Why is the change in enthalpy zero for isothermal processes?

In an isothermal process, the temperature of a system remains constant while it undergoes a change in pressure and volume. This characteristic leads to some interesting implications regarding enthalpy, particularly why the change in enthalpy is zero. Let’s break this down step by step.

Understanding Enthalpy

Enthalpy, represented as H, is a thermodynamic property that combines internal energy (U) with the product of pressure (P) and volume (V). The formula for enthalpy is:

H = U + PV

When we talk about changes in enthalpy, we refer to the difference between the final and initial states of the system:

ΔH = H_final - H_initial

Isothermal Conditions Defined

In an isothermal process, the system is in thermal equilibrium with its surroundings, meaning that any heat added to the system is used to do work rather than change the internal energy. For an ideal gas, the internal energy is a function of temperature alone. Since the temperature remains constant during an isothermal process, the internal energy does not change:

ΔU = 0

Connecting Enthalpy and Internal Energy

Now, let’s see how this relates to enthalpy. Since ΔU is zero, we can substitute this into the enthalpy change equation:

ΔH = ΔU + Δ(PV)

Given that ΔU = 0, we have:

ΔH = 0 + Δ(PV)

Analyzing the PV Term

For an ideal gas undergoing an isothermal process, the relationship between pressure and volume can be described by the ideal gas law:

PV = nRT

Since the temperature (T) is constant, any change in volume (V) will result in a corresponding change in pressure (P) such that the product PV remains constant. Therefore, when we calculate Δ(PV), it also equals zero:

Δ(PV) = 0

Final Thoughts on Enthalpy Change

Putting this all together, we find that:

ΔH = 0 + 0 = 0

This means that for an isothermal process, the change in enthalpy is indeed zero. This concept is particularly useful in thermodynamics, especially when analyzing processes involving ideal gases, as it simplifies calculations and helps us understand energy transfers in a system.

Real-World Example

Consider a piston filled with an ideal gas that is allowed to expand isothermally. As the gas expands, it absorbs heat from the surroundings to maintain a constant temperature. The work done by the gas is balanced by the heat absorbed, leading to no change in internal energy and, consequently, no change in enthalpy.

In summary, the zero change in enthalpy during isothermal processes is a direct result of the constant temperature condition, which keeps both internal energy and the PV product unchanged. This principle is foundational in thermodynamics and helps us understand how energy is conserved and transferred in various systems.