What is the meaning of isothermal process?

An isothermal process is a thermodynamic process where the temperature of a system remains constant and uniform throughout its duration. This means that any heat exchanged between the system and its surroundings occurs slowly enough to allow the system's temperature to equalize, ensuring it stays at a constant value.

Understanding Isothermal Processes

An isothermal process is a process that occurs under constant temperature, though other parameters of the system, such as pressure and volume, can change accordingly. For temperature to remain constant during a process where work is done (e.g., expansion or compression), there must be a continuous exchange of heat between the system and its surroundings. If the system expands, it does work and its internal energy might decrease, leading to a temperature drop; thus, heat must be supplied to maintain constant temperature. Conversely, if the system is compressed, work is done on it, increasing its internal energy and potentially its temperature; in this case, heat must be removed.

Key Characteristics of an Isothermal Process

• Constant Temperature (ΔT = 0): This is the defining characteristic. The temperature of the system does not change from its initial to its final state, nor does it fluctuate significantly during the process.
• Internal Energy Change (ΔU = 0 for Ideal Gases): For an ideal gas, internal energy depends solely on temperature. Therefore, if the temperature remains constant, the change in internal energy (ΔU) is zero. According to the First Law of Thermodynamics (ΔU = Q - W), this implies that for an ideal gas, the heat absorbed by the system (Q) is equal to the work done by the system (W), or Q = W.
• Heat Exchange (Q ≠ 0): Unlike an adiabatic process, heat transfer does occur in an isothermal process. This heat exchange is precisely what allows the temperature to be maintained constant as work is done.
• Work Done (W ≠ 0): Work is typically done by or on the system. For an ideal gas undergoing a reversible isothermal process, the work done during expansion or compression can be calculated.
• Boyle's Law Applicability: For an ideal gas undergoing an isothermal process, Boyle's Law applies, stating that pressure (P) and volume (V) are inversely proportional (PV = constant). This means P₁V₁ = P₂V₂.

Formulas for Ideal Gases

For an ideal gas undergoing a reversible isothermal process:

• Change in Internal Energy:
  ΔU = 0 (since ΔT = 0)
• Heat Exchanged (Q) and Work Done (W):
  According to the First Law of Thermodynamics, ΔU = Q - W. Since ΔU = 0, it follows that:
  Q = W
  The work done by the gas during a reversible isothermal expansion from volume V₁ to V₂ is:
  W = nRT ln(V₂/V₁)
  Where:
  • n = number of moles of gas
  • R = ideal gas constant
  • T = constant temperature (in Kelvin)
  • ln = natural logarithm
    Since P₁V₁ = P₂V₂, we can also write:
    W = nRT ln(P₁/P₂)

Practical Examples and Applications

Isothermal processes are fundamental in various natural phenomena and engineered systems:

• Phase Transitions: Processes like melting (ice to water) or boiling (water to steam) occur at a constant temperature (e.g., 0°C for melting ice, 100°C for boiling water at standard atmospheric pressure), even as heat is continuously added or removed.
• Carnot Cycle: The theoretical Carnot engine, which represents the most efficient heat engine possible, includes two isothermal processes (isothermal expansion and isothermal compression) and two adiabatic processes.
• Refrigeration and Heat Pumps: These systems rely on thermodynamic cycles that involve heat transfer at constant or near-constant temperatures to achieve cooling or heating.
• Biological Systems: Many biological processes occur under conditions of constant temperature, as living organisms maintain a stable internal temperature (homeostasis).

Isothermal vs. Other Thermodynamic Processes

Understanding isothermal processes is often clearer when contrasted with other common thermodynamic processes: