At the vicinity of absolute zero

Options

A. `Cp+Cv=0`
B. `CpltCv`
C. `Cp-Cv=0`
D. `CpgtCv`

Answer

### Step-by-Step Solution:

1. **Understanding Absolute Zero**:
- Absolute zero is defined as the lowest possible temperature, which is 0 Kelvin (-273.15°C). At this temperature, the motion of particles is minimal, and they are considered to be in their ground state.

2. **Behavior of Particles Near Absolute Zero**:
- As we approach absolute zero, the particles of a substance become almost motionless. This means that their kinetic energy approaches zero, and they exhibit minimal thermal motion.

3. **Perfect Crystalline Structure**:
- At absolute zero, substances tend to form a perfect crystalline structure. This means that the arrangement of particles is highly ordered, and there is no disorder (entropy is at its minimum).

4. **Specific Heat Capacities**:
- The specific heat at constant pressure (Cp) and the specific heat at constant volume (Cv) are two important thermodynamic properties. Near absolute zero, it is observed that Cp becomes equal to Cv. This is a significant observation in thermodynamics.

5. **Relation Between Cp and Cv**:
- The relationship between Cp and Cv can be expressed as:
\[ Cp - Cv = T \left( \frac{ds}{dv} + \frac{ds}{dp} \right) \]
- At absolute zero (0 K), the temperature (T) is zero, which implies that:
\[ Cp - Cv = 0 \]
- Therefore, we conclude that:
\[ Cp = Cv \]

6. **Conclusion**:
- The final conclusion is that at the vicinity of absolute zero, the difference between the specific heat at constant pressure and the specific heat at constant volume is zero, which means:
\[ Cp - Cv = 0 \]
- Hence, the answer to the question is that \( Cp = Cv \).