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: Basic idea for an ideal gas. 
In an ideal gas, molecules are assumed to have no intermolecular attraction or repulsion. Because of this assumption, many thermodynamic properties simplify and depend only on temperature.

Step 2: Expression for enthalpy.
Enthalpy (\(H\)) is defined as the sum of internal energy and the pressure–volume term: 
\[ H = U + PV \]

Step 3: Why enthalpy depends only on temperature.
For an ideal gas, Joule’s law states that internal energy depends only on temperature: 
\[ U = f(T) \] 

Using the ideal gas equation: 
\[ PV = nRT \] 
Substituting into the enthalpy formula: 
\[ H = U(T) + nRT \] 

Both terms on the right-hand side are functions of temperature alone. Hence, enthalpy for an ideal gas does not depend on pressure or volume, only on temperature.

Step 4: Final conclusion.
For an ideal gas, the thermodynamic property that depends solely on temperature is enthalpy.