Thermodynamics – absolute zero pressure: At what temperature can absolute zero pressure (a perfect vacuum with zero molecular collisions) be attained?

Introduction / Context:
Pressure arises from molecular impacts. 'Absolute zero pressure' would imply no molecules and therefore no impacts—a perfect vacuum. The question explores the distinction between very low pressures achievable in practice and the idealized concept of zero pressure.

Given Data / Assumptions:

• Real systems contain residual gas molecules and outgassing surfaces.
• Temperature may approach cryogenic values, but perfect emptiness is unattainable in practice.
• Rankine (°R) is an absolute temperature scale where 0 °R equals 0 K.

Concept / Approach:
Even at extremely low temperatures, vacuum systems still contain some molecules unless the volume is perfectly evacuated and isolated—an impossibility due to quantum fluctuations, permeation, and outgassing. Absolute zero temperature (0 K or 0 °R) is itself unattainable per the third law of thermodynamics; thus tying zero pressure to any listed temperature is incorrect. Therefore, the only correct choice is 'None of these'.

Step-by-Step Solution:
Define absolute zero pressure: P = 0, implying no gas molecules.Recognize practical limits: ultra-high vacuum reaches ~10^-10 to 10^-12 mbar, not zero.Note 0 K (0 °R) is unattainable; and even were it approached, pressure would not be identically zero.Hence, zero pressure cannot be 'attained' at any of the given temperatures.

Verification / Alternative check:
Vacuum technology references define 'perfect vacuum' as a theoretical limit. Laboratories achieve extreme vacuum but never P = 0 exactly, confirming the conceptual nature of absolute zero pressure.

Why Other Options Are Wrong:
0 °C and 50 K are finite temperatures with abundant molecular motion.

0 °R corresponds to 0 K (also unattainable); associating it with zero pressure is incorrect.

Common Pitfalls:

• Confusing absolute temperature zero with absolute pressure zero; both are theoretical limits, neither is realized exactly.
• Assuming cooling alone produces vacuum without evacuation.

Final Answer:
None of these