Question

Internal energy of an ideal gas depends only on:

• A. P
• B. V
• C. T
• D. P and T

Hint:

For an ideal gas, always remember Joule’s law: internal energy depends only on temperature, not on pressure or volume.

Answer 1

The Correct Option is C

Concept: An ideal gas is a hypothetical gas in which intermolecular forces are absent and molecules are treated as point particles undergoing only elastic collisions. Hence, its internal energy is purely kinetic in nature.

Step 1: Nature of internal energy.
For any gas, internal energy consists of:

• kinetic energy of molecules

• potential energy due to intermolecular forces
For an ideal gas, intermolecular forces are absent, so potential energy is zero. Therefore, internal energy depends only on molecular kinetic energy.

Step 2: Relation with temperature.
From kinetic theory of gases, the average kinetic energy of a molecule is directly proportional to absolute temperature: \[ \text{KE}_{avg} \propto T \] Hence total internal energy is: \[ U = \frac{f}{2} nRT \] where \(f\) is degrees of freedom, \(n\) is number of moles, and \(R\) is gas constant. This shows: \[ U \propto T \]

Step 3: Conclusion.
Since \(U\) depends only on absolute temperature and is independent of pressure and volume for an ideal gas: \[ \boxed{U = U(T)} \]