remains fixed from start to end. The word “isochoric” comes from the Greek words iso meaning “same” and choros meaning “space” or “volume.” Since the volume remains constant, no expansion or compression is possible during the process.

Because volume is constant, no mechanical work (W) is done by or on the system. This is the most important characteristic of an isochoric process. However, the system may still exchange heat with its surroundings, causing changes in pressure and temperature.

Condition for Isochoric Process

The condition that defines an isochoric process is:

Volume (V) = constant

This means:

• ΔV = 0
• Work done (W) = P × ΔV = 0

Thus, in an isochoric process, no work is performed.

Heat Transfer in an Isochoric Process

Even though no work is done, heat may still enter or leave the system. The effect of heat in an isochoric process is:

1. Heating at Constant Volume

• Heat is supplied
• Temperature rises
• Pressure increases
• Gas molecules move faster

2. Cooling at Constant Volume

• Heat is removed
• Temperature decreases
• Pressure decreases
• Molecular speed reduces

This behavior is explained by Gay-Lussac’s law.

Isochoric Process and Gas Laws

An isochoric process follows Gay-Lussac’s Law, which states:

P ∝ T (at constant volume)
or
P₁ / T₁ = P₂ / T₂

This means pressure increases when temperature increases and decreases when temperature decreases, as long as the volume stays unchanged.

Graph of Isochoric Process

On a P–V (pressure–volume) diagram, an isochoric process is shown as a vertical line because volume is constant and does not change.

Characteristics of the graph:

• Line is vertical
• Moves upward for heating (pressure increases)
• Moves downward for cooling (pressure decreases)

This vertical line clearly represents no change in volume.

Work Done in an Isochoric Process

Work done by a gas is given by:

W = PΔV

But in an isochoric process:

ΔV = 0

Therefore:

W = 0

This makes the isochoric process different from isothermal, isobaric, and adiabatic processes.

Examples of Isochoric Process

Isochoric processes occur practically in many situations:

1. Heating a Gas in a Rigid Container

If a sealed rigid box is heated, pressure rises because the gas cannot expand.

2. Gas in a Steel Cylinder

Oxygen, nitrogen, or LPG cylinders are rigid; heating them increases pressure while volume remains fixed.

3. Explosion Inside a Bomb Calorimeter

A bomb calorimeter is designed to undergo isochoric combustion, where volume does not change.

4. Refrigeration Cycle

Certain steps in refrigeration involve constant volume conditions inside some chambers.

5. Gas in Fixed-Walled Tanks

Industrial storage tanks undergo isochoric processes when heated by sunlight.

Importance of Isochoric Process

Isochoric processes are useful in many applications:

1. Studying Internal Energy

Since no work is done, any heat added goes directly into changing internal energy.

2. Designing Calorimeters

Bomb calorimeters depend on constant volume combustion to measure heat accurately.

3. Engineering and Industry

Knowledge of pressure rise at constant volume helps design safe gas containers.

4. Thermodynamic Cycles

The Otto cycle (used in petrol engines) includes isochoric heating and cooling steps.

5. Safety Analysis

Isochoric heating explains why gas cylinders may burst if overheated.

Comparison with Other Processes (Brief)

An isochoric process differs from:

• Isobaric process (constant pressure)
• Isothermal process (constant temperature)
• Adiabatic process (no heat exchange)

Isochoric processes stand out because volume remains constant and no work is done.

Conclusion

An isochoric process is a thermodynamic process where the volume stays constant while temperature and pressure can change. Since there is no change in volume, no work is done by or on the system. This process follows Gay-Lussac’s law and plays an important role in understanding heat transfer, internal energy changes, and pressure variations in rigid containers. Isochoric processes are essential in engines, calorimeters, industry, and safety engineering.