Corresponding states principle: For most gases, the compressibility factor Z shows near-universal behavior at the same values of which pair of variables?

Introduction:
The law of corresponding states provides a powerful way to generalize real-gas behavior. By scaling variables relative to their critical properties, diverse gases collapse onto similar Z = f(Tr, Pr) curves, enabling estimation of P–V–T properties without gas-specific equations in preliminary design.

Given Data / Assumptions:

• Reduced temperature Tr = T / Tc (absolute units).
• Reduced pressure Pr = P / Pc.
• Compressibility factor Z = PV / RT for the gas.

Concept / Approach:
When properties are expressed in reduced form with respect to critical constants, many gases exhibit similar deviations from ideality. Generalized compressibility charts plot Z versus Pr for various Tr, allowing quick estimates of real-gas properties using only Tc and Pc of the gas along with P and T of the state point.

Step-by-Step Solution:
Recognize that “corresponding states” requires reduced variables.Identify the standard pair: (Pr, Tr).Conclude that Z is approximately the same for many gases at the same Pr and Tr.

Verification / Alternative check:
Generalized charts and Lee–Kesler correlations explicitly use Pr and Tr to correlate Z across substances.

Why Other Options Are Wrong:

• Pressure and temperature (absolute) do not collapse behaviors across different gases.
• Critical pressure and temperature are constants of the substance, not state variables to match between gases.

Common Pitfalls:
Using Celsius instead of Kelvin for reduced temperature; always use absolute scales.

Final Answer:
reduced pressure and reduced temperature