“Reduced” properties in corresponding states theory:\r Identify the WRONG statement among the following definitions of reduced temperature, reduced pressure, and reduced volume.

Introduction:
Reduced properties are central to the law of corresponding states and generalized correlations (e.g., compressibility charts). Precise definitions matter because incorrect temperature scales or reference values lead to serious design errors in phase behavior calculations.

Given Data / Assumptions:

• T_c, P_c, and V_c denote critical temperature, pressure, and molar (or molal) volume.
• Reduced properties are dimensionless ratios.
• Thermodynamic temperatures must be in absolute units.

Concept / Approach:
Reduced temperature is defined as Tr = T / Tc with T and Tc in absolute temperature units (Kelvin or Rankine). Using the Celsius scale is incorrect because Celsius is not an absolute scale; zero Celsius does not represent zero thermal energy. Reduced pressure is Pr = P / Pc. Reduced volume is often Vr = V / Vc (for molar volume) or expressed inversely with compressibility charts. Statements (b) and (c) are correct in spirit; (a) is wrong due to the temperature scale error.

Step-by-Step Solution:
Check (a): requires absolute temperature → Celsius is wrong.Check (b): ratio of P to Pc is correct.Check (c): ratio of molar (molal) volume to its critical counterpart is correct in definition.Hence, the wrong statement is (a).

Verification / Alternative check:
Generalized compressibility charts and equations of state explicitly define Tr with absolute scales.

Why Other Options Are Wrong:

• (d) “None” is invalid since (a) is indeed wrong.
• (e) True: corresponding states correlations employ reduced properties.

Common Pitfalls:
Plugging Celsius into reduced-temperature formulas causes large numerical errors; always convert to Kelvin.

Final Answer:
'Reduced temperature' of a substance is the ratio of its existing temperature to its critical temperature, both expressed on celsius scale.