Question

For an ideal gas, which of the following thermodynamic quantities depends only on temperature?

• A. Enthalpy
• B. Entropy
• C. Gibbs free energy
• D. Pressure

Hint:

Remember that for real gases, enthalpy depends on both pressure and temperature due to intermolecular interactions.
For ideal gases, always look for \( U \) and \( H \) as temperature-dependent functions.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
For an ideal gas, the intermolecular forces of attraction are negligible.
This leads to specific thermodynamic relationships where internal energy and enthalpy become state functions of temperature alone.
Step 2: Key Formula or Approach:
The definition of Enthalpy (\( H \)) is:
\[ H = U + PV \]
Where \( U \) is internal energy, \( P \) is pressure, and \( V \) is volume.
Step 3: Detailed Explanation:
According to Joule's Law for an ideal gas, the internal energy \( (U) \) is a function of temperature only, i.e., \( U = f(T) \).
Using the ideal gas equation:
\[ PV = nRT \]
Substituting this into the enthalpy equation:
\[ H = U(T) + nRT \]
Since both terms on the right side of the equation (\( U \) and \( nRT \)) are functions of temperature only, enthalpy \( (H) \) is also a function of temperature only for an ideal gas.
In contrast, Entropy (\( S \)) and Gibbs free energy (\( G \)) depend on both temperature and pressure (or volume) as they involve logarithmic terms of \( P \) or \( V \).
Step 4: Final Answer:
For an ideal gas, enthalpy is the quantity that depends only on temperature.