Which of the following quantities is zero on an average for the molecules of an ideal gas in equilibrium?

Options

A. (a)Kinetic energy
B. (b)Momentum
C. (c)denesity
D. (d)speed

Answer

To solve the question of which quantity is zero on average for the molecules of an ideal gas in equilibrium, we can analyze the options provided: kinetic energy, momentum, density, and speed.

### Step-by-Step Solution:

1. **Understanding the Properties of Ideal Gas:**
- An ideal gas consists of a large number of molecules that are in constant random motion. In equilibrium, the average properties of these molecules can be analyzed.

2. **Analyzing the Options:**
- **Density:** Density is defined as mass per unit volume. Since an ideal gas occupies a certain volume and has mass, the average density cannot be zero.
- **Kinetic Energy:** Kinetic energy is a scalar quantity given by the formula \( KE = \frac{1}{2} mv^2 \). Since molecules of an ideal gas are in motion, they possess kinetic energy. Therefore, the average kinetic energy cannot be zero.
- **Speed:** Speed is also a scalar quantity representing how fast an object is moving. Although the molecules are moving randomly, they have a non-zero average speed in terms of magnitude. Thus, the average speed cannot be zero.
- **Momentum:** Momentum is a vector quantity defined as \( p = mv \), where \( m \) is mass and \( v \) is velocity. In equilibrium, the gas molecules have random velocities in all directions. When we consider the average momentum, the positive and negative components of momentum cancel each other out, leading to an average momentum of zero.

3. **Conclusion:**
- Based on the analysis, the quantity that is zero on average for the molecules of an ideal gas in equilibrium is **momentum**.

### Final Answer:
The average momentum of the molecules of an ideal gas in equilibrium is zero.

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