For an ideal gas molecules the following quantities having zero average values are.

Options

A. Velocity
B. momentum
C. kinetic energy
D. density

Answer

To solve the question regarding which quantities for ideal gas molecules have zero average values, we will analyze each quantity step by step.

### Step 1: Analyze Average Velocity
- For an ideal gas, the molecules move randomly in all directions.
- The average velocity (\( \bar{V} \)) is calculated as:
\[ \bar{V} = \frac{\sum \vec{V}_i}{N} \]
where \( \vec{V}_i \) is the velocity of each molecule and \( N \) is the total number of molecules.
- Since velocity is a vector quantity, the velocities in opposite directions can cancel each other out.
- Therefore, the average velocity for an ideal gas is:
\[ \bar{V} = 0 \]

### Step 2: Analyze Average Momentum
- Momentum (\( \vec{P} \)) is given by:
\[ \vec{P} = m \vec{V} \]
where \( m \) is the mass of the molecule and \( \vec{V} \) is its velocity.
- The average momentum (\( \bar{P} \)) can be expressed as:
\[ \bar{P} = \frac{\sum \vec{P}_i}{N} = \frac{\sum m \vec{V}_i}{N} \]
- Since the average velocity is zero, the average momentum also becomes:
\[ \bar{P} = 0 \]

### Step 3: Analyze Average Kinetic Energy
- The average kinetic energy (\( KE \)) of an ideal gas is given by:
\[ KE = \frac{3}{2} kT \]
where \( k \) is the Boltzmann constant and \( T \) is the temperature.
- This formula indicates that the average kinetic energy is always positive and never zero, as it depends on temperature.
- Therefore, the average kinetic energy is not zero.

### Step 4: Analyze Average Density
- Density (\( \rho \)) is defined as mass per unit volume:
\[ \rho = \frac{m}{V} \]
- Since every molecule has a non-zero mass and occupies space, the density of an ideal gas is also non-zero.
- Thus, the average density is not zero.

### Conclusion
From the analysis:
- The quantities that have zero average values for ideal gas molecules are:
- Average Velocity: \( \bar{V} = 0 \)
- Average Momentum: \( \bar{P} = 0 \)
- The average kinetic energy and average density are not zero.

### Final Answer
The quantities having zero average values for ideal gas molecules are:
1. Average Velocity
2. Average Momentum