At `0 K`, which of the following properties of a gas will be zero ?

Options

A. volume
B. density
C. kinetic energy
D. protential energy

Answer

To determine which property of a gas will be zero at 0 K, we will analyze each option provided: volume, density, kinetic energy, and potential energy.

### Step-by-Step Solution:

1. **Understanding Absolute Zero (0 K)**:
- Absolute zero (0 K) is the theoretical temperature at which a system's entropy reaches its minimum value. At this temperature, the motion of particles theoretically comes to a complete stop.

2. **Analyzing Volume**:
- Volume is a measure of the space occupied by a substance. According to the principles of thermodynamics, matter cannot occupy zero volume. Therefore, the volume of a gas at 0 K cannot be zero.
- **Conclusion**: Volume ≠ 0 at 0 K.

3. **Analyzing Density**:
- Density is defined as mass per unit volume (Density = Mass/Volume). Since mass is a property of matter that does not change with temperature (it remains constant), and volume cannot be zero, the density of a gas at 0 K cannot be zero either.
- **Conclusion**: Density ≠ 0 at 0 K.

4. **Analyzing Kinetic Energy**:
- Kinetic energy (KE) is given by the formula KE = (1/2)mv², where m is mass and v is the velocity of the particles. At absolute zero (0 K), the velocity of gas molecules approaches zero, which means the kinetic energy also approaches zero.
- **Conclusion**: Kinetic Energy = 0 at 0 K.

5. **Analyzing Potential Energy**:
- Potential energy in gases is related to the intermolecular forces and configurations. Even at absolute zero, there may still be some potential energy present due to the interactions between particles, although the kinetic energy is zero.
- **Conclusion**: Potential Energy ≠ 0 at 0 K.

### Final Answer:
The property of a gas that will be zero at 0 K is **Kinetic Energy**.