Which of the following is incorrect for critical temperature ?

Options

A. It is the highest temperature at which liquid and vapour can coexist
B. Beyond the critical temperature, there is no distinction between the two phases and a gas cannot be liquefied by compression
C. At critical temperature the surface tension of the system is zero
D. At critical temperature the gas and the liquid phases have different critical densities

Answer

To determine which statement is incorrect regarding critical temperature, we first need to understand what critical temperature is and its implications for the behavior of gases and liquids. Let's break down the concepts step by step.

### Step-by-Step Solution:

1. **Definition of Critical Temperature**:
- Critical temperature (T_c) is the highest temperature at which a substance can exist as a liquid. Above this temperature, the substance cannot be liquefied by pressure alone.

**Hint**: Remember that critical temperature is specific to each substance and indicates the temperature above which the gas cannot be condensed into a liquid regardless of pressure.

2. **Understanding the Critical Point**:
- At the critical point, the properties of the liquid and gas phases become indistinguishable. This means that at this point, the density, pressure, and temperature of both phases are equal.

**Hint**: Visualize the phase diagram of a substance to see how the liquid and gas phases converge at the critical point.

3. **Analyzing the Options**:
- **Option 1**: "It is the highest temperature at which liquid and vapor coexist."
- This statement is correct as it describes the critical temperature accurately.

- **Option 2**: "Beyond the critical temperature, there is no distinction between two phases and a gas cannot be liquefied by temperature."
- This statement is also correct, as it reflects the behavior of substances above the critical temperature.

- **Option 3**: "At critical temperature, the surface tension of the system is zero."
- This statement is correct because, at the critical point, the distinction between liquid and gas disappears, leading to zero surface tension.

- **Option 4**: "At critical temperature, the gas and the liquid phase have different critical densities."
- This statement is incorrect. At the critical temperature, the densities of the gas and liquid phases become equal, not different.

**Hint**: Compare the properties of phases at the critical point; they should converge rather than diverge.

4. **Conclusion**:
- The incorrect statement regarding critical temperature is: "At critical temperature, the gas and the liquid phase have different critical densities."

### Final Answer:
The incorrect statement regarding critical temperature is: "At critical temperature, the gas and the liquid phase have different critical densities."