During an isothermal expansion of an ideal gas, its:

• A. Internal energy decrease
• B. Enthalpy decreases
• C. Enthalpy remains unaffected
• D. Enthalpy reduce to zero

In an isothermal expansion of an ideal gas, the correct answer is C: Enthalpy remains unaffected. Let's break down why this is the case by examining the concepts involved in isothermal processes and the properties of ideal gases.

Understanding Isothermal Expansion

Isothermal expansion refers to a process where a gas expands at a constant temperature. For an ideal gas, this means that the internal energy of the gas remains constant throughout the process. This is because the internal energy of an ideal gas is solely a function of its temperature. Since the temperature does not change during an isothermal process, the internal energy also does not change.

Internal Energy and Temperature

The internal energy (U) of an ideal gas can be expressed as:

• U = n * C_v * T

Where:

• n = number of moles of gas
• C_v = molar heat capacity at constant volume
• T = absolute temperature

Since T remains constant in an isothermal process, U does not change, which means it neither increases nor decreases.

Examining Enthalpy

Enthalpy (H) is defined as:

• H = U + PV

In this equation, P is the pressure and V is the volume of the gas. During an isothermal expansion, although the gas does do work on the surroundings (which requires energy), it also absorbs an equivalent amount of heat from the surroundings to maintain the constant temperature. This means that any change in internal energy is balanced by the heat added to the system.

Why Enthalpy Remains Unchanged

For an ideal gas, the change in enthalpy (ΔH) during an isothermal process can be expressed as:

• ΔH = ΔU + Δ(PV)

Since ΔU is zero (as established earlier), we need to consider the term Δ(PV). For an ideal gas, the relationship PV = nRT holds true. During isothermal expansion, while both P and V change, the product PV remains constant at a given temperature. Therefore, Δ(PV) also equals zero, leading to:

• ΔH = 0 + 0 = 0

This indicates that the enthalpy remains unchanged during the isothermal expansion of an ideal gas.

Summary of Key Points

• Isothermal processes occur at constant temperature.
• Internal energy of an ideal gas is a function of temperature only, so it remains constant.
• Enthalpy, which includes internal energy and the PV term, also remains unchanged during isothermal expansion.

In conclusion, during an isothermal expansion of an ideal gas, the enthalpy remains unaffected, making option C the correct choice. This understanding is crucial for analyzing thermodynamic processes involving gases and their behavior under different conditions.