What is an isothermal process?

Short Answer:

An isothermal process is a thermodynamic process in which the temperature of the system remains constant throughout the process. Even though the system may do work or absorb heat, the internal temperature does not change. This happens because any heat added to the system is used to do work, not to increase temperature.

Isothermal processes usually occur slowly, allowing continuous heat exchange with the surroundings to maintain a constant temperature. These processes are often used in gas expansion and compression studies, and they follow Boyle’s Law, where the product of pressure and volume remains constant (PV = constant).

Detailed Explanation:

Isothermal process

In thermodynamics, an isothermal process refers to a process where the temperature remains constant during the change of state. The name comes from the Greek words “iso” (same) and “thermal” (heat), meaning same temperature. Even if the system undergoes changes in pressure or volume, its temperature stays fixed throughout the process.

This type of process is very important in understanding the behavior of gases and is used in the design and analysis of many thermal systems. It is also one of the basic types of ideal thermodynamic processes, along with adiabatic, isobaric, and isochoric processes.

Basic Characteristics of Isothermal Process

  1. Constant temperature (T = constant):
    During the entire process, the system’s temperature does not increase or decrease.
  2. Heat and work are exchanged:
    Even though the temperature is constant, heat (Q) is either added or removed so that the system can perform work (W).
  3. Change in internal energy is zero (ΔU = 0):
    According to the First Law of Thermodynamics,
    ΔU = Q – W
    Since temperature is constant and internal energy depends only on temperature for ideal gases,
    ΔU = 0, so Q = W.
  4. Slow process:
    The system must stay in thermal contact with surroundings to allow heat exchange and maintain constant temperature.
  5. Follows Boyle’s Law:
    For ideal gases, PV = constant during an isothermal process.

Examples of Isothermal Process

  • Expansion of gas in a piston:
    If a gas expands slowly in a cylinder kept at a constant temperature (with heat exchange), the process is isothermal.
  • Compression of gas in a thermal bath:
    When gas is compressed inside a piston while being kept in a heat-conducting bath at constant temperature.
  • Melting of ice at 0°C:
    Even though heat is added to melt the ice, the temperature remains constant until all ice turns to water.

Mathematical Form of Isothermal Process

For an ideal gas, the relation used in isothermal conditions is:

PV = constant
Or,
P₁V₁ = P₂V₂

Also, the work done by an ideal gas in an isothermal process is given by:

W = nRT ln(V₂/V₁)

Where:

  • W = Work done
  • n = number of moles
  • R = universal gas constant
  • T = temperature (constant)
  • V₁, V₂ = initial and final volume

This shows that the work depends on the ratio of volumes and the constant temperature.

Applications of Isothermal Processes

Isothermal processes are commonly used in the following areas:

  1. Gas Compression and Expansion:
    In systems where gases are compressed or expanded slowly, like in certain air compressors or vacuum pumps.
  2. Heat Engines (Ideal models):
    In Carnot cycles, the isothermal process is one of the stages for ideal heat engine performance.
  3. Phase Change Processes:
    Like melting or boiling, where heat is added but the temperature stays the same until the phase changes fully.
  4. Chemical Reactions in Reactors:
    Some reactions are carried out at constant temperature for uniform product formation.

Importance in Thermodynamics

The isothermal process provides a clear example of how heat and work interact when temperature is kept fixed. It helps in understanding the energy balance in systems like engines, refrigerators, and gas containers. It also gives insight into how pressure and volume change when temperature is not allowed to vary.

This process is also important for comparing real-life operations with ideal cycles, especially when designing machines that involve gases.

Conclusion

An isothermal process is a process where temperature remains constant, and any heat added to the system is completely used to do work. It is one of the fundamental thermodynamic processes and is very useful in understanding gas behavior, designing thermal systems, and studying ideal cycles. Though difficult to achieve perfectly in real life, the isothermal process gives a strong base for theoretical and practical analysis in mechanical engineering.