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

Step 1: Understand what an ideal gas is.
In an ideal gas the molecules are treated as tiny points with no forces pulling between them. They only move and bounce. This simple picture decides what internal energy can depend on.
Step 2: Break internal energy into parts.
In general, internal energy of a gas has two parts: the kinetic energy of moving molecules, and the potential energy stored in forces between molecules.
Step 3: Remove the potential part.
Since an ideal gas has no forces between molecules, its potential energy part is zero. So only the kinetic part is left.
Step 4: Link kinetic energy to temperature.
From kinetic theory, the average kinetic energy of each molecule grows directly with the absolute temperature: \[ KE_{avg} \propto T \]
Step 5: Write the internal energy.
Adding up over all molecules gives: \[ U = \frac{f}{2}nRT \] where $f$ is the degrees of freedom. This depends only on $T$.
Step 6: Conclude.
So for an ideal gas the internal energy depends only on temperature: \[ \boxed{U = U(T)} \]