Short Answer

An isothermal process is a thermodynamic process in which the temperature of the system remains constant throughout the change. Even though pressure and volume may change, the temperature does not change at any stage.

During an isothermal process, the system must exchange heat with the surroundings to maintain constant temperature. For example, slow expansion or compression of a gas in contact with a heat reservoir is an isothermal process.

Detailed Explanation :

Isothermal Process

An isothermal process is a type of thermodynamic process in which the temperature (T) of the system remains constant. The word “isothermal” comes from two Greek words: iso meaning “same” and therme meaning “heat” or “temperature.” In this process, even if the system undergoes changes in pressure (P), volume (V), or internal energy, its temperature stays fixed.

To maintain constant temperature, the system must exchange heat with its surroundings. If the system expands, it absorbs heat; if it is compressed, it gives off heat. This transfer of heat ensures that the temperature remains unchanged.

Condition for Isothermal Process

The condition for an isothermal process is:

Temperature (T) = constant

Since temperature is constant, the internal energy of an ideal gas also remains constant, because internal energy depends only on temperature.

How an Isothermal Process Occurs

An isothermal process can occur only when:

1. The process is carried out very slowly, allowing temperature to remain constant.
2. The system is in good thermal contact with a large heat reservoir, which can supply or absorb heat without changing its own temperature.
3. The system is allowed to exchange heat to maintain constant temperature.

This slow and controlled nature of the process ensures equilibrium at every step.

Isothermal Process and Ideal Gas Law

For an ideal gas undergoing an isothermal process:

PV = constant

Since temperature is constant, the equation of state becomes:

P₁V₁ = P₂V₂

This is Boyle’s law.

This means:

• If volume increases, pressure decreases
• If volume decreases, pressure increases

The relationship between pressure and volume is inversely proportional.

Graph of Isothermal Process

On a P–V diagram (pressure-volume graph), an isothermal process is shown as a smooth, downward-sloping curve called an isotherm.

Characteristics of an isotherm:

• It gets closer to both axes but never touches them
• It is less steep than the adiabatic curve
• It represents constant temperature

Each isotherm corresponds to a particular temperature.

Heat Transfer in an Isothermal Process

In an isothermal process, heat transfer occurs to maintain temperature:

1. During expansion

The gas expands and does work on the surroundings.
To keep temperature constant, the gas must absorb heat from the surroundings.

2. During compression

The surroundings do work on the gas.
To maintain constant temperature, the gas must release heat.

Thus, heat exchange is necessary for an isothermal process.

Internal Energy in Isothermal Process

For an ideal gas:

Internal energy depends only on temperature.

If temperature is constant:

• Change in internal energy ΔU = 0
• According to the first law of thermodynamics:

Q = W

This means the heat absorbed by the gas equals the work done by the gas.

Examples of Isothermal Processes

1. Slow Expansion of Gas in a Cylinder

If a cylinder is placed in a heat bath and expanded slowly, temperature remains constant.

2. Melting of Ice at 0°C

Ice absorbs heat but temperature stays at 0°C until fully melted.

3. Boiling of Water at 100°C

Water stays at 100°C while it absorbs heat and changes state.

4. Breathing Under Slow Conditions

Air entering and leaving lungs under controlled conditions approximates an isothermal process.

5. Inflating a Balloon Slowly

If air is pumped slowly in a balloon, temperature remains nearly constant.

Applications of Isothermal Process

The isothermal process plays an important role in many fields:

1. Heat Engines

Certain parts of engine cycles operate under isothermal conditions.

2. Refrigeration

Isothermal expansion is used in refrigerators and heat pumps.

3. Thermodynamics Studies

Used to study real gases and derive equations.

4. Chemical Reactions

Some reactions occur at constant temperature requiring isothermal conditions.

5. Industrial Processes

Used in gas compressors, distillation, and drying processes.

Comparison with Adiabatic Process

• Isothermal: Temperature remains constant, heat exchange occurs.
• Adiabatic: No heat exchange, but temperature changes.

Isothermal curves are less steep than adiabatic curves on a P–V diagram.

Conclusion

An isothermal process is a thermodynamic process in which the temperature of the system stays constant while pressure and volume may change. This requires slow operation and continuous heat exchange with the surroundings. It follows Boyle’s law, where PV remains constant. Isothermal processes are essential in understanding thermodynamics and are widely applied in engines, refrigeration, industry, and natural processes.