Which is/are correct for real gases?

Options

A. `underset(Prarr0)(Lim)(PV_(m))=` constant at constant high temperature
B. `underset(V_(m)rarr0)(Lim)(PV_(m))=` constant at constant low temperature
C. `underset(Prarr0)(Lim)((PV_(m))/(RT))=1` at high temperature
D. `underset(Vrarr0)(Lim)((PV_(m))/(RT))=R`

Explanation

To determine which statements are correct for real gases, we can analyze the behavior of real gases under different conditions of temperature and pressure.

### Step-by-Step Solution:

1. **Understanding Real Gases**: Real gases do not follow the ideal gas law perfectly due to interactions between gas molecules and the volume occupied by the gas molecules themselves. The behavior of real gases can be described using the Van der Waals equation:
\[ \left(P + \frac{a}{V_m^2}\right)(V_m - b) = RT \]
where \(P\) is the pressure, \(V_m\) is the molar volume, \(R\) is the gas constant, \(T\) is the temperature, and \(a\) and \(b\) are constants specific to each gas.

2. **Analyzing Behavior at High Temperature and Low Pressure**:
- At high temperatures and low pressures, the volume of the gas becomes very large, and the interactions between gas molecules become negligible.
- In this case, we can neglect the term involving \(a\) (the attraction between molecules) and the term involving \(b\) (the volume occupied by gas molecules).
- Thus, the equation simplifies to:
\[ PV_m = RT \]
- This implies that \(PV_m\) is a constant, which is a correct statement.

3. **Analyzing Behavior at Low Temperature and High Pressure**:
- At low temperatures and high pressures, the volume of the gas is significantly reduced, and the interactions between molecules become significant.
- In this scenario, we cannot neglect the terms involving \(a\) and \(b\).
- Therefore, the equation cannot be simplified to \(PV_m = RT\), which makes this statement false.

4. **Conclusion**:
- The correct statements for real gases are those that hold true under conditions where the ideal gas law approximations fail.
- From our analysis, we conclude that at high temperature and low pressure, \(PV_m = RT\) holds true, while at low temperature and high pressure, it does not.

### Final Answer:
The correct statements for real gases are:
- At high temperature and low pressure, \(PV_m = RT\) is true.
- At low temperature and high pressure, \(PV_m = RT\) is false.