Which of the following statement `(s)` is true
`I-` Slpe of isotherm at critical point is maximum
`II -` Larger is the value of `T_(C)` easier is the liquification of gas.
`III-` Vander walls equation of state is applicable below critical temperature at all pressure.

Options

A. only 1
B. `I & II`
C. `II & III`
D. only II

Answer

To determine which of the given statements is true, let's analyze each statement step by step.

### Step 1: Analyze Statement I
**Statement I:** "Slope of isotherm at critical point is maximum."

- The critical point is defined as the temperature and pressure at which the gas and liquid phases become indistinguishable.
- At the critical point, the slope of the isotherm (which represents the relationship between pressure and volume) is zero.
- Before reaching the critical point, the slope is negative, and after the critical point, the slope becomes positive.
- Therefore, the slope at the critical point is not maximum; it is zero.

**Conclusion for Statement I:** This statement is **false**.

### Step 2: Analyze Statement II
**Statement II:** "Larger is the value of \( T_C \), easier is the liquefaction of gas."

- The critical temperature (\( T_C \)) is the temperature above which a gas cannot be liquefied, regardless of the pressure applied.
- A higher \( T_C \) means that the gas can be liquefied at higher temperatures, making it easier to liquefy the gas because the temperature difference required to reach the critical temperature is smaller.
- Thus, if \( T_C \) is larger, the gas can be liquefied more easily at a given temperature.

**Conclusion for Statement II:** This statement is **true**.

### Step 3: Analyze Statement III
**Statement III:** "Van der Waals equation of state is applicable below critical temperature at all pressure."

- The Van der Waals equation is an adjustment of the ideal gas law that accounts for intermolecular forces and the volume occupied by gas molecules.
- While it is true that the Van der Waals equation is applicable below the critical temperature, it is not applicable at all pressures.
- At high pressures, the gas may condense into a liquid, and the Van der Waals equation does not accurately describe the behavior of liquids.

**Conclusion for Statement III:** This statement is **false**.

### Final Conclusion
- The only true statement among the three is **Statement II**.

### Summary of True Statements:
- **True Statements:** II
- **False Statements:** I, III