Question

For an ideal gas, internal energy is a function of:

• A. Pressure only
• B. Volume only
• C. Temperature only
• D. Pressure and volume

Hint:

For real gases, internal energy is a function of both temperature and volume \( U = f(T, V) \) due to intermolecular forces.
However, for ideal gases, Joule's law holds perfectly.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to inter-particle interactions.
The internal energy \( (U) \) of a substance is the sum of the kinetic and potential energies of its molecules.
Step 2: Key Formula or Approach:
According to Joule's Law for an ideal gas:
\[ U = f(T) \]
The change in internal energy is given by:
\[ dU = m C_v dT \]
Where \( C_v \) is the specific heat at constant volume and \( T \) is the absolute temperature.
Step 3: Detailed Explanation:
In an ideal gas, there are no intermolecular forces of attraction or repulsion (potential energy is zero).
Thus, the internal energy consists solely of kinetic energy.
According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to the absolute temperature.
Therefore, the internal energy of an ideal gas does not depend on pressure or volume, but only on temperature.
Step 4: Final Answer:
Internal energy is a function of temperature only for an ideal gas.